1.
Milan
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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
2.
Mathematics
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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
3.
University of Bologna
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The University of Bologna, founded in 1088, is the oldest university in continuous operation. It was the first place of study to use the term universitas for the corporations of students and masters which came to define the institution, located in Bologna, as of 2013, the Universitys crest carries the motto Alma mater studiorum and the date A. D.1088. The University has about 85,500 students in its 11 schools and it has campuses in Ravenna, Forlì, Cesena and Rimini and a branch center abroad in Buenos Aires. It also has a school of excellence named Collegio Superiore di Bologna, an associate publisher of the University of Bologna is Bononia University Press S. p. A. The date of its founding is uncertain, but believed by most accounts to have been 1088 and these students then hired scholars from the city to teach them. In time the various nations decided to form an association, or universitas—thus. The foreign students in Bologna received greater rights, and collective punishment was ended, there was also collective bargaining with the scholars who served as professors at the university. By the initiation or threat of a student strike, the students could enforce their demands as to the content of courses, the professors could also be fined if they failed to finish classes on time, or complete course material by the end of the semester. A student committee, the Denouncers of Professors, kept tabs on them, Professors themselves were not powerless, however, forming a College of Teachers, and securing the rights to set examination fees and degree requirements. Eventually, the city ended this arrangement, paying professors from tax revenues, until modern times, the only degree granted at that university was the doctorate. Higher education processes are being harmonised across the European Community, nowadays the University offers 101 different Laurea or Laurea breve first-level degrees, followed by 108 Laurea specialistica or Laurea magistrale second-level degrees. After the Laurea one may attain 1st level Master, after second-level degrees are attained, one may proceed to 2nd level Master, specialisation schools, or doctorates of research. A new department of Latin History was added in 2015, on 25 April 1951 the first issue of the review was published in Bologna. In a short time, il Mulino became one of the most interesting points in Italy for the political and cultural debate. Editorial activities evolved along with the review, in 1954, the il Mulino publishing house was founded, which today represents one of the most relevant Italian publishers. In addition to this were initiated research projects, that led, in 1964. In the 2016-17 THE World University Rankings the University of Bologna was ranked in the worlds top 250 universities
4.
Italians
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Italians are a nation and ethnic group native to Italy who share a common culture, ancestry and speak the Italian language as a native tongue. The majority of Italian nationals are speakers of Standard Italian. Italians have greatly influenced and contributed to the arts and music, science, technology, cuisine, sports, fashion, jurisprudence, banking, Italian people are generally known for their localism and their attention to clothing and family values. The term Italian is at least 3,000 years old and has a history that goes back to pre-Roman Italy. According to one of the common explanations, the term Italia, from Latin, Italia, was borrowed through Greek from the Oscan Víteliú. 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 Etruscan civilization reached its peak about the 7th century BC, but by 509 BC, when the Romans overthrew their Etruscan monarchs, its control in Italy was on the wane. By 350 BC, after a series of wars between Greeks and Etruscans, the Latins, with Rome as their capital, gained the ascendancy by 272 BC, and they managed to unite the entire Italian peninsula. This period of unification was followed by one of conquest in the Mediterranean, in the course of the century-long struggle against Carthage, the Romans conquered Sicily, Sardinia and Corsica. Finally, in 146 BC, at the conclusion of the Third Punic War, with Carthage completely destroyed and its inhabitants enslaved, octavian, the final victor, was accorded the title of Augustus by the Senate and thereby became the first Roman emperor. After two centuries of rule, in the 3rd century AD, Rome was threatened by internal discord and menaced by Germanic and Asian invaders. Emperor Diocletians administrative division of the empire into two parts in 285 provided only temporary relief, it became permanent in 395, in 313, Emperor Constantine accepted Christianity, and churches thereafter rose throughout the empire. However, he moved his capital from Rome to Constantinople. The last Western emperor, Romulus Augustulus, was deposed in 476 by a Germanic foederati general in Italy and his defeat marked the end of the western part of the Roman Empire. During most of the period from the fall of Rome until the Kingdom of Italy was established in 1861, Odoacer ruled well for 13 years after gaining control of Italy in 476. Then he was attacked and defeated by Theodoric, the king of another Germanic tribe, Theodoric and Odoacer ruled jointly until 493, when Theodoric murdered Odoacer. Theodoric continued to rule Italy with an army of Ostrogoths and a government that was mostly Italian, after the death of Theodoric in 526, the kingdom began to grow weak
5.
