1.
Portrait of Luca Pacioli
–
The Portrait of Luca Pacioli is a painting attributed to the Italian Renaissance artist Jacopo de Barbari, dating to around 1500 and housed in the Capodimonte Museum, Naples, southern Italy. The painting, which portrays the Renaissance mathematician Luca Pacioli, is mentioned for the first time in a 1631 inventory of the Ducal Palace of Urbino and it was later moved to Florence through Vittoria della Rovere-Medici, belonging to both the reigning dynasties of Urbino and Tuscany. The painting reappeared in the 19th century, as a property of the Ottaviano branch of the Medicis and it was subsequently acquired by the Italian state to prevent its being sold to England. The painting has been attributed to Jacopo de Barbari due to the presence of a cartouche with the inscription IACO. BAR. P.1495, with the presence of a fly above it. However, the attribution to the Venetian painter is now regarded as wrong. The painting has been attributed to Leonardo da Vinci, who had collaborated with Pacioli when he moved to Milan in 1496. The painting portrays the friar and mathematician with a filled with geometrical tools, slate, chalk, compass. A rhombicuboctahedron, half-filled with water and characterized by a detailed triple reflection effect of the Ducal Palace of Urbino, is suspended from the ceiling, Pacioli is demonstrating a theorem by Euclid written in an open book. The closed book, with the inscription LI. RI. LUC. BUR. is supposed to be his Summa de arithmetica, Luca Pacioli The enigmas in the Portrait of Luca Pacioli
Portrait of Luca Pacioli
–
Portrait of Luca Pacioli
2.
Sansepolcro
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Sansepolcro, formerly Borgo Santo Sepolcro, is a town and comune in Tuscany, Italy, in the province of Arezzo. Situated on the reaches of the Tiber river, the town is the birthplace of the painters Piero della Francesca, Raffaellino del Colle, Santi di Tito. It was also the birthplace of the Italian mathematician Luca Pacioli, and of Matteo Cioni, today, the economy is based on agriculture, industrial manufacturing, food processing and pharmaceuticals. It is the home of Buitoni pasta, founded by Giulia Buitoni in 1827, according to tradition, the town was founded around 1000 AD by two pilgrims, Arcanus and Aegidius, who brought a stone from the Church of the Holy Sepulchre with them from the Holy Land. They founded an oratory dedicated to Saint Leonard, on the site of the current Cathedral, the first historical mentions of Sansepolcro are slightly later, referring to the Benedictine Abbey, the Badia, around which the walled commune clustered. During the conflicts between Guelfs and Ghibellines, the factions were headed by prominent local families, including the Pichi, Bercordati, Graziani. The main church is the Cathedral, built in Gothic-Romanesque style in 1012–49, other churches of note are San Francesco and San Lorenzo. The latter church has a Deposition by Rosso Fiorentino, the English writer Aldous Huxley described the Resurrection by Piero della Francesca, which is in the Museo Civico, as the greatest painting in the world. The museum collection includes three works by Piero della Francesca and many other treasures including paintings by Santi di Tito, Raffaellino del Colle. Diocese of Sansepolcro Eduino Francini St. Quentin Teatro Dante Sansepolcro is twinned with, Neuchâtel, Switzerland Neuves-Maisons, France Sinj, Croatia
Sansepolcro
–
Aerial view of Sansepolcro.
3.
Republic of Florence
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The Republic of Florence, also known as the Florentine Republic, was a medieval and early modern state that was centered on the Italian city of Florence in Tuscany. The republic originated in 1115, when the Florentine people rebelled against the Margraviate of Tuscany upon the death of Matilda, the Florentines formed a commune in her successors place. The republic was ruled by a council, known as the signoria, the signoria was chosen by the gonfaloniere, who was elected every two months by Florentine guild members. The republic had a history of coups and counter-coups against various factions. The Medici faction gained governance of the city in 1434, upon Cosimo de Medicis counter-coup against the faction that had sent him into exile the previous year, the Medici kept control of Florence until 1494. Giovanni de Medici re-conquered the republic in 1512, Florence repudiated Medici authority for a second time in 1527, during the War of the League of Cognac. The Medici re-assumed their rule in 1531, after an 11-month siege of the city, the republican government was disestablished in 1532, when Pope Clement VII appointed Alessandro de Medici Duke of the Florentine Republic, making the republic a hereditary monarchy. The city of Florence was established in 59 B. C. by Julius Caesar, the city had been part of the Marquisate of Tuscany before the death of Margravine Matilda in 1115. The city did not submit readily to her successor, Rabodo, the first official mention of the republic was in 1138 when several cities around Tuscany formed a league against Henry X of Bavaria. The country was part of the Holy Roman Empire. Florence prospered in the 12th century, trading extensively with foreign countries and this, in turn, provided a platform for demographic growth of the city. The growth of Florences population mirrored the rate of construction, many churches and this prosperity was shattered when Emperor Frederick I Barbarossa invaded the Italian peninsula in 1185. The Margraves of Tuscany re-acquired Florence and its townlands, the Florentines re-asserted their independence when Holy Roman Emperor Henry VI died in 1197. Florences population continued to grow into the 13th century, reaching 30,000 inhabitants, as has been said, the extra inhabitants supported the citys trade and vice versa. Several new bridges and churches were built, most prominently the cathedral of Santa Maria del Fiore, the buildings from the era serve as Florences best example of Gothic Architecture. Politically, Florence was barely able to maintain peace between factions, the precarious peace that existed at the beginning of the century was destroyed in 1216 when two factions known as the Guelphs and the Ghibellines began to war. The Ghibellines were the rulers of Florence. The Ghibellines, who under Frederick of Antioch had ruled the city since 1244, were deposed in 1250 by the Guelphs, the Guelphs led Florence to prosper further
Republic of Florence
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Front and back of a Florentine florin
Republic of Florence
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Flag
Republic of Florence
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Cosimo de' Medici, founder of the
House of Medici
Republic of Florence
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Lorenzo de' Medici
4.
Summa de arithmetica
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Summa de arithmetica, geometria, proportioni et proportionalita is a book on mathematics written by Luca Pacioli and first published in 1494. It contains a summary of Renaissance mathematics, including practical arithmetic, basic algebra, basic geometry and accounting. The Summa is the first printed work on algebra in a vernacular language, the Summa de arithmetica as originally printed consists of ten chapters on a series of mathematical topics, collectively covering essentially all of Renaissance mathematics. The first seven chapters form a summary of arithmetic in 222 pages, the eighth chapter explains contemporary algebra in 78 pages. The ninth chapter discusses various topics relevant to business and trade, including barter, bills of exchange, weights and measures and bookkeeping, the tenth and final chapter describes practical geometry in 151 pages. The work was dedicated to Guidobaldo da Montefeltro, Duke of Urbino, paciolis work likewise teaches through examples, but it also develops arguments for the validity of its solutions through reference to general principles, axioms and logical proof. In this way the Summa begins to reintegrate the logical methods of classical Greek geometry into the discipline of algebra. The business chapter also introduces the rule of 72 for predicting a future value. The book was published in Venice in 1494 by Paganino Paganini. While the Summa contained little or no original work by Pacioli. Its thoroughness and clarity made it a point of reference for European mathematicians through the sixteenth century. It includes the first printed example of a set of plus and minus signs that were to standard in Italian Renaissance mathematics, p with a tilde above for plus. In 1994 Italy issued a 750-lira postage stamp honoring the 500th anniversary of the Summas publication, depicting Pacioli surrounded by mathematical, the image on the stamp was inspired by the Portrait of Luca Pacioli, and contains many of the same elements
Summa de arithmetica
–
Title page of second (1523) edition
Summa de arithmetica
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1994 Italian 750-lira postage stamp commemorating the 500th anniversary of the Summa' s publication
5.
De divina proportione
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De divina proportione is a book on mathematics written by Luca Pacioli and illustrated by Leonardo da Vinci, composed around 1498 in Milan and first printed in 1509. Its subject was mathematical proportions and their applications to geometry, visual art through perspective, the clarity of the written material and Leonardos excellent diagrams helped the book to achieve an impact beyond mathematical circles, popularizing contemporary geometric concepts and images. The book consists of three manuscripts, which Pacioli worked on between 1496 and 1498. The first part, Compendio divina proportione, studies the golden ratio from a perspective and explores its applications to various arts. The second part, Trattato dellarchitettura, discusses the ideas of Vitruvius on the application of mathematics to architecture in twenty chapters, the text compares the proportions of the human body to those of artificial structures, with examples from classical Greco-Roman architecture. The third part, Libellus in tres partiales divisus, is mainly an Italian translation of Piero della Francescas Latin writings On Five Regular Solids and mathematical examples. In 1550 Giorgio Vasari wrote a biography of della Francesca, in which he accused Pacioli of plagiarism and claimed that he stole della Francescas work on perspective, on arithmetic, Leonardo drew the illustrations of the regular solids while he lived with and took mathematics lessons from Pacioli. Leonardos drawings are probably the first illustrations of skeletonic solids which allowed an easy distinction between front and back, Pacioli produced three manuscripts of the treatise by different scribes. He gave the first copy with a dedication to the Duke of Milan, Ludovico il Moro, a second copy was donated to Galeazzo da Sanseverino and now rests at the Biblioteca Ambrosiana in Milan. The third, which has gone missing, was given to Pier Soderini, on 1 June 1509 the first printed edition was published in Venice by Paganino Paganini, it has since been reprinted several times. The book was displayed as part of an exhibition in Milan between October 2005 and October 2006 together with the Codex Atlanticus, the M logo used by the Metropolitan Museum of Art in New York is adapted from one in De divina proportione. Full text of original edition Full text of 1509 edition Title page of a reprint in Vienna,1889 A video featuring a 1509 edition on display at Stevens Institute of Technology
De divina proportione
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Forms
De divina proportione
–
Title page of 1509 edition
6.
Double-entry bookkeeping system
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Double-entry bookkeeping, in accounting, is a system of bookkeeping so named because every entry to an account requires a corresponding and opposite entry to a different account. For instance, recording earnings of $100 would require making two entries, an entry of $100 to an account named Cash and a credit entry of $100 to an account named Revenue. Deciding which account has to be debited and which account has to be credited is accomplished using the equation which is expressed as. This equation serves as a detection tool, if at any point the sum of debits for all accounts does not equal the corresponding sum of credits for all accounts. It follows that the sum of debits and the sum of the credits must be equal in value, Double-entry bookkeeping is no guarantee that errors have not been made, for example, the wrong ledger account may have been debited or credited, or the entries completely reversed. The oldest record of a complete system is the Messari accounts of the Republic of Genoa in 1340. By the end of the 15th century, the bankers and merchants of Florence, Genoa, Venice, however, the double-entry accounting method was said to be developed independently earlier in Korea during the Goryeo dynasty when Kaesong was a center of trade and industry at that time. The Four-element bookkeeping system was said to be originated in the 11th or 12th century, the earliest extant accounting records that follow the modern double-entry system in Europe come from Amatino Manucci, a Florentine merchant at the end of the 13th century. Manucci was employed by the Farolfi firm and the ledger of 1299-1300 evidences full double-entry bookkeeping. Giovannino Farolfi & Company, a firm of Florentine merchants headquartered in Nîmes, acted as moneylenders to the Archbishop of Arles, some sources suggest that Giovanni di Bicci de Medici introduced this method for the Medici bank in the 14th century. Historical records show that since the second caliphate, AD 634-644, critics of claims that Muslims invented double-entry bookkeeping accept that several features of pre-double-entry accounting were used in the Muslim world before they were used in the West. Pacioli is often called the father of accounting because he was the first to publish a description of the double-entry system, thus enabling others to study. In pre-modern Europe, double-entry bookkeeping had theological and cosmological connotations, in the double-entry accounting system, at least two accounting entries are required to record each financial transaction. These entries may occur in asset, liability, equity, expense, recording of a debit amount to one or more accounts and an equal credit amount to one or more accounts results in total debits being equal to total credits for all accounts in the general ledger. If the accounting entries are recorded without error, the balance of all accounts having Debit balances will be equal to the aggregate balance of all accounts having Credit balances. The rules for formulating accounting entries are known as Golden Rules of Accounting, the accounting entries are recorded in the Books of Accounts. Regardless of which accounts and how many are impacted by a given transaction, there are two different ways to memorize the effects of debits and credits on accounts in the double entry system of bookkeeping. They are the Traditional Approach and the Accounting Equation Approach, irrespective of the approach used, the effect on the books of accounts remains the same, with two aspects in each of the transactions
Double-entry bookkeeping system
–
Accounting
7.
Italy
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Italy, officially the Italian Republic, is a unitary parliamentary republic in Europe. Located in the heart of the Mediterranean Sea, Italy shares open land borders with France, Switzerland, Austria, Slovenia, San Marino, Italy covers an area of 301,338 km2 and has a largely temperate seasonal and Mediterranean climate. Due to its shape, it is referred to in Italy as lo Stivale. With 61 million inhabitants, it is the fourth most populous EU member state, the Italic tribe known as the Latins formed the Roman Kingdom, which eventually became a republic that conquered and assimilated other nearby civilisations. The legacy of the Roman Empire is widespread and can be observed in the distribution of civilian law, republican governments, Christianity. The Renaissance began in Italy and spread to the rest of Europe, bringing a renewed interest in humanism, science, exploration, Italian culture flourished at this time, producing famous scholars, artists and polymaths such as Leonardo da Vinci, Galileo, Michelangelo and Machiavelli. The weakened sovereigns soon fell victim to conquest by European powers such as France, Spain and Austria. Despite being one of the victors in World War I, Italy entered a period of economic crisis and social turmoil. The subsequent participation in World War II on the Axis side ended in defeat, economic destruction. Today, Italy has the third largest economy in the Eurozone and it has a very high level of human development and is ranked sixth in the world for life expectancy. The country plays a prominent role in regional and global economic, military, cultural and diplomatic affairs, as a reflection of its cultural wealth, Italy is home to 51 World Heritage Sites, the most in the world, and is the fifth most visited country. The assumptions on the etymology of the name Italia are very numerous, according to one of the more common explanations, the term Italia, from Latin, Italia, was borrowed through Greek from the Oscan Víteliú, meaning land of young cattle. The bull was a symbol of the southern Italic tribes and was often depicted goring the Roman wolf as a defiant symbol of free Italy during the Social War. Greek historian Dionysius of Halicarnassus states this account together with the legend that Italy was named after Italus, mentioned also by Aristotle and Thucydides. The name Italia originally applied only to a part of what is now Southern Italy – according to Antiochus of Syracuse, but by his time Oenotria and Italy had become synonymous, and the name also applied to most of Lucania as well. The Greeks gradually came to apply the name Italia to a larger region, excavations throughout Italy revealed a Neanderthal presence dating back to the Palaeolithic period, some 200,000 years ago, modern Humans arrived about 40,000 years ago. Other ancient Italian peoples of undetermined language families but of possible origins include the Rhaetian people and Cammuni. Also the Phoenicians established colonies on the coasts of Sardinia and Sicily, the Roman legacy has deeply influenced the Western civilisation, shaping most of the modern world
Italy
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The
Colosseum in Rome, built c. 70 – 80 AD, is considered one of the greatest works of
architecture and
engineering of ancient history.