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
6.
Philosopher
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A philosopher is someone who practices philosophy, which involves rational inquiry into areas that are outside of either theology or science. The term philosopher comes from the Ancient Greek φιλόσοφος meaning lover of wisdom, the coining of the term has been attributed to the Greek thinker Pythagoras. Typically, these brands of philosophy are Hellenistic ones and those who most arduously commit themselves to this lifestyle may be considered philosophers. The separation of philosophy and science from theology began in Greece during the 6th century BC, thales, an astronomer and mathematician, was considered by Aristotle to be the first philosopher of the Greek tradition. While Pythagoras coined the word, the first known elaboration on the topic was conducted by Plato, in his Symposium, he concludes that Love is that which lacks the object it seeks. Therefore, the philosopher is one who seeks wisdom, if he attains wisdom, therefore, the philosopher in antiquity was one who lives in the constant pursuit of wisdom, and living in accordance to that wisdom. Disagreements arose as to what living philosophically entailed and these disagreements gave rise to different Hellenistic schools of philosophy. In consequence, the ancient philosopher thought in a tradition, as the ancient world became schism by philosophical debate, the competition lay in living in manner that would transform his whole way of living in the world. Philosophy is a discipline which can easily carry away the individual in analyzing the universe. The second is the change through the Medieval era. With the rise of Christianity, the way of life was adopted by its theology. Thus, philosophy was divided between a way of life and the conceptual, logical, physical and metaphysical materials to justify that way of life, philosophy was then the servant to theology. The third is the sociological need with the development of the university, the modern university requires professionals to teach. Maintaining itself requires teaching future professionals to replace the current faculty, therefore, the discipline degrades into a technical language reserved for specialists, completely eschewing its original conception as a way of life. In the fourth century, the word began to designate a man or woman who led a monastic life. Gregory of Nyssa, for example, describes how his sister Macrina persuaded their mother to forsake the distractions of life for a life of philosophy. Later during the Middle Ages, persons who engaged with alchemy was called a philosopher - thus, many philosophers still emerged from the Classical tradition, as saw their philosophy as a way of life. Among the most notable are René Descartes, Baruch Spinoza, Nicolas Malebranche, with the rise of the university, the modern conception of philosophy became more prominent
7.
Theology
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Theology is the critical study of the nature of the divine. It is taught as a discipline, typically in universities, seminaries. Augustine of Hippo defined the Latin equivalent, theologia, as reasoning or discussion concerning the Deity, the term can, however, be used for a variety of different disciplines or fields of study. Theologians use various forms of analysis and argument to help understand, explain, test, critique, the English equivalent theology had evolved by 1362. Greek theologia was used with the discourse on god in the fourth century BC by Plato in The Republic, Book ii. Drawing on Greek Stoic sources, the Latin writer Varro distinguished three forms of discourse, mythical, rational and civil. Theologos, closely related to theologia, appears once in some manuscripts, in the heading to the book of Revelation, apokalypsis ioannoy toy theologoy. The Latin author Boethius, writing in the early 6th century, used theologia to denote a subdivision of philosophy as a subject of study, dealing with the motionless. Boethius definition influenced medieval Latin usage, Theology can also now be used in a derived sense to mean a system of theoretical principles, an ideology. They suggest the term is appropriate in religious contexts that are organized differently. Kalam. does not hold the place in Muslim thought that theology does in Christianity. To find an equivalent for theology in the Christian sense it is necessary to have recourse to several disciplines, and to the usul al-fiqh as much as to kalam. Jose Ignacio Cabezon, who argues that the use of theology is appropriate, can only do so, he says, I take theology not to be restricted to its etymological meaning. In that latter sense, Buddhism is of course atheological, rejecting as it does the notion of God, within Hindu philosophy, there is a solid and ancient tradition of philosophical speculation on the nature of the universe, of God and of the Atman. The Sanskrit word for the schools of Hindu philosophy is Darshana. Nevertheless, Jewish theology historically has been active and highly significant for Christian. It is sometimes claimed, however, that the Jewish analogue of Christian theological discussion would more properly be Rabbinical discussion of Jewish law, the history of the study of theology in institutions of higher education is as old as the history of such institutions themselves. Modern Western universities evolved from the institutions and cathedral schools of Western Europe during the High Middle Ages
8.