Italy
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Flag
Italy
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The
Iron Crown of Lombardy, for centuries symbol of the
Kings of Italy.
Italy
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Castel del Monte, built by German Emperor
Frederick II,
UNESCO World Heritage site
8.
Mathematician
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A mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems. Mathematics is concerned with numbers, data, quantity, structure, space, models, one of the earliest known mathematicians was Thales of Miletus, he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, the number of known mathematicians grew when Pythagoras of Samos established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was All is number. It was the Pythagoreans who coined the term mathematics, and with whom the study of mathematics for its own sake begins, the first woman mathematician recorded by history was Hypatia of Alexandria. She succeeded her father as Librarian at the Great Library and wrote works on applied mathematics. Because of a dispute, the Christian community in Alexandria punished her, presuming she was involved, by stripping her naked. Science and mathematics in the Islamic world during the Middle Ages followed various models and it was extensive patronage and strong intellectual policies implemented by specific rulers that allowed scientific knowledge to develop in many areas. As these sciences received wider attention from the elite, more scholars were invited and funded to study particular sciences, an example of a translator and mathematician who benefited from this type of support was al-Khawarizmi. A notable feature of many working under Muslim rule in medieval times is that they were often polymaths. Examples include the work on optics, maths and astronomy of Ibn al-Haytham, the Renaissance brought an increased emphasis on mathematics and science to Europe. As time passed, many gravitated towards universities. Moving into the 19th century, the objective of universities all across Europe evolved from teaching the “regurgitation of knowledge” to “encourag productive thinking. ”Thus, seminars, overall, science became the focus of universities in the 19th and 20th centuries. Students could conduct research in seminars or laboratories and began to produce doctoral theses with more scientific content. According to Humboldt, the mission of the University of Berlin was to pursue scientific knowledge. ”Mathematicians usually cover a breadth of topics within mathematics in their undergraduate education, and then proceed to specialize in topics of their own choice at the graduate level. In some universities, a qualifying exam serves to test both the breadth and depth of an understanding of mathematics, the students, who pass, are permitted to work on a doctoral dissertation. Mathematicians involved with solving problems with applications in life are called applied mathematicians. Applied mathematicians are mathematical scientists who, with their knowledge and professional methodology. With professional focus on a variety of problems, theoretical systems
Mathematician
–
Euclid (holding
calipers), Greek mathematician, known as the "Father of Geometry"
Mathematician
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In 1938 in the United States, mathematicians were desired as teachers, calculating machine operators, mechanical engineers, accounting auditor bookkeepers, and actuary statisticians
Mathematician
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Archimedes, c. 287 – 212 BC
Mathematician
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Brahmagupta, c. 598 - 670
9.
Franciscan
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The Franciscans are a group of related mendicant religious orders within the Catholic Church, founded in 1209 by Francis of Assisi. These orders include the Order of Friars Minor, the Order of Saint Clare, Francis began preaching around 1207 and traveled to Rome to seek approval from the Pope in 1209. The original Rule of Saint Francis approved by the Pope disallowed ownership of property, the austerity was meant to emulate the life and ministry of Jesus Christ. Franciscans traveled and preached in the streets, while boarding in church properties, Saint Clare, under Franciss guidance, founded the Poor Clares in 1212, which remains a Second Order of the Franciscans. The extreme poverty required of members was relaxed in final revision of the Rule in 1223, the degree of observance required of members remained a major source of conflict within the order, resulting in numerous secessions. The Order of Friars Minor, previously known as the Observant branch, is one of the three Franciscan First Orders within the Catholic Church, the others being the Capuchins and Conventuals. The Order of Friars Minor, in its current form, is the result of an amalgamation of smaller orders completed in 1897 by Pope Leo XIII. The latter two, the Capuchin and Conventual, remain distinct religious institutes within the Catholic Church, observing the Rule of Saint Francis with different emphases, Franciscans are sometimes referred to as minorites or greyfriars because of their habit. In Poland and Lithuania they are known as Bernardines, after Bernardino of Siena, the name of original order, Friars Minor, means lesser brothers, and stems from Francis of Assisis rejection of extravagance. Francis was the son of a cloth merchant, but gave up his wealth to pursue his faith more fully. Francis adopted of the tunic worn by peasants as the religious habit for his order. Those who joined him became the original Order of Friars Minor and they all live according to a body of regulations known as the Rule of St Francis. First Order The First Order or the Order of Friars Minor are commonly called simply the Franciscans and this Order is a mendicant religious order of men, some of whom trace their origin to Francis of Assisi. Their official Latin name is the Ordo Fratrum Minorum, St. Francis thus referred to his followers as Fraticelli, meaning Little Brothers. Franciscan brothers are informally called friars or the Minorites and they all live according to a body of regulations known as the Rule of St Francis. These are The Order of Friars Minor, known as the Observants, most commonly simply called Franciscan friars, official name, the Order of Friars Minor Capuchin or simply Capuchins, official name, Friars Minor Capuchin. The Conventual Franciscans or Minorites, official name, Friars Minor Conventual, Second Order The Second Order, most commonly called Poor Clares in English-speaking countries, consists of religious sisters. The order is called the Order of St. Clare, but in the century, prior to 1263, this order was referred to as The Poor Ladies, The Poor Enclosed Nuns
Franciscan
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Francis of Assisi, founder of the Order of Friars Minor; oldest known portrait in existence of the saint, dating back to St. Francis' retreat to
Subiaco (1223–1224)
Franciscan
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Regula bullata, the Rule confirmed by
Honorius III
Franciscan
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"The Confirmation of the Franciscan Rule" by
Domenico Ghirlandaio (1449-1494), Capella Sassetti,
Florence.
Franciscan
–
Anthony of Padua (c1195-1231) with the
Infant Christ, painting by
Antonio de Pereda (c1611-1678)
10.
Friar
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The most significant orders of friars are the Dominicans, Franciscans, Augustinians and Carmelites. Friars are different from monks in that they are called to live the evangelical counsels in service to society, rather than through cloistered asceticism, whereas monks live in a self-sufficient community, friars work among laypeople and are supported by donations or other charitable support. A monk or nun makes their vows and commits to a community in a particular place. The English term Friar is derived from the Norman French word frere, from the Latin frater, Fray is sometimes used in former Spanish colonies such as the Philippines or the American Southwest as a title, such as in Fray Juan de Torquemada. In the Roman Catholic Church, there are two classes of orders known as friars, or mendicant orders, the four great orders, the four great orders were mentioned by the Second Council of Lyons, and are, The Carmelites, founded c. They are also known as the White Friars because of the cloak which covers their brown habit. They received papal approval from Honorius III in 1226 and later by Innocent IV in 1247, the Carmelites were founded as a purely contemplative order, but became mendicants in 1245. There are two types of Carmelites, those of the Ancient Observance and those of the Discalced Carmelites and they are also known as the Friars Minor. The Franciscans were founded by St. Francis of Assisi and received papal approval by Innocent III in 1209. Today the Friars Minor is composed of three branches, the Order of Friars Minor, Order of Friars Minor Capuchin and the Order of Friars Minor Conventual wearing grey or black habits. They are also known as the Friar Preachers, or the Black Friars, the Dominicans were founded by St. Dominic and received papal approval from Honorius III in 1216 as the Ordo Praedicatorum under the Rule of St. Augustine. They became a mendicant order in 1221, the Augustinians, founded in 1244 and enlarged in 1256. They are also known as the Hermits of St. Augustine and their rule is based on the writings of Augustine of Hippo. The Augustinians were assembled from various groups of hermits as a mendicant order by Pope Innocent IV in 1244, additional groups were added by Alexander IV in 1256. Francis, a branch of the Third Order of St, in the Anglican Communion there are also a number of mendicant groups such as the Anglican Friars Preachers and The Society of St. Francis. Several high schools, as well as Providence College, use friars as their school mascot, the Major League Baseball team San Diego Padres have the Swinging Friar. The University of Michigans oldest a cappella group is a male known as The Friars. The University of Pennsylvania has an honor society known as Friars
Friar
–
A group of friars; novices of the Order of
Augustinian Recollects at the Monastery of Marcilla,
Navarre
Friar
–
Conventual Franciscans in their variant grey habits
11.
Leonardo da Vinci
–
He has been variously called the father of palaeontology, ichnology, and architecture, and is widely considered one of the greatest painters of all time. Sometimes credited with the inventions of the parachute, helicopter and tank, many historians and scholars regard Leonardo as the prime exemplar of the Universal Genius or Renaissance Man, an individual of unquenchable curiosity and feverishly inventive imagination. Much of his working life was spent in the service of Ludovico il Moro in Milan. He later worked in Rome, Bologna and Venice, and he spent his last years in France at the home awarded to him by Francis I of France, Leonardo was, and is, renowned primarily as a painter. Among his works, the Mona Lisa is the most famous and most parodied portrait, Leonardos drawing of the Vitruvian Man is also regarded as a cultural icon, being reproduced on items as varied as the euro coin, textbooks, and T-shirts. Perhaps fifteen of his paintings have survived, Leonardo is revered for his technological ingenuity. He conceptualised flying machines, a type of armoured fighting vehicle, concentrated power, an adding machine. Some of his inventions, however, such as an automated bobbin winder. A number of Leonardos most practical inventions are nowadays displayed as working models at the Museum of Vinci. He made substantial discoveries in anatomy, civil engineering, geology, optics, and hydrodynamics, today, Leonardo is widely considered one of the most diversely talented individuals ever to have lived. Leonardo was born on 15 April 1452 at the hour of the night in the Tuscan hill town of Vinci. He was the son of the wealthy Messer Piero Fruosino di Antonio da Vinci, a Florentine legal notary, and Caterina. Leonardo had no surname in the modern sense – da Vinci simply meaning of Vinci, his birth name was Lionardo di ser Piero da Vinci, meaning Leonardo. The inclusion of the title ser indicated that Leonardos father was a gentleman, little is known about Leonardos early life. He spent his first five years in the hamlet of Anchiano in the home of his mother and his father had married a sixteen-year-old girl named Albiera Amadori, who loved Leonardo but died young in 1465 without children. When Leonardo was sixteen, his father married again to twenty-year-old Francesca Lanfredini, pieros legitimate heirs were born from his third wife Margherita di Guglielmo and his fourth and final wife, Lucrezia Cortigiani. Leonardo received an education in Latin, geometry and mathematics. In later life, Leonardo recorded only two childhood incidents, one, which he regarded as an omen, was when a kite dropped from the sky and hovered over his cradle, its tail feathers brushing his face
Leonardo da Vinci
–
Portrait of Leonardo
Leonardo da Vinci
–
Leonardo's childhood home in
Anchiano
Leonardo da Vinci
–
Leonardo's earliest known drawing, the Arno Valley (1473),
Uffizi
Leonardo da Vinci
–
The Baptism of Christ (1472–75)—
Uffizi, by Verrocchio and Leonardo
12.
Accounting
–
Accounting or accountancy is the measurement, processing and communication of financial information about economic entities such as businesses and corporations. The modern field was established by the Italian mathematician Luca Pacioli in 1494, practitioners of accounting are known as accountants. The terms accounting and financial reporting are often used as synonyms, Accounting can be divided into several fields including financial accounting, management accounting, external auditing, and tax accounting. Accounting information systems are designed to support accounting functions and related activities, Accounting is facilitated by accounting organizations such as standard-setters, accounting firms and professional bodies. Financial statements are audited by accounting firms, and are prepared in accordance with generally accepted accounting principles. GAAP is set by various standard-setting organizations such as the Financial Accounting Standards Board in the United States, as of 2012, all major economies have plans to converge towards or adopt the International Financial Reporting Standards. The history of accounting is thousands of old and can be traced to ancient civilizations. By the time of the Emperor Augustus, the Roman government had access to detailed financial information, double-entry bookkeeping developed in medieval Europe, and accounting split into financial accounting and management accounting with the development of joint-stock companies. The first work on a double-entry bookkeeping system was published in Italy, both the words accounting and accountancy were in use in Great Britain by the mid-1800s, and are derived from the words accompting and accountantship used in the 18th century. In Middle English the verb to account had the form accounten, which was derived from the Old French word aconter, which is in turn related to the Vulgar Latin word computare, meaning to reckon. The base of computare is putare, which meant to prune, to purify, to correct an account, hence, to count or calculate. The word accountant is derived from the French word compter, which is derived from the Italian. Accountancy refers to the occupation or profession of an accountant, particularly in British English, Accounting has several subfields or subject areas, including financial accounting, management accounting, auditing, taxation and accounting information systems. Financial accounting focuses on the reporting of a financial information to external users of the information, such as investors. It calculates and records business transactions and prepares financial statements for the users in accordance with generally accepted accounting principles. GAAP, in turn, arises from the agreement between accounting theory and practice, and change over time to meet the needs of decision-makers. This branch of accounting is also studied as part of the exams for qualifying as an actuary. It is interesting to note that two professionals, accountants and actuaries, have created a culture of being archrivals
Accounting
–
Accounting
Accounting
–
Portrait of Luca Pacioli, painted by
Jacopo de' Barbari, 1495, (
Museo di Capodimonte).
13.
Tuscany
–
Tuscany is a region in central Italy with an area of about 23,000 square kilometres and a population of about 3.8 million inhabitants. Tuscany is known for its landscapes, traditions, history, artistic legacy, Tuscany produces wines, including Chianti, Vino Nobile di Montepulciano, Morellino di Scansano and Brunello di Montalcino. Having a strong linguistic and cultural identity, it is considered a nation within a nation. Tuscany is traditionally a popular destination in Italy, and the main tourist destinations by number of tourist arrivals are Florence, Pisa, Montecatini Terme, Castiglione della Pescaia and Grosseto. The village of Castiglione della Pescaia is also the most visited destination in the region. Additionally, Siena, Lucca, the Chianti region, Versilia and Val dOrcia are also internationally renowned, Tuscany has over 120 protected nature reserves, making Tuscany and its capital Florence popular tourist destinations that attract millions of tourists every year. In 2012, the city of Florence was the worlds 89th most visited city, roughly triangular in shape, Tuscany borders the regions of Liguria to the northwest, Emilia-Romagna to the north and east, Umbria to the east and Lazio to the southeast. The comune of Badia Tedalda, in the Tuscan Province of Arezzo, has an exclave named Ca Raffaello within Emilia-Romagna, Tuscany has a western coastline on the Tyrrhenian Sea, containing the Tuscan Archipelago, of which the largest island is Elba. Tuscany has an area of approximately 22,993 square kilometres, surrounded and crossed by major mountain chains, and with few plains, the region has a relief that is dominated by hilly country used for agriculture. Hills make up nearly two-thirds of the total area, covering 15,292 square kilometres, and mountains. Plains occupy 8. 4% of the total area—1,930 square kilometres —mostly around the valley of the River Arno, many of Tuscanys largest cities lie on the banks of the Arno, including the capital Florence, Empoli and Pisa. The pre-Etruscan history of the area in the late Bronze and Iron Ages parallels that of the early Greeks, following this, the Villanovan culture saw Tuscany, and the rest of Etruria, taken over by chiefdoms. City-states developed in the late Villanovan before Orientalization occurred and the Etruscan civilization rose, the Etruscans created the first major civilization in this region, large enough to establish a transport infrastructure, to implement agriculture and mining and to produce vibrant art. The Etruscans lived in Etruria well into prehistory, throughout their existence, they lost territory to Magna Graecia, Carthage and Celts. Despite being seen as distinct in its manners and customs by contemporary Greeks, the cultures of Greece, one reason for its eventual demise was this increasing absorption by surrounding cultures, including the adoption of the Etruscan upper class by the Romans. Soon after absorbing Etruria, Rome established the cities of Lucca, Pisa, Siena, and Florence, endowed the area with new technologies and development, and ensured peace. These developments included extensions of existing roads, introduction of aqueducts and sewers, however, many of these structures have been destroyed by erosion due to weather. The Roman civilization in the West collapsed in the 5th century AD, in the years following 572, the Longobards arrived and designated Lucca the capital of their Duchy of Tuscia
Tuscany
–
Hilly landscape in
Val d'Orcia
Tuscany
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Tuscany Toscana
Tuscany
–
Tuscan landscape near
Siena
Tuscany
–
Cinerary urns of the
Villanovan culture
14.
Mathematics
–
Mathematics is the study of topics such as quantity, structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope, Mathematicians seek out patterns and use them to formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof, when mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, practical mathematics has been a human activity from as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry, rigorous arguments first appeared in Greek mathematics, most notably in Euclids Elements. Galileo Galilei said, The universe cannot be read until we have learned the language and it is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word. Without these, one is wandering about in a dark labyrinth, carl Friedrich Gauss referred to mathematics as the Queen of the Sciences. Benjamin Peirce called mathematics the science that draws necessary conclusions, David Hilbert said of mathematics, We are not speaking here of arbitrariness in any sense. Mathematics is not like a game whose tasks are determined by arbitrarily stipulated rules, rather, it is a conceptual system possessing internal necessity that can only be so and by no means otherwise. Albert Einstein stated that as far as the laws of mathematics refer to reality, they are not certain, Mathematics is essential in many fields, including natural science, engineering, medicine, finance and the social sciences. Applied mathematics has led to entirely new mathematical disciplines, such as statistics, Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind. There is no clear line separating pure and applied mathematics, the history of mathematics can be seen as an ever-increasing series of abstractions. The earliest uses of mathematics were in trading, land measurement, painting and weaving patterns, in Babylonian mathematics elementary arithmetic first appears in the archaeological record. Numeracy pre-dated writing and numeral systems have many and diverse. Between 600 and 300 BC the Ancient Greeks began a study of mathematics in its own right with Greek mathematics. Mathematics has since been extended, and there has been a fruitful interaction between mathematics and science, to the benefit of both. Mathematical discoveries continue to be made today, the overwhelming majority of works in this ocean contain new mathematical theorems and their proofs. The word máthēma is derived from μανθάνω, while the modern Greek equivalent is μαθαίνω, in Greece, the word for mathematics came to have the narrower and more technical meaning mathematical study even in Classical times
Mathematics
–
Euclid (holding
calipers), Greek mathematician, 3rd century BC, as imagined by
Raphael in this detail from
The School of Athens.
Mathematics
–
Greek mathematician
Pythagoras (c. 570 – c. 495 BC), commonly credited with discovering the
Pythagorean theorem
Mathematics
–
Leonardo Fibonacci, the
Italian mathematician who established the Hindu–Arabic numeral system to the Western World
Mathematics
–
Carl Friedrich Gauss, known as the prince of mathematicians
15.
Ludovico Sforza
–
Ludovico Maria Sforza, was Duke of Milan from 1494 until 1499, following the death of his nephew Gian Galeazzo Sforza. A member of the Sforza family, he was the son of Francesco I Sforza. He was famed as a patron of Leonardo da Vinci and other artists and he is probably best known as the man who commissioned The Last Supper. Ludovico Sforza was born on 27 July 1452 at Vigevano, in what is now Lombardy and he was the fourth son of Francesco I Sforza and Bianca Maria Visconti and, as such, was not expected to become ruler of Milan. Nevertheless, his mother, Bianca, prudently saw to it that his education was not restricted to the classical languages. Under the tutelage of the humanist Francesco Filelfo, Ludovico received instruction in the beauties of painting, sculpture, and letters and he later helped Leonardo paint with pastels. When their father Francesco died in 1466, the titles devolved upon the dissolute Galeazzo Maria. Galeazzo Maria ruled until his assassination in 1476, leaving his titles to his son, Gian Galeazzo Sforza. For the following 13 years he ruled Milan as its Regent, Leonardo da Vinci orchestrated the wedding celebration. Beatrice and Alfonso’s sister, Isabella dEste was married to Francesco II Gonzaga, the 15-year-old princess quickly charmed the Milanese court with her joy in life, her laughter, and even her extravagance. She helped to make Sforza Castle a center of sumptuous festivals and balls and she loved entertaining philosophers, poets, diplomats and she would become the mother of Maximilian Sforza and Francesco II Sforza, future Dukes of Milan. Prior to and throughout the duration of his marriage, Ludovico is known to have had mistresses, bernardina de Corradis was an early mistress who bore him a daughter, Bianca Giovanna. The child was legitimized and later married to Galeazzo da Sanseverino in 1496, cecilia Gallerani, believed to be a favourite, gave birth to a son named Cesare on 3 May 1491, in the same year in which he married Beatrice dEste. Gallerani is identified as the subject of Leonardo da Vincis Lady with an Ermine – the ermine was the animal of Ludovico il Moro. Another mistress was Lucrezia Crivelli, who bore him another son, Giovanni Paolo. Ludovico also fathered an illegitimate son, called Sforza, who was born around 1484 and died suddenly in 1487. Ludovico contented himself with the rather than the appearance of power. He invested in agriculture, horse and cattle breeding, and the metal industry, some 20,000 workers were employed in the silk industry
Ludovico Sforza
–
Ludovico Sforza
Ludovico Sforza
–
Ludovico Sforza in a portrait by
Giovanni Ambrogio de Predis.
16.
Milan
–
Milan is a city in Italy, capital of the Lombardy region, and the most populous metropolitan area and the second most populous comune in Italy. The population of the city proper is 1,351,000, Milan has a population of about 8,500,000 people. It is the industrial and financial centre of Italy and one of global significance. In terms of GDP, it has the largest economy among European non-capital cities, Milan is considered part of the Blue Banana and lies at the heart of one of the Four Motors for Europe. Milan is an Alpha leading global city, with strengths in the arts, commerce, design, education, entertainment, fashion, finance, healthcare, media, services, research, and tourism. Its business district hosts Italys Stock Exchange and the headquarters of the largest national and international banks, the city is a major world fashion and design capital, well known for several international events and fairs, including Milan Fashion Week and the Milan Furniture Fair. The city hosts numerous cultural institutions, academies and universities, with 11% of the national total enrolled students, Milans museums, theatres and landmarks attract over 9 million visitors annually. Milan – after Naples – is the second Italian city with the highest number of accredited stars from the Michelin Guide, the city hosted the Universal Exposition in 1906 and 2015. Milan is home to two of Europes major football teams, A. C. Milan and F. C. Internazionale, the etymology of Milan is uncertain. One theory holds that the Latin name Mediolanum comes from the Latin words medio, however, some scholars believe lanum comes from the Celtic root lan, meaning an enclosure or demarcated territory in which Celtic communities used to build shrines. Hence, Mediolanum could signify the central town or sanctuary of a Celtic tribe, indeed, the name Mediolanum is borne by about sixty Gallo-Roman sites in France, e. g. Saintes and Évreux. Alciato credits Ambrose for his account, around 400 BC, the Celtic Insubres settled Milan and the surrounding region. In 222 BC, the Romans conquered the settlement, renaming it Mediolanum, Milan was eventually declared the capital of the Western Roman Empire by Emperor Diocletian in 286 AD. Diocletian chose to stay in the Eastern Roman Empire and his colleague Maximianus ruled the Western one, immediately Maximian built several monuments, such as a large circus 470 m ×85 m, the Thermae Herculeae, a large complex of imperial palaces and several other buildings. With the Edict of Milan of 313, Emperor Constantine I guaranteed freedom of religion for Christians, after the city was besieged by the Visigoths in 402, the imperial residence was moved to Ravenna. In 452, the Huns overran the city, in 539, the Ostrogoths conquered and destroyed Milan during the Gothic War against Byzantine Emperor Justinian I. In the summer of 569, a Teutonic tribe, the Lombards, conquered Milan, some Roman structures remained in use in Milan under Lombard rule. Milan surrendered to the Franks in 774 when Charlemagne took the title of King of the Lombards, the Iron Crown of Lombardy dates from this period
Milan
–
Milan Cathedral,
La Scala opera house and
Porta Nuova business district
Milan
Milan
Milan
17.
Louis XII of France
–
Louis XII was a monarch of the House of Valois who ruled as King of France from 1498 to 1515 and King of Naples from 1501 to 1504. The son of Charles, Duke of Orléans, and Maria of Cleves, he succeeded his cousin Charles VIII, who died without a closer heir in 1498. Before his accession to the throne of France, he was known as Louis of Orléans and was compelled to be married to his disabled and supposedly sterile cousin Joan by his second cousin, king Louis XI. By doing so, Louis XI hoped to extinguish the Orléans cadet branch of the House of Valois, Louis of Orléans was one of the great feudal lords who opposed the French monarchy in the conflict known as the Mad War. At the royal victory in the Battle of Saint-Aubin-du-Cormier in 1488, Louis was captured and he subsequently took part in the Italian War of 1494–1498 as one of the French commanders. When Louis XII became king in 1498, he had his marriage with Joan annulled by Pope Alexander VI and instead married Anne of Brittany and this marriage allowed Louis to reinforce the personal Union of Brittany and France. Louis persevered in the Italian Wars, initiating a second Italian campaign for the control of the Kingdom of Naples, Louis conquered the Duchy of Milan in 1500 and pushed forward to the Kingdom of Naples, which fell to him in 1501. Proclaimed King of Naples, Louis faced a new coalition gathered by Ferdinand II of Aragon and was forced to cede Naples to Spain in 1504. A popular king, Louis was proclaimed Father of the People in 1506 by the Estates-General of Tours for his reduction of the tax known as taille, legal reforms, Louis XII died in 1515 without a male heir. He was succeeded by his cousin Francis from the Angoulême cadet branch of the House of Valois, Louis was born on 27 June 1462 in the Château de Blois, Touraine. The son of Charles, Duke of Orléans, and Marie of Cleves, however, Louis XI may have been more influenced in this opinion by his opposition to the entire Orleanist faction of the royal family than by the actual facts of this paternity case. Despite any alleged doubts that King Louis XI may have had, King Louis XI died on 30 August 1483. He was succeeded to the throne of France by his thirteen year-old son, nobody knew the direction which the new king would take in leading the kingdom. Accordingly, on 24 October 1483, a call went out for a convocation of the Estates General of the French kingdom, in January 1484, deputies of the Estates General began to arrive in Tours, France. The deputies represented three different estates in society, the First Estate was the Church, in France this meant the Roman Catholic Church. The Second Estate was composed of the nobility and the royalty of France, the Third Estate was generally composed of commoners and the class of traders and merchants in France. Louis, the current Duke of Orleans and future Louis XII, each estate brought their chief complaints to the Estates General in hopes to have some impact on the policies that the new King would pursue. The First Estate wanted a return to the Pragmatic Sanction, the Pragmatic Sanction had been first instituted by King Charles VII, the current King Charles VIIIs grandfather
Louis XII of France
–
Louis XII
Louis XII of France
–
Bronze cannon of Louis XII, with
porcupine emblem. Caliber: 172mm, length: 305 cm, weight: 1870kg. Recovered in
Algiers in 1830.
Musée de l'Armée.
Louis XII of France
–
Louis XII leaving
Alessandria to attack
Genoa; by
Jean Bourdichon
Louis XII of France
–
Litterae super abrogatione pragmatice sanctionis, 1512
18.
Rhombicuboctahedron
–
In geometry, the rhombicuboctahedron, or small rhombicuboctahedron, is an Archimedean solid with eight triangular and eighteen square faces. There are 24 identical vertices, with one triangle and three meeting at each. The polyhedron has octahedral symmetry, like the cube and octahedron and its dual is called the deltoidal icositetrahedron or trapezoidal icositetrahedron, although its faces are not really true trapezoids. Johannes Kepler in Harmonices Mundi named this polyhedron a rhombicuboctahedron, being short for truncated cuboctahedral rhombus and this truncation creates new vertices mid-edge to the rhombic dodecahedron, creating rectangular faces inside the original rhombic faces, and new square and triangle faces at the original vertices. The semiregular form here requires the geometry be adjusted so the rectangles become squares and it can also be called an expanded cube or cantellated cube or a cantellated octahedron from truncation operations of the uniform polyhedron. There are distortions of the rhombicuboctahedron that, while some of the faces are not regular polygons, are still vertex-uniform. Some of these can be made by taking a cube or octahedron and cutting off the edges, then trimming the corners, so the resulting polyhedron has six square and twelve rectangular faces. The lines along which a Rubiks Cube can be turned are, projected onto a sphere, similar, topologically identical, in fact, variants using the Rubiks Cube mechanism have been produced which closely resemble the rhombicuboctahedron. The rhombicuboctahedron is used in three uniform space-filling tessellations, the cubic honeycomb, the runcitruncated cubic honeycomb, and the runcinated alternated cubic honeycomb. The rhombicuboctahedron can be dissected into two square cupolae and an octagonal prism. A rotation of one cupola by 45 degrees creates the pseudorhombicuboctahedron, both of these polyhedra have the same vertex figure,3.4.4.4. There are three pairs of parallel planes that each intersect the rhombicuboctahedron in a regular octagon and these pieces can be reassembled to give a new solid called the elongated square gyrobicupola or pseudorhombicuboctahedron, with the symmetry of a square antiprism. The rhombicuboctahedron has six special orthogonal projections, centered, on a vertex, the last two correspond to the B2 and A2 Coxeter planes. The rhombicuboctahedron can also be represented as a tiling. This projection is conformal, preserving angles but not areas or lengths, straight lines on the sphere are projected as circular arcs on the plane. A half symmetry form of the rhombicuboctahedron, exists with pyritohedral symmetry, as Coxeter diagram, Schläfli symbol s2 and this form can be visualized by alternatingly coloring the edges of the 6 squares. These squares can then be distorted into rectangles, while the 8 triangles remain equilateral, the 12 diagonal square faces will become isosceles trapezoids. Cartesian coordinates for the vertices of a rhombicuboctahedron centred at the origin, if the original rhombicuboctahedron has unit edge length, its dual strombic icositetrahedron has edge lengths 2710 −2 and 4 −22
Rhombicuboctahedron
–
(Click here for rotating model)
Rhombicuboctahedron
–
Deltoidal icositetrahedron (
dual polyhedron)
Rhombicuboctahedron
–
Rhombicuboctahedron in top left of 1495
Portrait of Luca Pacioli.
Rhombicuboctahedron
–
A
Cabela's branded "self-healing" target made of ballistic material
19.