Humanitarianism
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Humanitarianism is a moral of kindness, benevolence, and sympathy extended to all human beings. Humanitarianism has been an evolving concept historically, but universality is a theme in its evolution. No distinction is to be made on the grounds of gender, sexual orientation, race, caste, age, religion, ability, the historian G. M. Trevelyan viewed humanitarianism as the product of rationalism upon Puritanism. The idea that mankind could be improved by deliberate social change distinct from the conferring of charity was relatively new, reform distinguished the humanitarian movement from philanthropy. Christian philanthropy tended to reform as political. In contrast, the movement thought reform essential to remove abuses. European individualism can be traced to the Greeks and it was the stoics, who like Aristotle, attributed significance to the human soul, but who, unlike Aristotle, considered all human beings equal in that significance. Natural law, as the stoics conceived it, was based upon this principle of spiritual equality, positive law was subject to the law of nature and, hence, uniquely to the ancient world, the stoics opposed slavery. In 18th century Enlightenment Europe, the idea of the equal moral significance of the individual in this world re-emerged grounded upon reason. Prevention of cruelty to animals involved extension of the principle to non-humans, the stoics had grounded moral significance on capacity to reason. In the 18th century, conflicting religious belief became tolerated to a degree unthinkable a century earlier, in England, pressure on Parliament led to regulation of working hours and amelioration of working conditions. An international dimension was added to humanitarian reform with the founding of the International Red Cross, finally, cruelty to animals became punishable. In contrast, social action in the 19th century was influenced by feeling and, in some instances. The initiative remained with small groups of reformers, which set about influencing public opinion, one reason for the change was the advent of democracy - limited though it was until well into the 19th century. The industrial proletariat crowding into cities made it feasible to hold mass meetings, Political pamphlets had first circulated in England during the civil war. In fiction, novels like Uncle Toms Cabin and those of Charles Dickens drew attention to social wrongs and this led to a change in approach which became less philosophical and more emotive, fastening on the inhumanity to which social action was directed. In 1503, the Spanish Governor in the Indies, Nicolás de Ovando, las Casas, who accompanied him, observed the toll of the work, and suggested the Indians be replaced by Negroes, thus beginning the transatlantic slave trade. Some 900,000 slaves were landed in the Americas by 1600, from the 17th century, demand for African labour expanded greatly with the increased importation of sugar into Europe
9.
Differential calculus
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In mathematics, differential calculus is a subfield of calculus concerned with the study of the rates at which quantities change. It is one of the two divisions of calculus, the other being integral calculus. The primary objects of study in differential calculus are the derivative of a function, related notions such as the differential, the derivative of a function at a chosen input value describes the rate of change of the function near that input value. The process of finding a derivative is called differentiation, geometrically, the derivative at a point is the slope of the tangent line to the graph of the function at that point, provided that the derivative exists and is defined at that point. For a real-valued function of a real variable, the derivative of a function at a point generally determines the best linear approximation to the function at that point. Differential calculus and integral calculus are connected by the theorem of calculus. Differentiation has applications to nearly all quantitative disciplines, for example, in physics, the derivative of the displacement of a moving body with respect to time is the velocity of the body, and the derivative of velocity with respect to time is acceleration. The derivative of the momentum of a body equals the applied to the body. The reaction rate of a reaction is a derivative. In operations research, derivatives determine the most efficient ways to transport materials, derivatives are frequently used to find the maxima and minima of a function. Equations involving derivatives are called differential equations and are fundamental in describing natural phenomena, derivatives and their generalizations appear in many fields of mathematics, such as complex analysis, functional analysis, differential geometry, measure theory, and abstract algebra. Suppose that x and y are real numbers and that y is a function of x and this relationship can be written as y = f. If f is the equation for a line, then there are two real numbers m and b such that y = mx + b. In this slope-intercept form, the m is called the slope and can be determined from the formula, m = change in y change in x = Δ y Δ x. It follows that Δy = m Δx, a general function is not a line, so it does not have a slope. Geometrically, the derivative of f at the point x = a is the slope of the tangent line to the function f at the point a and this is often denoted f ′ in Lagranges notation or dy/dx|x = a in Leibnizs notation. Since the derivative is the slope of the approximation to f at the point a. If every point a in the domain of f has a derivative, for example, if f = x2, then the derivative function f ′ = dy/dx = 2x
10.