Golden ratio
–
In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. The figure on the right illustrates the geometric relationship, expressed algebraically, for quantities a and b with a > b >0, a + b a = a b = def φ, where the Greek letter phi represents the golden ratio. Its value is, φ =1 +52 =1.6180339887 …, A001622 The golden ratio is also called the golden mean or golden section. Other names include extreme and mean ratio, medial section, divine proportion, divine section, golden proportion, golden cut, the golden ratio appears in some patterns in nature, including the spiral arrangement of leaves and other plant parts. The golden ratio has also used to analyze the proportions of natural objects as well as man-made systems such as financial markets. Two quantities a and b are said to be in the golden ratio φ if a + b a = a b = φ, one method for finding the value of φ is to start with the left fraction. Through simplifying the fraction and substituting in b/a = 1/φ, a + b a =1 + b a =1 +1 φ, multiplying by φ gives φ +1 = φ2 which can be rearranged to φ2 − φ −1 =0. First, the line segment A B ¯ is about doubled and then the semicircle with the radius A S ¯ around the point S is drawn, now the semicircle is drawn with the radius A B ¯ around the point B. The arising intersection point E corresponds 2 φ, next up, the perpendicular on the line segment A E ¯ from the point D will be establish. The subsequent parallel F S ¯ to the line segment C M ¯, produces, as it were and it is well recognizable, this triangle and the triangle M S C are similar to each other. The hypotenuse F S ¯ has due to the cathetuses S D ¯ =1 and D F ¯ =2 according the Pythagorean theorem, finally, the circle arc is drawn with the radius 5 around the point F. The golden ratio has been claimed to have held a fascination for at least 2,400 years. But the fascination with the Golden Ratio is not confined just to mathematicians, biologists, artists, musicians, historians, architects, psychologists, and even mystics have pondered and debated the basis of its ubiquity and appeal. In fact, it is fair to say that the Golden Ratio has inspired thinkers of all disciplines like no other number in the history of mathematics. Ancient Greek mathematicians first studied what we now call the golden ratio because of its frequent appearance in geometry, the division of a line into extreme and mean ratio is important in the geometry of regular pentagrams and pentagons. Euclid explains a construction for cutting a line in extreme and mean ratio, throughout the Elements, several propositions and their proofs employ the golden ratio. The golden ratio is explored in Luca Paciolis book De divina proportione, since the 20th century, the golden ratio has been represented by the Greek letter φ or less commonly by τ. Timeline according to Priya Hemenway, Phidias made the Parthenon statues that seem to embody the golden ratio, plato, in his Timaeus, describes five possible regular solids, some of which are related to the golden ratio
Golden ratio
–
Michael Maestlin, first to publish a decimal approximation of the golden ratio, in 1597
Golden ratio
–
Line segments in the golden ratio
Golden ratio
–
Many of the proportions of the
Parthenon are alleged to exhibit the golden ratio.
Golden ratio
–
The drawing of a man's body in a
pentagram suggests relationships to the golden ratio.
20.
Mathematics and art
–
Mathematics and art are related in a variety of ways. Mathematics has itself been described as an art motivated by beauty, Mathematics can be discerned in arts such as music, dance, painting, architecture, sculpture, and textiles. This article focuses, however, on mathematics in the visual arts, Mathematics and art have a long historical relationship. Artists have used mathematics since the 5th century BC when the Greek sculptor Polykleitos wrote his Canon, prescribing proportions based on the ratio 1, persistent popular claims have been made for the use of the golden ratio in ancient art and architecture, without reliable evidence. In the Italian Renaissance, Luca Pacioli wrote the influential treatise De Divina Proportione, illustrated with woodcuts by Leonardo da Vinci, another Italian painter, Piero della Francesca, developed Euclids ideas on perspective in treatises such as De Prospectiva Pingendi, and in his paintings. The engraver Albrecht Dürer made many references to mathematics in his work Melencolia I, in modern times, the graphic artist M. C. Mathematics has inspired textile arts such as quilting, knitting, cross-stitch, crochet, embroidery, weaving, Turkish and other carpet-making, as well as kilim. In Islamic art, symmetries are evident in forms as varied as Persian girih and Moroccan zellige tilework, Mughal jaali pierced stone screens, and widespread muqarnas vaulting. Mathematics has directly influenced art with conceptual tools such as perspective, the analysis of symmetry, and mathematical objects such as polyhedra. Magnus Wenninger creates colourful stellated polyhedra, originally as models for teaching, mathematical concepts such as recursion and logical paradox can be seen in paintings by Rene Magritte and in engravings by M. C. Computer art often makes use of including the Mandelbrot set. Polykleitos the elder was a Greek sculptor from the school of Argos, and his works and statues consisted mainly of bronze and were of athletes. While his sculptures may not be as famous as those of Phidias, Polykleitos uses the distal phalanx of the little finger as the basic module for determining the proportions of the human body. Next, he takes the length and multiplies that by √2 to get the length of the palm from the base of the finger to the ulna. This geometric series of measurements progresses until Polykleitos has formed the arm, chest, body, the influence of the Canon of Polykleitos is immense in Classical Greek, Roman, and Renaissance sculpture, many sculptors following Polykleitoss prescription. While none of Polykleitoss original works survive, Roman copies demonstrate his ideal of physical perfection, some scholars argue that Pythagorean thought influenced the Canon of Polykleitos. In classical times, rather than making distant figures smaller with linear perspective, painters sized objects, in the Middle Ages, some artists used reverse perspective for special emphasis. The Muslim mathematician Alhazen described a theory of optics in his Book of Optics in 1021, the Renaissance saw a rebirth of Classical Greek and Roman culture and ideas, among them the study of mathematics to understand nature and the arts
Mathematics and art
–
Mathematics in art:
Albrecht Dürer 's copper plate engraving
Melencolia I, 1514. Mathematical references include a compass for
geometry, a
magic square and a
truncated rhombohedron, while measurement is indicated by the scales and
hourglass.
Mathematics and art
Mathematics and art
–
Roman copy in marble of
Doryphoros, originally a bronze by
Polykleitos
Mathematics and art
–
Brunelleschi 's experiment with
linear perspective
21.
Venice
–
Venice is a city in northeastern Italy and the capital of the Veneto region. It is situated across a group of 118 small islands that are separated by canals and these are located in the shallow Venetian Lagoon, an enclosed bay that lies between the mouths of the Po and the Piave Rivers. Parts of Venice are renowned for the beauty of their settings, their architecture, the lagoon and a part of the city are listed as a World Heritage Site. In 2014,264,579 people resided in Comune di Venezia, together with Padua and Treviso, the city is included in the Padua-Treviso-Venice Metropolitan Area, with a total population of 2.6 million. PATREVE is a metropolitan area without any degree of autonomy. The name is derived from the ancient Veneti people who inhabited the region by the 10th century BC, the city was historically the capital of the Republic of Venice. Venice has been known as the La Dominante, Serenissima, Queen of the Adriatic, City of Water, City of Masks, City of Bridges, The Floating City, and City of Canals. The City State of Venice is considered to have been the first real international financial center which gradually emerged from the 9th century to its peak in the 14th century and this made Venice a wealthy city throughout most of its history. It is also known for its several important artistic movements, especially the Renaissance period, Venice has played an important role in the history of symphonic and operatic music, and it is the birthplace of Antonio Vivaldi. Venice has been ranked the most beautiful city in the world as of 2016, the name Venetia, however, derives from the Roman name for the people known as the Veneti, and called by the Greeks Eneti. The meaning of the word is uncertain, although there are other Indo-European tribes with similar-sounding names, such as the Celtic Veneti, Baltic Veneti, and the Slavic Wends. Linguists suggest that the name is based on an Indo-European root *wen, so that *wenetoi would mean beloved, lovable, a connection with the Latin word venetus, meaning the color sea-blue, is also possible. The alternative obsolete form is Vinegia, some late Roman sources reveal the existence of fishermen on the islands in the original marshy lagoons. They were referred to as incolae lacunae, the traditional founding is identified with the dedication of the first church, that of San Giacomo on the islet of Rialto — said to have taken place at the stroke of noon on 25 March 421. Beginning as early as AD166 to 168, the Quadi and Marcomanni destroyed the center in the area. The Roman defences were again overthrown in the early 5th century by the Visigoths and, some 50 years later, New ports were built, including those at Malamocco and Torcello in the Venetian lagoon. The tribuni maiores, the earliest central standing governing committee of the islands in the Lagoon, the traditional first doge of Venice, Paolo Lucio Anafesto, was actually Exarch Paul, and his successor, Marcello Tegalliano, was Pauls magister militum. In 726 the soldiers and citizens of the Exarchate rose in a rebellion over the controversy at the urging of Pope Gregory II
Venice
–
A collage of Venice: at the top left is the
Piazza San Marco, followed by a view of the city, then the
Grand Canal, and (smaller) the interior of
La Fenice and, finally, the Island of San Giorgio Maggiore
Venice
–
UNESCO World Heritage Site
Venice
–
Photography of Venice at dusk
Venice
–
The Grand Canal seen from the bridge at
Ponte di Rialto
22.
Double-entry accounting system
–
Double-entry bookkeeping, in accounting, is a system of bookkeeping so named because every entry to an account requires a corresponding and opposite entry to a different account. For instance, recording earnings of $100 would require making two entries, an entry of $100 to an account named Cash and a credit entry of $100 to an account named Revenue. Deciding which account has to be debited and which account has to be credited is accomplished using the equation which is expressed as. This equation serves as a detection tool, if at any point the sum of debits for all accounts does not equal the corresponding sum of credits for all accounts. It follows that the sum of debits and the sum of the credits must be equal in value, Double-entry bookkeeping is no guarantee that errors have not been made, for example, the wrong ledger account may have been debited or credited, or the entries completely reversed. The oldest record of a complete system is the Messari accounts of the Republic of Genoa in 1340. By the end of the 15th century, the bankers and merchants of Florence, Genoa, Venice, however, the double-entry accounting method was said to be developed independently earlier in Korea during the Goryeo dynasty when Kaesong was a center of trade and industry at that time. The Four-element bookkeeping system was said to be originated in the 11th or 12th century, the earliest extant accounting records that follow the modern double-entry system in Europe come from Amatino Manucci, a Florentine merchant at the end of the 13th century. Manucci was employed by the Farolfi firm and the ledger of 1299-1300 evidences full double-entry bookkeeping. Giovannino Farolfi & Company, a firm of Florentine merchants headquartered in Nîmes, acted as moneylenders to the Archbishop of Arles, some sources suggest that Giovanni di Bicci de Medici introduced this method for the Medici bank in the 14th century. Historical records show that since the second caliphate, AD 634-644, critics of claims that Muslims invented double-entry bookkeeping accept that several features of pre-double-entry accounting were used in the Muslim world before they were used in the West. Pacioli is often called the father of accounting because he was the first to publish a description of the double-entry system, thus enabling others to study. In pre-modern Europe, double-entry bookkeeping had theological and cosmological connotations, in the double-entry accounting system, at least two accounting entries are required to record each financial transaction. These entries may occur in asset, liability, equity, expense, recording of a debit amount to one or more accounts and an equal credit amount to one or more accounts results in total debits being equal to total credits for all accounts in the general ledger. If the accounting entries are recorded without error, the balance of all accounts having Debit balances will be equal to the aggregate balance of all accounts having Credit balances. The rules for formulating accounting entries are known as Golden Rules of Accounting, the accounting entries are recorded in the Books of Accounts. Regardless of which accounts and how many are impacted by a given transaction, there are two different ways to memorize the effects of debits and credits on accounts in the double entry system of bookkeeping. They are the Traditional Approach and the Accounting Equation Approach, irrespective of the approach used, the effect on the books of accounts remains the same, with two aspects in each of the transactions
Double-entry accounting system
–
Accounting
23.
Balance sheet
–
Assets, liabilities and ownership equity are listed as of a specific date, such as the end of its financial year. A balance sheet is often described as a snapshot of a companys financial condition, of the four basic financial statements, the balance sheet is the only statement which applies to a single point in time of a business calendar year. A standard company balance sheet has two sides, assets, on the left and financing, which itself has two parts, liabilities and ownership equity, on the right, the main categories of assets are usually listed first, and typically in order of liquidity. Assets are followed by the liabilities, another way to look at the balance sheet equation is that total assets equals liabilities plus owners equity. Looking at the equation in this way shows how assets were financed, balance sheets are usually presented with assets in one section and liabilities and net worth in the other section with the two sections balancing. A business operating entirely in cash can measure its profits by withdrawing the entire bank balance at the end of the period, however, many businesses are not paid immediately, they build up inventories of goods and they acquire buildings and equipment. In other words, businesses have assets and so they cannot, even if they want to, often, these businesses owe money to suppliers and to tax authorities, and the proprietors do not withdraw all their original capital and profits at the end of each period. In other words, businesses also have liabilities, a balance sheet summarizes an organization or individuals assets, equity and liabilities at a specific point in time. Two forms of balance sheet exist and they are the report form and the account form. Individuals and small businesses tend to have simple balance sheets, larger businesses tend to have more complex balance sheets, and these are presented in the organizations annual report. Large businesses also may prepare balance sheets for segments of their businesses, a balance sheet is often presented alongside one for a different point in time for comparison. Securities and real values are listed at market value rather than at historical cost or cost basis. Personal net worth is the difference between a total assets and total liabilities. Contingent liabilities such as warranties are noted in the footnotes to the balance sheet, the small businesss equity is the difference between total assets and total liabilities. Guidelines for balance sheets of public entities are given by the International Accounting Standards Board. The standard used by companies in the USA adhere to U. S, balance sheet account names and usage depend on the organizations country and the type of organization. Government organizations do not generally follow standards established for individuals or businesses, if applicable to the business, summary values for the following items should be included in the balance sheet, Assets are all the things the business owns. This will include property, tools, vehicles, furniture, machinery, bearer biological assets are plants or animals which bear agricultural produce for harvest, such as apple trees grown to produce apples and sheep raised to produce wool
Balance sheet
–
Accounting
24.
Income statement
–
An income statement or profit and loss account is one of the financial statements of a company and shows the company’s revenues and expenses during a particular period. It indicates how the revenues are transformed into the net income and it displays the revenues recognized for a specific period, and the cost and expenses charged against these revenues, including write-offs and taxes. The purpose of the statement is to show managers and investors whether the company made or lost money during the period being reported. One important thing to remember about a statement is that it represents a period of time like the cash flow statement. This contrasts with the sheet, which represents a single moment in time. Charitable organizations that are required to publish financial statements do not produce an income statement, instead, they produce a similar statement that reflects funding sources compared against program expenses, administrative costs, and other operating commitments. This statement is referred to as the statement of activities. Revenues and expenses are further categorized in the statement of activities by the restrictions on the funds received and expended. The income statement can be prepared in one of two methods, the Single Step income statement takes the simpler approach, totaling revenues and subtracting expenses to find the bottom line. The more complex Multi-Step income statement takes several steps to find the bottom line and it then calculates operating expenses and, when deducted from the gross profit, yields income from operations. Adding to income from operations is the difference of other revenues, when combined with income from operations, this yields income before taxes. The final step is to deduct taxes, which produces the net income for the period measured. However, information of a statement has several limitations, Items that might be relevant. Some numbers depend on accounting methods used, some numbers depend on judgments and estimates. S. Names and usage of different accounts in the income statement depend on the type of organization, industry practices and it is usually presented as sales minus sales discounts, returns, and allowances. Every time a business sells a product or performs a service and this often is referred to as gross revenue or sales revenue. Cost of Goods Sold / Cost of Sales - represents the direct costs attributable to goods produced and it includes material costs, direct labour, and overhead costs, and excludes operating costs such as selling, administrative, advertising or R&D, etc. Selling, General and Administrative expenses - consist of the combined payroll costs, SGA is usually understood as a major portion of non-production related costs, in contrast to production costs such as direct labour
Income statement
–
Accounting
25.