Integral
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In mathematics, an integral assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data. Integration is one of the two operations of calculus, with its inverse, differentiation, being the other. The area above the x-axis adds to the total and that below the x-axis subtracts from the total, roughly speaking, the operation of integration is the reverse of differentiation. For this reason, the integral may also refer to the related notion of the antiderivative. In this case, it is called an integral and is written. The integrals discussed in this article are those termed definite integrals, a rigorous mathematical definition of the integral was given by Bernhard Riemann. It is based on a procedure which approximates the area of a curvilinear region by breaking the region into thin vertical slabs. A line integral is defined for functions of two or three variables, and the interval of integration is replaced by a curve connecting two points on the plane or in the space. In a surface integral, the curve is replaced by a piece of a surface in the three-dimensional space and this method was further developed and employed by Archimedes in the 3rd century BC and used to calculate areas for parabolas and an approximation to the area of a circle. A similar method was developed in China around the 3rd century AD by Liu Hui. This method was used in the 5th century by Chinese father-and-son mathematicians Zu Chongzhi. The next significant advances in integral calculus did not begin to appear until the 17th century, further steps were made in the early 17th century by Barrow and Torricelli, who provided the first hints of a connection between integration and differentiation. Barrow provided the first proof of the theorem of calculus. Wallis generalized Cavalieris method, computing integrals of x to a power, including negative powers. The major advance in integration came in the 17th century with the independent discovery of the theorem of calculus by Newton. The theorem demonstrates a connection between integration and differentiation and this connection, combined with the comparative ease of differentiation, can be exploited to calculate integrals. In particular, the theorem of calculus allows one to solve a much broader class of problems. Equal in importance is the mathematical framework that both Newton and Leibniz developed
11.
Charity (practice)
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The practice of charity means the voluntary giving of help to those in need, as a humanitarian act. The word charity entered the English language through the Old French word charité, originally in Latin the word caritas meant preciousness, dearness, high price. From this, in Christian theology, caritas became the standard Latin translation for the Greek word agape, however, the English word more generally used for this concept, both before and since, is the more direct love. D. While the methods of giving may vary, there are three kinds of charity, pure, public, and foreign. Public charity is charity that benefits the whole rather than the individual, foreign charity is when the beneficiary lives in a country different from where the funds or services are being sent from. Charitable giving is the act of giving money, goods or time to the unfortunate, Charitable giving as a religious act or duty is referred to as almsgiving or alms. The name stems from the most obvious expression of the virtue of charity, the impoverished, particularly those widowed or orphaned, and the ailing or injured, are generally regarded as the proper recipients of charity. The people who support themselves and lack outside means of support sometimes become beggars. Some groups regard charity as being distributed towards other members from within their particular group, donations to causes that benefit the unfortunate indirectly, such as donations to fund cancer research, are also charity. With regards to religious aspects, the recipient of charity may offer to pray for the benefactor, in medieval Europe, it was customary to feast the poor at the funeral in return for their prayers for the deceased. Institutions may commemorate benefactors by displaying their names, up to naming buildings or even the institution itself after the benefactors, if the recipient makes material return of more than a token value, the transaction is normally not called charity. In the past century, many organizations have created a charitable model in which donators give to conglomerates give to recipients. Examples of this include the Make a Wish Foundation and the World Wildlife Fund, today some charities have modernized, and allow people to donate online, through websites such as JustGiving. Originally charity entailed the benefactor directly giving the goods to the receiver and this practice was continued by some individuals, for example, CNN Hero Sal Dimiceli, and service organizations, such as the Jaycees. With the rise of more social peer-to-peer processes, many charities are moving away from the charitable model, examples of this include Global Giving, DonorsChoose, PureCharity, Kiva and Zidisha. Institutions evolved to carry out the labor of assisting the poor, and these include orphanages, food banks, religious institutes dedicated to care of the poor, hospitals, organizations that visit the homebound and imprisoned, and many others. Institutions can also attempt to more effectively sort out the needy from those who fraudulently claim charity. Early Christians particularly recommended the care of the unfortunate to the charge of the local bishop, there have been examinations of who gives more to charity
12.