Trial balance
–
A trial balance is a list of all the general ledger accounts contained in the ledger of a business. This list will contain the name of each nominal ledger account, each nominal ledger account will hold either a debit balance or a credit balance. The debit balance values will be listed in the column of the trial balance. The trading profit and loss statement and balance sheet and other financial reports can then be produced using the ledger accounts listed on the trial balance, the process was first described by Luca Pacioli in the 1494 work Particularis de Computis et Scripturis. Although it did not use the term, he prescribed a technique similar to a post-closing trial balance. The purpose of a balance is to prove that the value of all the debit value balances equal the total of all the credit value balances. If the total of the debit column does not equal the value of the credit column then this would show that there is an error in the nominal ledger accounts. This error must be found before a profit and loss statement, the trial balance is usually prepared by a bookkeeper or accountant who has used daybooks to record financial transactions and then post them to the nominal ledgers and personal ledger accounts. The trial balance is a part of the double-entry bookkeeping system, a trial balance only checks the sum of debits against the sum of credits. That is why it does not guarantee that there are no errors, the following are the main classes of errors that are not detected by the trial balance. An error of original entry is when both sides of a transaction include the wrong amount, an error of omission is when a transaction is completely omitted from the accounting records. As the debits and credits for the transaction would balance, omitting it would leave the totals balanced. A variation of this error is omitting one of the ledger account totals from the trial balance, an error of reversal is when entries are made to the correct amount, but with debits instead of credits, and vice versa. For example, if a sale for £100 is debited to the Sales account. Such an error will not affect the totals, an error of commission is when the entries are made at the correct amount, and the appropriate side, but one or more entries are made to the wrong account of the correct type. For example, if costs are incorrectly debited to the postage account. This will not affect the totals, an error of principle is when the entries are made to the correct amount, and the appropriate side, as with an error of commission, but the wrong type of account is used. For example, if fuel costs, are debited to stock and this will not affect the totals
Trial balance
–
Accounting
26.
Accounting ethics
–
Accounting ethics is primarily a field of applied ethics and is part of business ethics and human ethics, the study of moral values and judgments as they apply to accountancy. It is an example of professional ethics, Accounting introduced by Luca Pacioli, and later expanded by government groups, professional organizations, and independent companies. Ethics are taught in accounting courses at higher education institutions as well as by companies training accountants, due to the diverse range of accounting services and recent corporate collapses, attention has been drawn to ethical standards accepted within the accounting profession. These collapses have resulted in a widespread disregard for the reputation of the accounting profession, the nature of the work carried out by accountants and auditors requires a high level of ethics. They rely on the opinion of the accountants who prepared the statements, as well as the auditors that verified it, to present a true, most countries have differing focuses on enforcing accounting laws. In Germany, accounting legislation is governed by tax law, in Sweden, by accounting law, in addition, countries have their own organizations which regulate accounting. For example, Sweden has the Bokföringsnämden, Spain the Instituto de Comtabilidad y Auditoria de Cuentas, Luca Pacioli, the Father of Accounting, wrote on accounting ethics in his first book Summa de arithmetica, geometria, proportioni, et proportionalita, published in 1494. Ethical standards have since then developed through government groups, professional organizations. These various groups have led accountants to follow several codes of ethics to perform their duties in a work environment. Accountants must follow the code of ethics set out by the body of which they are a member. In 1887, the American Association of Public Accountants was created, by 1905, the AAPAs first ethical codes were formulated to educate its members. During its twentieth anniversary meeting in October 1907, ethics was a topic of the conference among its members. As a result of discussions, a list of ethics was incorporated into the organizations bylaws. However, because membership to the organization was voluntary, the association could not require individuals to conform to the suggested behaviors, other accounting organizations, such as the Illinois Institute of Accountants, also pursued discussion on the importance of ethics for the field. The AAPA was renamed several times throughout its history, before becoming the American Institute of Certified Public Accountants as its named today, each of these divisions provided guidelines on how a Certified Public Accountant should act as a professional. Failure to comply with the guidelines could have caused an accountant to be barred from practicing, when developing the ethical principles, the AICPA also considered how the profession would be viewed by those outside of the accounting industry. Courses on this subject have grown significantly in the last couple of decades, teaching accountants about ethics can involve role playing, lectures, case studies, guest lectures, as well as other mediums. Recent studies indicate that nearly all accounting textbooks touch on ethics in some way, in 1993, the first United States center that focused on the study of ethics in the accounting profession opened at Binghamton University
Accounting ethics
–
Luca Pacioli, here in
a 1495 portrait by an unknown Renaissance artist, wrote on accounting ethics in 1494.
27.
Cost accounting
–
Cost accounting is a process of collecting, recording, classifying, analyzing, summarizing, allocating and evaluating various alternative courses of action & control of costs. Its goal is to advise the management on the most appropriate course of action based on the cost efficiency, Cost accounting provides the detailed cost information that management needs to control current operations and plan for the future. Since managers are making decisions only for their own organization, there is no need for the information to be comparable to similar information from other organizations, instead, information must be relevant for a particular environment. Cost accounting information is used in financial accounting information. As a result, there is variety in the cost accounting systems of the different companies and sometimes even in different parts of the same company or organization. All types of businesses, whether service, manufacturing or trading, Cost accounting has long been used to help managers understand the costs of running a business. In the early age, most of the costs incurred by a business were what modern accountants call variable costs because they varied directly with the amount of production. Money was spent on labor, raw materials, power to run a factory, managers could simply total the variable costs for a product and use this as a rough guide for decision-making processes. Some costs tend to remain the same even during busy periods, unlike variable costs, over time, these fixed costs have become more important to managers. In the early century, these costs were of little importance to most businesses. Managers must understand fixed costs in order to make decisions about products, for example, A company produced railway coaches and had only one product. To make each coach, the company needed to purchase $60 of raw materials and components, therefore, total variable cost for each coach was $300. Knowing that making a coach required spending $300, managers knew they couldnt sell below that price without losing money on each coach, any price above $300 became a contribution to the fixed costs of the company. Financial accounting aims at finding out results of accounting year in the form of Profit and Loss Account, Cost Accounting aims at computing cost of production/service in a scientific manner and facilitate cost control and cost reduction. Financial accounting reports the results and position of business to government, creditors, investors, Cost Accounting is an internal reporting system for an organization’s own management for decision making. In financial accounting, cost classification is based on type of transactions, e. g. salaries, repairs, insurance, stores etc. In cost accounting, classification is basically on the basis of functions, activities, products, process and on internal planning and control and information needs of the organization. Financial accounting aims at presenting ‘true and fair’ view of transactions, profit and loss for a period and it aims at computing ‘true and fair’ view of the cost of production/services offered by the firm
Cost accounting
–
Accounting
28.
Rule of 72
–
In finance, the rule of 72, the rule of 70 and the rule of 69.3 are methods for estimating an investments doubling time. The rule number is divided by the interest percentage per period to obtain the number of periods required for doubling. Although scientific calculators and spreadsheet programs have functions to find the accurate doubling time, the rules are useful for mental calculations and these rules apply to exponential growth and are therefore used for compound interest as opposed to simple interest calculations. They can also be used for decay to obtain a halving time, the choice of number is mostly a matter of preference,69 is more accurate for continuous compounding, while 72 works well in common interest situations and is more easily divisible. There are a number of variations to the rules that improve accuracy, for periodic compounding, the exact doubling time for an interest rate of r per period is T = ln ln ≈72 r, where T is the number of periods required. The formula above can be used for more than calculating the doubling time, if one wants to know the tripling time, for example, simply replace the constant 2 in the numerator with 3. As another example, if one wants to know the number of periods it takes for the value to rise by 50%. To estimate the number of required to double an original investment, divide the most convenient rule-quantity by the expected growth rate. Similarly, to determine the time it takes for the value of money to halve at a given rate, to determine the time for moneys buying power to halve, financiers simply divide the rule-quantity by the inflation rate. Thus at 3. 5% inflation using the rule of 70, to estimate the impact of additional fees on financial policies, divide 72 by the fee. The value 72 is a convenient choice of numerator, since it has many divisors,1,2,3,4,6,8,9. It provides an approximation for annual compounding, and for compounding at typical rates. The approximations are less accurate at higher interest rates, for continuous compounding,69 gives accurate results for any rate. This is because ln is about 69. 3%, see derivation below, since daily compounding is close enough to continuous compounding, for most purposes 69,69.3 or 70 are better than 72 for daily compounding. For lower annual rates than those above,69.3 would also be accurate than 72. An early reference to the rule is in the Summa de arithmetica of Luca Pacioli, roughly translated, For higher rates, a bigger numerator would be better. This is because, as above, the rule of 72 is only an approximation that is accurate for interest rates from 6% to 10%, for every three percentage points away from 8% the value 72 could be adjusted by 1. The rule of 69.3 is normally only accurate at the lowest end of interest rates, to compute the E-M approximation, simply multiply the rule of 69.3 result by 200/ as follows, t ≈69.3 r ×200200 − r
Rule of 72
–
Graphs comparing doubling times and half lives of exponential growths (bold lines) and decay (faint lines), and their 70/ t and 72/ t approximations
29.
John Napier
–
John Napier of Merchiston, also signed as Neper, Nepair, nicknamed Marvellous Merchiston) was a Scottish landowner known as a mathematician, physicist, and astronomer. He was the 8th Laird of Merchiston and his Latinized name was Ioannes Neper. John Napier is best known as the discoverer of logarithms and he also invented the so-called Napiers bones and made common the use of the decimal point in arithmetic and mathematics. Napiers birthplace, Merchiston Tower in Edinburgh, is now part of the facilities of Edinburgh Napier University, Napier died from the effects of gout at home at Merchiston Castle and his remains were buried in the kirkyard of St Giles. Following the loss of the kirkyard there to build Parliament House, archibald Napier was 16 years old when John Napier was born. As was the practice for members of the nobility at that time, he was privately tutored and did not have formal education until he was 13. He did not stay in very long. It is believed that he dropped out of school in Scotland, in 1571, Napier, aged 21, returned to Scotland, and bought a castle at Gartness in 1574. On the death of his father in 1608, Napier and his family moved into Merchiston Castle in Edinburgh and he died at the age of 67. In such conditions, it is surprising that many mathematicians were acutely aware of the issues of computation and were dedicated to relieving practitioners of the calculation burden. In particular, the Scottish mathematician John Napier was famous for his devices to assist with computation and he invented a well-known mathematical artifact, the ingenious numbering rods more quaintly known as “Napiers bones, ” that offered mechanical means for facilitating computation. He appreciated that, for the most part, practitioners who had laborious computations generally did them in the context of trigonometry, therefore, as well as developing the logarithmic relation, Napier set it in a trigonometric context so it would be even more relevant. His work, Mirifici Logarithmorum Canonis Descriptio contained fifty-seven pages of explanatory matter, the book also has an excellent discussion of theorems in spherical trigonometry, usually known as Napiers Rules of Circular Parts. Modern English translations of both Napiers books on logarithms, and their description can be found on the web, as well as a discussion of Napiers Bones and his invention of logarithms was quickly taken up at Gresham College, and prominent English mathematician Henry Briggs visited Napier in 1615. Among the matters discussed were a re-scaling of Napiers logarithms. Napier delegated to Briggs the computation of a revised table, the computational advance available via logarithms, the converse of powered numbers or exponential notation, was such that it made calculations by hand much quicker. The way was opened to later scientific advances, in astronomy, dynamics and he improved Simon Stevins decimal notation. Lattice multiplication, used by Fibonacci, was more convenient by his introduction of Napiers bones
John Napier
–
John Napier (1550–1617)
John Napier
–
Merchiston Castle
John Napier
–
Merchiston Castle from an 1834 woodcut
John Napier
–
Bust of Napier, holding his 'bones', at the Craighouse Campus of Napier University, Edinburgh
30.
David Singmaster
–
David Breyer Singmaster is a retired professor of mathematics at London South Bank University, England, UK. A self-described metagrobologist, he has a personal collection of mechanical puzzles. He is most famous for being an early adopter and enthusiastic promoter of the Rubiks Cube and his Notes on Rubiks Magic Cube which he began compiling in 1979 provided the first mathematical analysis of the Cube as well as providing one of the first published solutions. The book contained his cube notation which has become standard and he is both a puzzle historian and a composer of puzzles, and many of his puzzles have been published in newspapers and magazines. In combinatorial number theory, Singmasters conjecture states that there is a bound on the number of times a number other than 1 can appear in Pascals triangle. David Singmaster was a student at the California Institute of Technology in the late 1950s and he intended to be a chemist, then changed to physics. He only became interested in mathematics in his final year when he took some courses in algebra. In his last semester, his algebra teacher posed a question the teacher didnt know the answer to and Singmaster solved it and he gained his PhD at the University of California, Berkeley, in 1966. Singmaster moved to London in 1970, the Polytechnic of the South Bank had been created from a merger of institutions in 1970, and Singmaster became a lecturer in the department of Mathematical Sciences. Around 1972 he attended the Istituto di Matematica in Pisa for a year having won a research scholarship and he was promoted to a Readership at the South Bank polytechnic in September 1984. The polytechnic became London South Bank University in 1992, and Singmaster was the professor of mathematics at the School of Computing, Information Systems and he also became an honorary research fellow at University College London. Singmasters association with Rubiks Cubes dates from August 1978, when he saw a Cube at the International Congress of Mathematicians in Helsinki, some other mathematicians at the conference, including John Conway and Roger Penrose, already had one. Singmaster quickly acquired a Cube and was able to solve it by early September 1978 and he has said that it took him two weeks, on and off to find a general solution for the Cube. He devised his notation for recording moves in December 1978, in June 1979 he wrote one of the first articles about the Cube in The Observer newspaper. In October 1979 he self-published his Notes on the Magic Cube, the booklet contained his mathematical analysis of Rubiks Cube, allowing a solution to be constructed using basic group theory. In August 1980 he published an expanded 5th edition of the book retitled as Notes on Rubiks Magic Cube and it included the results of his correspondence with other cubologists, and included details on monotwists, U-flips, Cayley graphs, and wreath products. The book contained his own step by step solution for the Cube, if you managed to solve the Cube using his method then Singmaster suggested that you should, Scream HOORAY. Tell the orderlies that they can let you out now, the book also contained a catalogue of pretty patterns including his cube in a cube in a cube pattern which he had discovered himself and was very pleased with
David Singmaster
–
March 2006
31.
Euclid
–
Euclid, sometimes called Euclid of Alexandria to distinguish him from Euclides of Megara, was a Greek mathematician, often referred to as the father of geometry. He was active in Alexandria during the reign of Ptolemy I, in the Elements, Euclid deduced the principles of what is now called Euclidean geometry from a small set of axioms. Euclid also wrote works on perspective, conic sections, spherical geometry, number theory, Euclid is the anglicized version of the Greek name Εὐκλείδης, which means renowned, glorious. Very few original references to Euclid survive, so little is known about his life, the date, place and circumstances of both his birth and death are unknown and may only be estimated roughly relative to other people mentioned with him. He is rarely mentioned by name by other Greek mathematicians from Archimedes onward, the few historical references to Euclid were written centuries after he lived by Proclus c.450 AD and Pappus of Alexandria c.320 AD. Proclus introduces Euclid only briefly in his Commentary on the Elements, Proclus later retells a story that, when Ptolemy I asked if there was a shorter path to learning geometry than Euclids Elements, Euclid replied there is no royal road to geometry. This anecdote is questionable since it is similar to a story told about Menaechmus, a detailed biography of Euclid is given by Arabian authors, mentioning, for example, a birth town of Tyre. This biography is generally believed to be completely fictitious, however, this hypothesis is not well accepted by scholars and there is little evidence in its favor. The only reference that historians rely on of Euclid having written the Elements was from Proclus, although best known for its geometric results, the Elements also includes number theory. The geometrical system described in the Elements was long known simply as geometry, today, however, that system is often referred to as Euclidean geometry to distinguish it from other so-called non-Euclidean geometries that mathematicians discovered in the 19th century. In addition to the Elements, at least five works of Euclid have survived to the present day and they follow the same logical structure as Elements, with definitions and proved propositions. Data deals with the nature and implications of information in geometrical problems. On Divisions of Figures, which only partially in Arabic translation. It is similar to a first-century AD work by Heron of Alexandria, catoptrics, which concerns the mathematical theory of mirrors, particularly the images formed in plane and spherical concave mirrors. The attribution is held to be anachronistic however by J J OConnor, phaenomena, a treatise on spherical astronomy, survives in Greek, it is quite similar to On the Moving Sphere by Autolycus of Pitane, who flourished around 310 BC. Optics is the earliest surviving Greek treatise on perspective, in its definitions Euclid follows the Platonic tradition that vision is caused by discrete rays which emanate from the eye. One important definition is the fourth, Things seen under a greater angle appear greater, proposition 45 is interesting, proving that for any two unequal magnitudes, there is a point from which the two appear equal. Other works are attributed to Euclid, but have been lost
Euclid
–
Euclid by
Justus van Gent, 15th century
Euclid
–
One of the oldest surviving fragments of Euclid's Elements, found at
Oxyrhynchus and dated to circa AD 100 (
P. Oxy. 29). The diagram accompanies Book II, Proposition 5.
Euclid
–
Statue in honor of Euclid in the
Oxford University Museum of Natural History
32.
Architecture
–
Architecture is both the process and the product of planning, designing, and constructing buildings and other physical structures. Architectural works, in the form of buildings, are often perceived as cultural symbols. Historical civilizations are often identified with their surviving architectural achievements, Architecture can mean, A general term to describe buildings and other physical structures. The art and science of designing buildings and nonbuilding structures, the style of design and method of construction of buildings and other physical structures. A unifying or coherent form or structure Knowledge of art, science, technology, the design activity of the architect, from the macro-level to the micro-level. The practice of the architect, where architecture means offering or rendering services in connection with the design and construction of buildings. The earliest surviving work on the subject of architecture is De architectura. According to Vitruvius, a building should satisfy the three principles of firmitas, utilitas, venustas, commonly known by the original translation – firmness, commodity. An equivalent in modern English would be, Durability – a building should stand up robustly, utility – it should be suitable for the purposes for which it is used. Beauty – it should be aesthetically pleasing, according to Vitruvius, the architect should strive to fulfill each of these three attributes as well as possible. Leon Battista Alberti, who elaborates on the ideas of Vitruvius in his treatise, De Re Aedificatoria, saw beauty primarily as a matter of proportion, for Alberti, the rules of proportion were those that governed the idealised human figure, the Golden mean. The most important aspect of beauty was, therefore, an inherent part of an object, rather than something applied superficially, Gothic architecture, Pugin believed, was the only true Christian form of architecture. The 19th-century English art critic, John Ruskin, in his Seven Lamps of Architecture, Architecture was the art which so disposes and adorns the edifices raised by men. That the sight of them contributes to his health, power. For Ruskin, the aesthetic was of overriding significance and his work goes on to state that a building is not truly a work of architecture unless it is in some way adorned. For Ruskin, a well-constructed, well-proportioned, functional building needed string courses or rustication, but suddenly you touch my heart, you do me good. I am happy and I say, This is beautiful, le Corbusiers contemporary Ludwig Mies van der Rohe said Architecture starts when you carefully put two bricks together. The notable 19th-century architect of skyscrapers, Louis Sullivan, promoted an overriding precept to architectural design, function came to be seen as encompassing all criteria of the use, perception and enjoyment of a building, not only practical but also aesthetic, psychological and cultural
Architecture
–
Brunelleschi, in the building of the dome of
Florence Cathedral in the early 15th-century, not only transformed the building and the city, but also the role and status of the architect.
Architecture
–
Section of
Brunelleschi 's dome drawn by the architect
Cigoli (c. 1600)
Architecture
–
The
Parthenon,
Athens,
Greece, "the supreme example among architectural sites."
(Fletcher).
Architecture
–
The
Houses of Parliament, Westminster, master-planned by
Charles Barry, with interiors and details by A.W.N. Pugin
33.
Piero della Francesca
–
Piero della Francesca was an Italian painter of the Early Renaissance. As testified by Giorgio Vasari in his Lives of the Most Excellent Painters, Sculptors, nowadays Piero della Francesca is chiefly appreciated for his art. His painting is characterized by its humanism, its use of geometric forms. His most famous work is the cycle of frescoes The History of the True Cross in the church of San Francesco in the Tuscan town of Arezzo. He was most probably apprenticed to the local painter Antonio di Giovanni dAnghiari, because in documents about payments it is noted that he was working with Antonio in 1432 and May 1438. Besides, he took notice of the work of some of the Sienese artists active in San Sepolcro during his youth. In 1439 Piero received, together with Domenico Veneziano, payments for his work on frescoes for the church of SantEgidio in Florence, in Florence he must have met leading masters like Fra Angelico, Luca della Robbia, Donatello and Brunelleschi. The classicism of Masaccios frescoes and his figures in the Santa Maria del Carmine were for him an important source of inspiration. Dating of Pieros undocumented work is difficult because his style does not seem to have developed over the years, in 1442 he was listed as eligible for the City Council of San Sepolcro. Three years later, he received the commission for the Madonna della Misericordia altarpiece for the church of the Misericordia in Sansepolcro, in 1449 he executed several frescoes in the Castello Estense and the church of SantAndrea of Ferrara, also lost. His influence was strong in the later Ferrarese allegorical works of Cosimo Tura. Two years later he was in Rimini, working for the condottiero Sigismondo Pandolfo Malatesta, in this sojourn he executed in 1451 the famous fresco of St. Sigismund and Sigismondo Pandolfo Malatesta in the Tempio Malatestiano, as well as Sigismondos portrait. Thereafter Piero was active in Ancona, Pesaro and Bologna, in 1454 he signed a contract for the Polyptych of Saint Augustine in the church of SantAgostino in Sansepolcro. The central panel of this polyptic is lost and the four panels of the wings, a few years later, summoned by Pope Nicholas V, he moved to Rome, here he executed frescoes in the Basilica di Santa Maria Maggiore, of which only fragments remain. Two years later he was again in the Papal capital, for frescoes in Vatican Palace which have also been destroyed, the Baptism of Christ, in The National Gallery in London, was executed around 1460 for the high altar of the church of the Priory of S. Other notable works of Piero della Francescas maturity are the frescoes of the Resurrection of Christ in Sansepolcro, in 1452, Piero della Francesca was called to Arezzo to replace Bicci di Lorenzo in painting the frescoes of the basilica of San Francesco. The work was finished before 1466, probably between 1452 and 1456, the cycle of frescoes, depicting the Legend of the True Cross, is generally considered among his masterworks and those of Renaissance painting in general. The story in these frescoes derives from medieval sources as to how timber relics of the True Cross came to be found
Piero della Francesca
–
A self-portrait, detail from
The Resurrection
Piero della Francesca
–
The
Baptism of Christ, (c. 1450) (
National Gallery, London).
Piero della Francesca
–
St. Sigismund and Sigismondo Pandolfo Malatesta (1451)
Piero della Francesca
–
Legend of the True Cross – the
Queen of Sheba meeting with
King Solomon.
34.
Marco Palmezzano
–
Marco Palmezzano was an Italian painter and architect, belonging to the Forlì painting school, who painted in a style recalling earlier Northern Renaissance models, and was mostly active near Forlì. Palmezzano was born and died in Forlì, Romagna and it is rumored that Palmezzano may have then traveled to Jerusalem to join the team painting frescoes at the Holy Cross church there, but no documentary evidence exists. He is, however, noted in property records as residing in Venice in 1495, among his pupils in Forlì, are listed Baldassarre Carrari il Giovane. Venetian painting, in general, and the work of Giovanni Bellini and Cima da Conegliano, moreover, he remained faithful to the Venetian style of the later 15th and early 16th century. Mannerism entirely passed him by, and he seemed immune to subsequent developments in Venetian painting, one of the most attractive facets of Palmezzanos oeuvre are the distinctive and suggestive landscapes that form the backdrops of many of his altarpieces. These are a blend of the ideal and lyrical, and of the reality of the Apennine foothills. These landscapes are also employed to subtle and imaginative effect to convey the symbolic religious messages of the works, crucifixion in the Pinacoteca Civica of Forlì.2006,1237, p. 294-295
Marco Palmezzano
–
Marco Palmezzano, self-portrait
Marco Palmezzano
–
Saint Sebastian, (Museum of Fine Arts, Budapest)
Marco Palmezzano
–
Crucifixion, (Uffizi,
Florence)
35.
Metropolitan Museum of Art
–
The Metropolitan Museum of Art, colloquially the Met, is located in New York City and is the largest art museum in the United States, and is among the most visited art museums in the world. Its permanent collection contains two million works, divided among seventeen curatorial departments. The main building, on the edge of Central Park along Manhattans Museum Mile, is by area one of the worlds largest art galleries. A much smaller second location, The Cloisters at Fort Tryon Park in Upper Manhattan, contains a collection of art, architecture. On March 18,2016, the museum opened the Met Breuer museum at Madison Avenue in the Upper East Side, it extends the museums modern, the Met maintains extensive holdings of African, Asian, Oceanian, Byzantine, Indian, and Islamic art. The museum is home to collections of musical instruments, costumes and accessories, as well as antique weapons. Several notable interiors, ranging from first-century Rome through modern American design, are installed in its galleries, the Metropolitan Museum of Art was founded in 1870. The founders included businessmen and financiers, as well as leading artists and thinkers of the day and it opened on February 20,1872, and was originally located at 681 Fifth Avenue. The Met maintains extensive holdings of African, Asian, Oceanian, Byzantine, the museum is also home to encyclopedic collections of musical instruments, costumes and accessories, and antique weapons and armor from around the world. A number of interiors, ranging from 1st century Rome through modern American design, are permanently installed in the Mets galleries. In addition to its permanent exhibitions, the Met organizes and hosts traveling shows throughout the year. The director of the museum is Thomas P. Campbell, a long-time curator and it was announced on February 28th,2017 that Campbell will be stepping down as the Mets director and CEO, effective June. On March 1st,2017 the BBC reported that Daniel Weiss shall be the acting CEO until a replacement is found, Beginning in the late 19th century, the Met started to acquire ancient art and artifacts from the Near East. From a few tablets and seals, the Mets collection of Near Eastern art has grown to more than 7,000 pieces. The highlights of the include a set of monumental stone lamassu, or guardian figures. The Mets Department of Arms and Armor is one of the museums most popular collections. Among the collections 14,000 objects are many pieces made for and used by kings and princes, including armor belonging to Henry VIII of England, Henry II of France, Rockefeller donated his more than 3, 000-piece collection to the museum. The Mets Asian department holds a collection of Asian art, of more than 35,000 pieces, the collection dates back almost to the founding of the museum, many of the philanthropists who made the earliest gifts to the museum included Asian art in their collections
Metropolitan Museum of Art
–
The Metropolitan Museum of Art
Metropolitan Museum of Art
Metropolitan Museum of Art
–
The facade of the Met dominates the city's "
Museum Mile ".
Metropolitan Museum of Art
–
The Great Hall
36.
Giorgio Vasari
–
Vasari was born in Arezzo, Tuscany. Recommended at an age by his cousin Luca Signorelli, he became a pupil of Guglielmo da Marsiglia. He was befriended by Michelangelo whose painting style would influence his own, in 1529, he visited Rome where he studied the works of Raphael and other artists of the Roman High Renaissance. Vasaris own Mannerist paintings were admired in his lifetime than afterwards. In 1547 he completed the hall of the chancery in Palazzo della Cancelleria in Rome with frescoes that received the name Sala dei Cento Giorni and he was consistently employed by members of the Medici family in Florence and Rome, and worked in Naples, Arezzo and other places. He also helped to organize the decoration of the Studiolo, now reassembled in the Palazzo Vecchio, aside from his career as a painter, Vasari was also successful as an architect. In Florence, Vasari also built the long passage, now called Vasari Corridor, the enclosed corridor passes alongside the River Arno on an arcade, crosses the Ponte Vecchio and winds around the exterior of several buildings. He also renovated the medieval churches of Santa Maria Novella and Santa Croce, at both he removed the original rood screen and loft, and remodelled the retro-choirs in the Mannerist taste of his time. In Santa Croce, he was responsible for the painting of The Adoration of the Magi which was commissioned by Pope Pius V in 1566 and it was recently restored, before being put on exhibition in 2011 in Rome and in Naples. Eventually it is planned to return it to the church of Santa Croce in Bosco Marengo, in 1562 Vasari built the octagonal dome on the Basilica of Our Lady of Humility in Pistoia, an important example of high Renaissance architecture. In Rome, Vasari worked with Giacomo Barozzi da Vignola and Bartolomeo Ammanati at Pope Julius IIIs Villa Giulia, the Lives also included a novel treatise on the technical methods employed in the arts. The book was rewritten and enlarged in 1568, with the addition of woodcut portraits of artists. The work has a consistent and notorious bias in favour of Florentines, and tends to attribute to them all the developments in Renaissance art – for example, Venetian art in particular, is systematically ignored in the first edition. Between the first and second editions, Vasari visited Venice and while the edition gave more attention to Venetian art. Vasaris biographies are interspersed with amusing gossip, with a few exceptions, however, Vasaris aesthetic judgement was acute and unbiased. He did not research archives for exact dates, as art historians do, and naturally his biographies are most dependable for the painters of his own generation. Modern criticism – with new materials opened up by research – has corrected many of his traditional dates and attributions. Vasari includes a sketch of his own biography at the end of the Lives, according to the historian Richard Goldthwaite, Vasari was one of the earliest authors to use the term competition in its economic sense
Giorgio Vasari
–
Vasari's self-portrait
Giorgio Vasari
–
Giorgio Vasari, Italian humanists, Tuscan Poets: Dante, Petrarch, Guido Cavalcanti, Boccaccio, Cino da Pistoia and Guittone d'Arezzo
Giorgio Vasari
–
Giorgio Vasari, The Garden of Gethsemane
Giorgio Vasari
–
The Uffizi Loggia.
37.