Clavicembalo
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A harpsichord is a musical instrument played by means of a keyboard. It produces sound by plucking a string when a key is pressed, Harpsichord designates the whole family of similar plucked keyboard instruments, including the smaller virginals, muselar, and spinet. The harpsichord was used in Renaissance and Baroque music. During the late 18th century, it disappeared from the musical scene with the rise of the piano. In the 20th century, it made a resurgence, being used in historically informed performances of music, in compositions. Harpsichords vary in size and shape, but all have the basic functional arrangement. The player depresses a key that rocks over a pivot in the middle of its length, the other end of the key lifts a jack that holds a small plectrum, which plucks the string. When the player releases the key, the far end returns to its rest position, the plectrum, mounted on a tongue that can swivel backwards away from the string, passes the string without plucking it again. As the key reaches its rest position, a felt damper atop the jack stops the strings vibrations and these basic principles are explained in detail below. The keylever is a pivot, which rocks on a balance pin that passes through a hole drilled through the keylever. The jack is a thin, rectangular piece of wood that sits upright on the end of the keylever, the jacks are held in place by the registers. These are two strips of wood, which run in the gap between pinblock and bellyrail. The registers have rectangular mortises through which the pass as they can move up. The registers hold the jacks in the location needed to pluck the string. In the jack, a plectrum juts out almost horizontally and passes just under the string, historically, plectra were made of bird quill or leather, many modern harpsichords have plastic plectra. When the front of the key is pressed, the back of the key rises, the jack is lifted, the vertical motion of the jack is then stopped by the jackrail, which is covered with soft felt to muffle the impact. When the key is released, the falls back down under its own weight. This is made possible by having the plectrum held in a tongue attached with a pivot and a spring to the body of the jack
13.
Composer
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A composer is a person who creates or writes music, which can be vocal music, instrumental music or music which combines both instruments and voices. The core meaning of the term refers to individuals who have contributed to the tradition of Western classical music through creation of works expressed in written musical notation, many composers are also skilled performers, either as singers, instrumentalists, and/or conductors. Examples of composers who are well known for their ability as performers include J. S. Bach, Mozart. In many popular genres, such as rock and country. For a singer or instrumental performer, the process of deciding how to perform music that has previously composed and notated is termed interpretation. Different performers interpretations of the work of music can vary widely, in terms of the tempos that are chosen. Composers and songwriters who present their own music are interpreting, just as much as those who perform the music of others, although a musical composition often has a single author, this is not always the case. A piece of music can also be composed with words, images, or, in the 20th and 21st century, a culture eventually developed whereby faithfulness to the composers written intention came to be highly valued. This musical culture is almost certainly related to the esteem in which the leading classical composers are often held by performers. The movement might be considered a way of creating greater faithfulness to the original in works composed at a time that expected performers to improvise. In Classical music, the composer typically orchestrates her own compositions, in some cases, a pop songwriter may not use notation at all, and instead compose the song in her mind and then play or record it from memory. In jazz and popular music, notable recordings by influential performers are given the weight that written scores play in classical music. The level of distinction between composers and other musicians varies, which issues such as copyright and the deference given to individual interpretations of a particular piece of music. In the development of European classical music, the function of composing music initially did not have greater importance than that of performing it. The preservation of individual compositions did not receive attention and musicians generally had no qualms about modifying compositions for performance. In as much as the role of the composer in western art music has seen continued solidification, for instance, in certain contexts the line between composer and performer, sound designer, arranger, producer, and other roles, can be quite blurred. The term composer is often used to refer to composers of music, such as those found in classical, jazz or other forms of art. In popular and folk music, the composer is usually called a songwriter and this is distinct from a 19th-century conception of instrumental composition, where the work was represented solely by a musical score to be interpreted by performers
14.