Chess
–
Chess is a two-player strategy board game played on a chessboard, a checkered gameboard with 64 squares arranged in an eight-by-eight grid. Chess is played by millions of people worldwide, both amateurs and professionals, each player begins the game with 16 pieces, one king, one queen, two rooks, two knights, two bishops, and eight pawns. Each of the six piece types moves differently, with the most powerful being the queen, the objective is to checkmate the opponents king by placing it under an inescapable threat of capture. To this end, a players pieces are used to attack and capture the opponents pieces, in addition to checkmate, the game can be won by voluntary resignation by the opponent, which typically occurs when too much material is lost, or if checkmate appears unavoidable. A game may result in a draw in several ways. Chess is believed to have originated in India, some time before the 7th century, chaturanga is also the likely ancestor of the Eastern strategy games xiangqi, janggi and shogi. The pieces took on their current powers in Spain in the late 15th century, the first generally recognized World Chess Champion, Wilhelm Steinitz, claimed his title in 1886. Since 1948, the World Championship has been controlled by FIDE, the international governing body. There is also a Correspondence Chess World Championship and a World Computer Chess Championship, online chess has opened amateur and professional competition to a wide and varied group of players. There are also many variants, with different rules, different pieces. FIDE awards titles to skilled players, the highest of which is grandmaster, many national chess organizations also have a title system. However, these are not recognised by FIDE, the term master may refer to a formal title or may be used more loosely for any skilled player. Until recently, chess was a sport of the International Olympic Committee. Chess was included in the 2006 and 2010 Asian Games, since the 1990s, computer analysis has contributed significantly to chess theory, particularly in the endgame. The computer IBM Deep Blue was the first machine to overcome a reigning World Chess Champion in a match when it defeated Garry Kasparov in 1997, the rise of strong computer programs that can be run on hand-held devices has led to increasing concerns about cheating during tournaments. The official rules of chess are maintained by FIDE, chesss international governing body, along with information on official chess tournaments, the rules are described in the FIDE Handbook, Laws of Chess section. Chess is played on a board of eight rows and eight columns. The colors of the 64 squares alternate and are referred to as light, the chessboard is placed with a light square at the right-hand end of the rank nearest to each player
Chess
–
Part of a
Staunton chess set (from left to right): a white
king, a black
rook, a black
queen, a white
pawn, a black
knight, and a white
bishop
Chess
–
Setup at the start of a game
Chess
–
A modern digital chess clock
Chess
–
Knights Templar playing chess,
Libro de los juegos, 1283
38.
De ludo scachorum
–
De ludo scachorum, also known as Schifanoia, is a Latin-language manuscript on the game of chess written around 1500 by Luca Pacioli, a leading mathematician of the Renaissance. The manuscript was discovered in 2006 by book historian Duilio Contin, in the 22, 000-volume library of the Palazzo Coronini Cronberg in Gorizia, the owner, Count Guglielmo Coronini, bought it alongside other old books from an unnamed Venetian poet and bibliophile in 1963. In addition, pawn promotion became more dangerous, since getting an additional queen now had bigger impact on the game and it is plausible that Leonardo da Vinci had a hand in the representation of the chess pieces. Pacioli and Leonardo were friends, and Leonardo is known to have provided illustrations for Paciolis book De divina proportione. De ludo scacchorum was created somewhere after 1499, when they fled from Milan to Mantua, where they were protected by the chess-loving Isabella dEste. It is plausible that Leonardo may have created the designs featured at the beginning. The design of the queen is similar to the form of a fountain drawn by the artist in his Codex Atlanticus. Furthermore, the pieces were drawn using both left and right hands, and Leonardo is known to have been left-handed, the proportions of the pieces follow the principle of the golden ratio, a phenomenon which fascinated both the polymaths. It was unclear whether the position was supposed to be played using the old or the new rules, furthermore, the diagram included a white pawn on the first rank, an illegal position. Keene surmised that the problem should be solved using modern rules, while the pawn should be replaced with a white knight, as it was most likely drawn mistakenly. Keene considers the author a genius, because of how he was able to quickly develop a deep understanding of the way the new rules will change chess. He also believes that it is possible Leonardo created some of the problems in the manuscript, 15th century in literature 2006 in chess 2008 in chess Latin literature List of manuscripts Rocco, Franco. Leonardo & Luca Pacioli – the Evidence, virtual book of facsimile edition About De Ludo Scachorum at leonardochess. com Luca Pacioli - De Ludo Scachorum - Review of Chess Puzzles on YouTube
De ludo scachorum
–
Portrait of the author
39.
Manuscript
–
A manuscript is any document written by hand or typewritten, as opposed to being mechanically printed or reproduced in some automated way. More recently, it is understood to be a written, typed, or word-processed copy of a work. Before the arrival of printing, all documents and books were manuscripts, manuscripts are not defined by their contents, which may combine writing with mathematical calculations, maps, explanatory figures or illustrations. Manuscripts may be in form, scrolls or in codex format. Illuminated manuscripts are enriched with pictures, border decorations, elaborately embossed initial letters or full-page illustrations. The traditional abbreviations are MS for manuscript and MSS for manuscripts, while the forms MS. ms or ms. for singular, and MSS. mss or mss. for plural are also accepted. The second s is not simply the plural, by an old convention, it doubles the last letter of the abbreviation to express the plural, just as pp. means pages. Before the invention of printing in China or by moveable type in a printing press in Europe. Historically, manuscripts were produced in form of scrolls or books, manuscripts were produced on vellum and other parchment, on papyrus, and on paper. In Russia birch bark documents as old as from the 11th century have survived, in India, the palm leaf manuscript, with a distinctive long rectangular shape, was used from ancient times until the 19th century. Paper spread from China via the Islamic world to Europe by the 14th century, when Greek or Latin works were published, numerous professional copies were made simultaneously by scribes in a scriptorium, each making a single copy from an original that was declaimed aloud. Manuscripts in Tocharian languages, written on leaves, survived in desert burials in the Tarim Basin of Central Asia. Volcanic ash preserved some of the Roman library of the Villa of the Papyri in Herculaneum, ironically, the manuscripts that were being most carefully preserved in the libraries of antiquity are virtually all lost. Originally, all books were in manuscript form, in China, and later other parts of East Asia, woodblock printing was used for books from about the 7th century. The earliest dated example is the Diamond Sutra of 868, in the Islamic world and the West, all books were in manuscript until the introduction of movable type printing in about 1450. Manuscript copying of books continued for a least a century, as printing remained expensive, private or government documents remained hand-written until the invention of the typewriter in the late 19th century. In the Philippines, for example, as early as 900AD, specimen documents were not inscribed by stylus and this type of document was rare compared to the usual leaves and bamboo staves that were inscribed. However, neither the leaves nor paper were as durable as the document in the hot
Manuscript
–
Christ Pantocrator seated in a capital "U" in an
illuminated manuscript from the Badische Landesbibliothek, Germany.
Manuscript
–
10th-century minuscule manuscript of
Thucydides 's
History of the Peloponnesian War
Manuscript
–
Armenian Manuscript
Manuscript
40.
Chess problem
–
A chess problem, also called a chess composition, is a puzzle set by somebody using chess pieces on a chess board, that presents the solver with a particular task to be achieved. For instance, a position might be given with the instruction that White is to move first, a person who creates such problems is known as a composer. There is a deal of specialized jargon used in connection with chess problems. The term chess problem is not sharply defined, there is no clear demarcation between chess compositions on the one hand and puzzles or tactical exercises on the other, in practice, however, the distinction is very clear. There are common characteristics shared by compositions in the section of chess magazines, in specialist chess problem magazines. There is a stipulation, that is, a goal to be achieved, for example. There is a theme that the problem has been composed to illustrate, the problem exhibits economy in its construction, no greater force is employed than that required to render the problem sound. Problems are experienced not only as puzzles but as objects of beauty and this is closely related to the fact that problems are organised to exhibit clear ideas in as economical a manner as possible. Problems can be contrasted with tactical puzzles often found in columns or magazines in which the task is to find the best move or sequence of moves from a given position. Such puzzles are often taken from games, or at least have positions which look as if they could have arisen during a game. Most such puzzles fail to exhibit the above features, there are various different types of chess problems, Directmates, White to move first and checkmate Black within a specified number of moves against any defence. These are often referred to as mate in n, where n is the number of moves within which mate must be delivered. In composing and solving competitions, directmates are further broken down into three classes, Two-movers, White to move and checkmate Black in two moves against any defence, three-movers, White to move and checkmate Black in no more than three moves against any defence. More-movers, White to move and checkmate Black in n moves against any defence, helpmates, Black to move first cooperates with White to get Blacks own king mated in a specified number of moves. Selfmates, White moves first and forces Black to checkmate White, helpselfmates, White to move first cooperates with Black to get a position of selfmate in one move. Reflexmates, a form of selfmate with the stipulation that each side must give mate if it is able to do so. Seriesmovers, one makes a series of moves without reply to achieve a stipulated aim. Check may not be given except on the last move, a seriesmover may take various forms, Seriesmate, a directmate with White playing a series of moves without reply to checkmate Black
Chess problem
41.
Della mercatura e del mercante perfetto
–
Della mercatura e del mercante perfetto written by Benedetto Cotrugli around 1400 was the first bookkeeping manuscript and trade manual. The title has been translated in English by the names of Of commerce and the perfect merchant, On merchantry and the perfect merchant, and On trade. It is widely thought that the reason why Luca Pacioli received credit as the father of accounting is because Cotruglis work was not officially published until 1573, an Italian version was published in Venice in 1573 by Franciscus Patricius. A French translation of this manuscript was published in Lyon in 1613 under the title Parfait négociant, an early copy of Della mercatura e del mercante perfetto from the end of the fifteenth century is at the National Library of Malta. Another early copy is at Biblioteca Marciana in Venice, the first is of the origin, form, and essence of being a merchant. The second talks of a religious commitment. The third is of moral virtues and policies, the fourth is administration of his home and family, and his economic matters. At the time of the merchandising was regarded as an art. The Perfect Merchant or Perfect Dealer was a man of culture motivated to moral conduct. He had to be sensitive to local interests in places where he conducted business. He had to know how to assess the situation and the customary laws in order to successfully conduct his business. He contrasted the Perfect Merchant to sailors and soldiers by saying that they were many times naive of these points. He said they were of such dull mind that when they would drink in a tavern, la partita doppia applicata alle scritture delle antiche aziende mercantili veneziane. Original from Columbia University Anzovin, Steven, hangers, Francis M. Historical-criticism on antichitla news, history and literature of Dubrovnik, divided into two volumes devoted Exalted and Senate of the Republic of Ragusa. Cotrugli, The Book of the Art of Trade, edited by Carlo Carraro and Giovanni Favero, translated in English by John Francis Phillimore, Palgrave Macmillan, Springer Nature,2017. Cotrugli, Libro de larte de la mercatura, critical edition of the original Italian manuscript by Vera Ribaudo, Cà Foscari University Press, Venice, Cotrugli B. Della mercatura e del mercante perfetto, libri quattro, Liber,1975 Cotrugli B. Il libero dellarte della mercatura edited by U
Della mercatura e del mercante perfetto
–
Della mercatura e del mercante perfetto
42.
The Guardian
–
The Guardian is a British daily newspaper, known from 1821 until 1959 as the Manchester Guardian. Along with its sister papers The Observer and The Guardian Weekly, The Guardian is part of the Guardian Media Group, the Scott Trust became a limited company in 2008, with a constitution to maintain the same protections for The Guardian. Profits are reinvested in journalism rather than to the benefit of an owner or shareholders, the Guardian is edited by Katharine Viner, who succeeded Alan Rusbridger in 2015. In 2016, The Guardians print edition had a daily circulation of roughly 162,000 copies in the country, behind The Daily Telegraph. The newspaper has an online UK edition as well as two international websites, Guardian Australia and Guardian US, the newspapers online edition was the fifth most widely read in the world in October 2014, with over 42.6 million readers. Its combined print and online editions reach nearly 9 million British readers, notable scoops include the 2011 News International phone hacking scandal, in particular the hacking of murdered English teenager Milly Dowlers phone. The investigation led to the closure of the UKs biggest selling Sunday newspaper, and one of the highest circulation newspapers in the world, in 2016, it led the investigation into the Panama Papers, exposing the then British Prime Minister David Camerons links to offshore bank accounts. The Guardian has been named Newspaper of the Year four times at the annual British Press Awards, the paper is still occasionally referred to by its nickname of The Grauniad, given originally for the purported frequency of its typographical errors. The Manchester Guardian was founded in Manchester in 1821 by cotton merchant John Edward Taylor with backing from the Little Circle and they launched their paper after the police closure of the more radical Manchester Observer, a paper that had championed the cause of the Peterloo Massacre protesters. They do not toil, neither do they spin, but they better than those that do. When the government closed down the Manchester Observer, the champions had the upper hand. The influential journalist Jeremiah Garnett joined Taylor during the establishment of the paper, the prospectus announcing the new publication proclaimed that it would zealously enforce the principles of civil and religious Liberty. Warmly advocate the cause of Reform, endeavour to assist in the diffusion of just principles of Political Economy and. Support, without reference to the party from which they emanate, in 1825 the paper merged with the British Volunteer and was known as The Manchester Guardian and British Volunteer until 1828. The working-class Manchester and Salford Advertiser called the Manchester Guardian the foul prostitute, the Manchester Guardian was generally hostile to labours claims. The Manchester Guardian dismissed strikes as the work of outside agitators –, if an accommodation can be effected, the occupation of the agents of the Union is gone. CP Scott made the newspaper nationally recognised and he was editor for 57 years from 1872, and became its owner when he bought the paper from the estate of Taylors son in 1907. Under Scott, the moderate editorial line became more radical, supporting William Gladstone when the Liberals split in 1886
The Guardian
–
The Guardian front page on 6 June 2014
The Guardian
–
The Guardian senior news writer Esther Addley interviewing Ecuadorian Foreign Minister
Ricardo Patiño for this article relating to
Julian Assange (August 2014)
The Guardian
–
The Guardian's HQ in
London
The Guardian
–
The Guardian' s Newsroom visitor centre and archive (No 60), with an old sign with the name The Manchester Guardian
43.
Catholic Encyclopedia
–
The first volume appeared in March 1907 and the last three volumes appeared in 1912, followed by a master index volume in 1914 and later supplementary volumes. It was designed to give its readers full and authoritative information on the cycle of Catholic interests, action. The Catholic Encyclopedia was published by the Robert Appleton Company, a company incorporated at New York in February 1905 for the express purpose of publishing the encyclopedia. The five members of the encyclopedias Editorial Board also served as the directors of the company, in 1912 the companys name was changed to The Encyclopedia Press. Publication of the volumes was the sole business conducted by the company during the projects lifetime. The encyclopedia was designed to serve the Roman Catholic Church, concentrating on information related to the Church and it records the accomplishments of Catholics and others in nearly all intellectual and professional pursuits, including artists, educators, poets and scientists. The volumes came out sequentially the first two in 1907 and the last three in 1912, The editors had their first editorial meeting at the office of The Messenger, on West 16th Street, New York City. The text received a nihil obstat from an official censor, Remy Lafort, on November 1,1908 and this review process was presumably accelerated by the reuse of older authorized publications. A first supplement was published in 1922, a supplement in nine loose-leaf sections was published by The Gilmary Society between 1950 and 1958. In 1912, a special completely illustrated commemorative volume was awarded to patrons who contributed to the start of the enterprise by buying multiple encyclopedia sets early on. The encyclopedia was later updated under the auspices of The Catholic University of America and a 17-volume New Catholic Encyclopedia was first published in 1967, and then in 2002. The Catholic Encyclopedia and its makers states that, The work is entirely new, the editors have insisted that the articles should contain the latest and most accurate information to be obtained from the standard works on each subject. Those who wrote new articles in English include Anthony Maas and Herbert Thurston, under United States copyright law, all works published in the United States before 1923 are in the public domain. Knight founded the website New Advent to house the undertaking, volunteers from the United States, Canada, France, and Brazil helped in the transcription of the original material. The site went online in 1995, and transcription work ended in 1997, in 2007, Catholic Answers published a watermarked version derived from page scans. This version has since replaced with a transcription of the Encyclopedia similar to that found at the New Advent website. The Catholic Answers transcription, however, is a transcription of the original text, whereas the New Advent version at times modernizes certain words. Other scanned copies of the 1913 Encyclopedia are available on Google Books, at the Internet Archive, wikisource also hosts a transcription project backed by the scans hosted at Commons
Catholic Encyclopedia
–
Cover page of 1913 Catholic Encyclopedia, Volume 1.
44.
International Standard Book Number
–
The International Standard Book Number is a unique numeric commercial book identifier. An ISBN is assigned to each edition and variation of a book, for example, an e-book, a paperback and a hardcover edition of the same book would each have a different ISBN. The ISBN is 13 digits long if assigned on or after 1 January 2007, the method of assigning an ISBN is nation-based and varies from country to country, often depending on how large the publishing industry is within a country. The initial ISBN configuration of recognition was generated in 1967 based upon the 9-digit Standard Book Numbering created in 1966, the 10-digit ISBN format was developed by the International Organization for Standardization and was published in 1970 as international standard ISO2108. Occasionally, a book may appear without a printed ISBN if it is printed privately or the author does not follow the usual ISBN procedure, however, this can be rectified later. Another identifier, the International Standard Serial Number, identifies periodical publications such as magazines, the ISBN configuration of recognition was generated in 1967 in the United Kingdom by David Whitaker and in 1968 in the US by Emery Koltay. The 10-digit ISBN format was developed by the International Organization for Standardization and was published in 1970 as international standard ISO2108, the United Kingdom continued to use the 9-digit SBN code until 1974. The ISO on-line facility only refers back to 1978, an SBN may be converted to an ISBN by prefixing the digit 0. For example, the edition of Mr. J. G. Reeder Returns, published by Hodder in 1965, has SBN340013818 -340 indicating the publisher,01381 their serial number. This can be converted to ISBN 0-340-01381-8, the check digit does not need to be re-calculated, since 1 January 2007, ISBNs have contained 13 digits, a format that is compatible with Bookland European Article Number EAN-13s. An ISBN is assigned to each edition and variation of a book, for example, an ebook, a paperback, and a hardcover edition of the same book would each have a different ISBN. The ISBN is 13 digits long if assigned on or after 1 January 2007, a 13-digit ISBN can be separated into its parts, and when this is done it is customary to separate the parts with hyphens or spaces. Separating the parts of a 10-digit ISBN is also done with either hyphens or spaces, figuring out how to correctly separate a given ISBN number is complicated, because most of the parts do not use a fixed number of digits. ISBN issuance is country-specific, in that ISBNs are issued by the ISBN registration agency that is responsible for country or territory regardless of the publication language. Some ISBN registration agencies are based in national libraries or within ministries of culture, in other cases, the ISBN registration service is provided by organisations such as bibliographic data providers that are not government funded. In Canada, ISBNs are issued at no cost with the purpose of encouraging Canadian culture. In the United Kingdom, United States, and some countries, where the service is provided by non-government-funded organisations. Australia, ISBNs are issued by the library services agency Thorpe-Bowker
International Standard Book Number
–
A 13-digit ISBN, 978-3-16-148410-0, as represented by an
EAN-13 bar code
45.
Internet Archive
–
The Internet Archive is a San Francisco–based nonprofit digital library with the stated mission of universal access to all knowledge. As of October 2016, its collection topped 15 petabytes, in addition to its archiving function, the Archive is an activist organization, advocating for a free and open Internet. Its web archive, the Wayback Machine, contains over 150 billion web captures, the Archive also oversees one of the worlds largest book digitization projects. Founded by Brewster Kahle in May 1996, the Archive is a 501 nonprofit operating in the United States. It has a budget of $10 million, derived from a variety of sources, revenue from its Web crawling services, various partnerships, grants, donations. Its headquarters are in San Francisco, California, where about 30 of its 200 employees work, Most of its staff work in its book-scanning centers. The Archive has data centers in three Californian cities, San Francisco, Redwood City, and Richmond, the Archive is a member of the International Internet Preservation Consortium and was officially designated as a library by the State of California in 2007. Brewster Kahle founded the Archive in 1996 at around the time that he began the for-profit web crawling company Alexa Internet. In October 1996, the Internet Archive had begun to archive and preserve the World Wide Web in large quantities, the archived content wasnt available to the general public until 2001, when it developed the Wayback Machine. In late 1999, the Archive expanded its collections beyond the Web archive, Now the Internet Archive includes texts, audio, moving images, and software. It hosts a number of projects, the NASA Images Archive, the contract crawling service Archive-It. According to its web site, Most societies place importance on preserving artifacts of their culture, without such artifacts, civilization has no memory and no mechanism to learn from its successes and failures. Our culture now produces more and more artifacts in digital form, the Archives mission is to help preserve those artifacts and create an Internet library for researchers, historians, and scholars. In August 2012, the Archive announced that it has added BitTorrent to its file download options for over 1.3 million existing files, on November 6,2013, the Internet Archives headquarters in San Franciscos Richmond District caught fire, destroying equipment and damaging some nearby apartments. The nonprofit Archive sought donations to cover the estimated $600,000 in damage, in November 2016, Kahle announced that the Internet Archive was building the Internet Archive of Canada, a copy of the archive to be based somewhere in the country of Canada. The announcement received widespread coverage due to the implication that the decision to build an archive in a foreign country was because of the upcoming presidency of Donald Trump. Kahle was quoted as saying that on November 9th in America and it was a firm reminder that institutions like ours, built for the long-term, need to design for change. For us, it means keeping our cultural materials safe, private and it means preparing for a Web that may face greater restrictions
Internet Archive
–
Since 2009, headquarters have been at 300 Funston Avenue in
San Francisco, a former
Christian Science Church
Internet Archive
–
Internet Archive
Internet Archive
–
Mirror of the Internet Archive in the
Bibliotheca Alexandrina
Internet Archive
–
From 1996 to 2009, headquarters were in the
Presidio of San Francisco, a former U.S. military base
46.
Katholieke Universiteit Leuven
–
The Katholieke Universiteit Leuven, also known as KU Leuven or University of Leuven, is a Dutch-speaking university in Leuven, Flanders, Belgium. The University of Leuven was founded at the centre of the town of Leuven in 1425. Since the fifteenth century, Louvain, as it is often called by French speaking Belgians, has been a major contributor to the development of Catholic theology. It is considered the oldest Catholic university still in existence, with 55,484 students in 2014–2015, the KU Leuven is the largest university in Belgium and the Low Countries. In addition to its campus in Leuven, it has satellite campuses in Kortrijk, Antwerp, Ghent, Bruges, Ostend, Geel, Diepenbeek, Aalst, Sint-Katelijne-Waver. The university now offers several programs in English. KU Leuven is consistently considered to be within the top 100 universities of the world, the KU Leuven is a strongly research-oriented university. Among its many accolades is to be reckoned among the top universities of Europe and its current 2015-2016 QS World University Ranking position is 82nd. KU Leuven Institute of Philosophy current ranks 24th in the world, in 2016, KU Leuven was ranked first on the Reuters list of Europes most innovative universities. KU Leuven Law School currently ranks 26th in the world, most courses, however, are taught in Dutch. The KU Leuven is a member of the Coimbra Group as well as of the LERU Group, since August 2013, the university has been led by Rik Torfs who replaced former rector Mark Waer. The Belgian archbishop, André-Joseph Léonard is the current Grand Chancellor, the KU Leuven is dedicated to Mary, the mother of Jesus, under her traditional attribute as Seat of Wisdom, and organizes an annual celebration on 2 February in her honour. On that day, the university awards its honorary doctorates. The seal used by the university shows the statue of the Sedes Sapientiae, Leuven. Despite its Catholic origin, the university students from different faith communities. For the history of the university see Catholic University of Leuven. Pieter De Somer became the first rector of the KU Leuven, in 1972, the KU Leuven set up a separate entity, Leuven Research & Development, to support industrial and commercial applications of university research. It has led to numerous spin-offs, such as the technology company Metris, on 11 July 2002, the KU Leuven became the dominant institution in the KU Leuven Association
Katholieke Universiteit Leuven
–
Inner view of the Adrian VI College
Katholieke Universiteit Leuven
–
KU Leuven Universiteit Leuven
Katholieke Universiteit Leuven
–
Kasteel van Arenberg, part of the Katholieke Universiteit Leuven.
Katholieke Universiteit Leuven
–
The University Library
47.
Virtual International Authority File
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The Virtual International Authority File is an international authority file. It is a joint project of national libraries and operated by the Online Computer Library Center. The project was initiated by the US Library of Congress, the German National Library, the National Library of France joined the project on October 5,2007. The project transitions to a service of the OCLC on April 4,2012, the aim is to link the national authority files to a single virtual authority file. In this file, identical records from the different data sets are linked together, a VIAF record receives a standard data number, contains the primary see and see also records from the original records, and refers to the original authority records. The data are available online and are available for research and data exchange. Reciprocal updating uses the Open Archives Initiative Protocol for Metadata Harvesting protocol, the file numbers are also being added to Wikipedia biographical articles and are incorporated into Wikidata. VIAFs clustering algorithm is run every month, as more data are added from participating libraries, clusters of authority records may coalesce or split, leading to some fluctuation in the VIAF identifier of certain authority records
Virtual International Authority File
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Screenshot 2012
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Integrated Authority File
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The Integrated Authority File or GND is an international authority file for the organisation of personal names, subject headings and corporate bodies from catalogues. It is used mainly for documentation in libraries and increasingly also by archives, the GND is managed by the German National Library in cooperation with various regional library networks in German-speaking Europe and other partners. The GND falls under the Creative Commons Zero license, the GND specification provides a hierarchy of high-level entities and sub-classes, useful in library classification, and an approach to unambiguous identification of single elements. It also comprises an ontology intended for knowledge representation in the semantic web, available in the RDF format
Integrated Authority File
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GND screenshot
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Union List of Artist Names
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The Union List of Artist Names is an online database using a controlled vocabulary currently containing around 293,000 names and other information about artists. Names in ULAN may include names, pseudonyms, variant spellings, names in multiple languages. Among these names, one is flagged as the preferred name, the focus of each ULAN record is an artist. Currently there are around 120,000 artists in the ULAN, in the database, each artist record is identified by a unique numeric ID. Linked to each artist record are names, related artists, sources for the data, the temporal coverage of the ULAN ranges from Antiquity to the present and the scope is global. The ULAN includes proper names and associated information about artists, artists may be either individuals or groups of individuals working together. Artists in the ULAN generally represent creators involved in the conception or production of visual arts, repositories and some donors are included as well. Work on the ULAN began in 1984, when the Getty decided to merge, in 1987 the Getty created a department dedicated to compiling and distributing terminology. The ULAN grows and changes via contributions from the user community, although originally intended only for use by Getty projects, the broader art information community outside the Getty expressed a need to use ULAN for cataloging and retrieval. Its scope was broadened to include corporate bodies such as firms and repositories of art. The ULAN was founded under the management of Eleanor Fink, the ULAN has been constructed over the years by numerous members of the user community and an army of dedicated editors, under the supervision of several managers. The ULAN was published in 1994 in hardcopy and machine-readable files, given the growing size and frequency of changes and additions to the ULAN, by 1997 it had become evident that hard-copy publication was impractical. It is now published in automated formats only, in both a searchable online Web interface and in data files available for licensing, final editorial control of the ULAN is maintained by the Getty Vocabulary Program, using well-established editorial rules. The current managers of the ULAN are Patricia Harpring, Managing Editor, entities in the Person facet typically have no children. Entities in the Corporate Body facet may branch into trees, there may be multiple broader contexts, making the ULAN structure polyhierarchical. In addition to the relationships, the ULAN also has equivalent. Contributors to the Getty Vocabularies and implementers of the licensed vocabulary data may consult these guidelines as well
Union List of Artist Names
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Contents
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National Diet Library
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The National Diet Library is the only national library in Japan. It was established in 1948 for the purpose of assisting members of the National Diet of Japan in researching matters of public policy, the library is similar in purpose and scope to the United States Library of Congress. The National Diet Library consists of two facilities in Tokyo and Kyoto, and several other branch libraries throughout Japan. The Diets power in prewar Japan was limited, and its need for information was correspondingly small, the original Diet libraries never developed either the collections or the services which might have made them vital adjuncts of genuinely responsible legislative activity. Until Japans defeat, moreover, the executive had controlled all political documents, depriving the people and the Diet of access to vital information. The U. S. occupation forces under General Douglas MacArthur deemed reform of the Diet library system to be an important part of the democratization of Japan after its defeat in World War II. In 1946, each house of the Diet formed its own National Diet Library Standing Committee, hani Gorō, a Marxist historian who had been imprisoned during the war for thought crimes and had been elected to the House of Councillors after the war, spearheaded the reform efforts. Hani envisioned the new body as both a citadel of popular sovereignty, and the means of realizing a peaceful revolution, the National Diet Library opened in June 1948 in the present-day State Guest-House with an initial collection of 100,000 volumes. The first Librarian of the Diet Library was the politician Tokujirō Kanamori, the philosopher Masakazu Nakai served as the first Vice Librarian. In 1949, the NDL merged with the National Library and became the national library in Japan. At this time the collection gained a million volumes previously housed in the former National Library in Ueno. In 1961, the NDL opened at its present location in Nagatachō, in 1986, the NDLs Annex was completed to accommodate a combined total of 12 million books and periodicals. The Kansai-kan, which opened in October 2002 in the Kansai Science City, has a collection of 6 million items, in May 2002, the NDL opened a new branch, the International Library of Childrens Literature, in the former building of the Imperial Library in Ueno. This branch contains some 400,000 items of literature from around the world. Though the NDLs original mandate was to be a library for the National Diet. In the fiscal year ending March 2004, for example, the library reported more than 250,000 reference inquiries, in contrast, as Japans national library, the NDL collects copies of all publications published in Japan. The NDL has an extensive collection of some 30 million pages of documents relating to the Occupation of Japan after World War II. This collection include the documents prepared by General Headquarters and the Supreme Commander of the Allied Powers, the Far Eastern Commission, the NDL maintains a collection of some 530,000 books and booklets and 2 million microform titles relating to the sciences
National Diet Library
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Tokyo Main Library of the National Diet Library
National Diet Library
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Kansai-kan of the National Diet Library
National Diet Library
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The National Diet Library
National Diet Library
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Main building in Tokyo