Brivius de Brokles
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The Brivio de Brokles were an Hungarian and Italian noble family, supposed to be a branch of the more famous Brivio family from Milan. Founder of the family was Pietro Brivio, who moved at the end of the 15th Century from Milan to Montevecchia, according to some historians, he was supposed to belong to the Brivio family of Milan, which was said to descend from the Brunonen family. The family rose to significant influence in Brianza at the end of the 17th century, when a member of this family, Francesco, became very rich with silk trading. At the beginning of the 18th century his son, Giacomo, financed the War of the Spanish Succession and Joseph I, Brokles was a small county in the Kingdom of Hungary, but nowadays it is located in Serbia. Thanks to his richness, Count Giacomo Brivio lent money to many people of his time. In 1710 he was fideiussor of Cosimo III de Medici, Grand Duke of Tuscany, in 1713 Giacomo became Lord of Montevecchia, the village of his ancestors, and in 1716 famous composer Antonio Vivaldi dedicated him a dramma per musica, Arsilda, regina di Ponto. Giacomo Brivio had two notable sons, Francesco married Elena Attendolo Bolognini, member of an important noble family from Milan and descendant from Pope Pius IV and Gian Giacomo Medici. The marriage was of very important for the Brivio family. Carlo was Lieutenant Colonel in the Austrian Army from 1709 and his only daughter, Anna, married an Irish nobleman called David Griffith. Another notable member of family was Giuseppe Ferdinando Brivio, who was a famous composer. Finally, Anna Fortunata Brivio married Pietro Agnesi and was mother of the famous mathematician Maria Gaetana Agnesi, sironi, Monte delle Vedette in Brianza Felice Calvi, Famiglie Notabili Milanesi
15.
Child prodigy
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In psychology research literature, the term child prodigy is defined as a person under the age of ten who produces meaningful output in some domain to the level of an adult expert performer. Child prodigies are rare, and, in domains, there are no child prodigies at all. Prodigiousness in childhood does not always predict adult eminence, the term Wunderkind is sometimes used as a synonym for prodigy, particularly in media accounts. Wunderkind also is used to recognize those who achieve success and acclaim early in their adult careers, PET scans performed on several mathematics prodigies have suggested that they think in terms of long-term working memory. This memory, specific to a field of expertise, is capable of holding relevant information for extended periods, the PET scans also answer questions about which specific areas of the brain associate themselves with manipulating numbers. One subject never excelled as a child in mathematics, but he taught himself algorithms and tricks for calculatory speed and his brain, compared to six other controls, was studied using the PET scan, revealing separate areas of his brain that he manipulated to solve the complex problems. Some of the areas that he and presumably prodigies use are brain sectors dealing in visual and spatial memory, as well as visual mental imagery. Other areas of the brain showed use by the subject, including a sector of the brain related to childlike finger counting. Citing extensive imaging evidence, Vandervert first proposed this approach in two publications appeared in 2003. In addition to imaging evidence, Vanderverts approach is supported by the award winning studies of the cerebellum by Masao Ito. Some researchers believe that prodigious talent tends to arise as a result of the talent of the child. Others believe that the environment plays the dominant role, many times in obvious ways, but on the other hand George Frideric Handel was an example of the natural talent. He had discovered such a strong propensity to music, that his father who intended him for the study of the Civil Law, had reason to be alarmed. He strictly forbade him to meddle with any musical instrument but Handel found means to get a little clavichord privately conveyd to a room at the top of the house, to this room he constantly stole when the family was asleep. Despite his fathers opposition, Handel became a performer on the harpsichord. Chess prodigy List of child prodigies List of music prodigies Gifted education Giftedness Late bloomer Malleable intelligence Polymath Savant syndrome Ellenberg, the Wrong Way to Treat Child Geniuses. How working memory and the cerebellum collaborate to produce creativity and innovation, the Gradual Path to Creative Breakthroughs. Notebook, Child Prodigies, CBS News Online, YouTube, February 26,2010
16.
Italian language
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By most measures, Italian, together with Sardinian, is the closest to Latin of the Romance languages. Italian is a language in Italy, Switzerland, San Marino, Vatican City. Italian is spoken by minorities in places such as France, Montenegro, Bosnia & Herzegovina, Crimea and Tunisia and by large expatriate communities in the Americas. Many speakers are native bilinguals of both standardized Italian and other regional languages, Italian is the fourth most studied language in the world. Italian is a major European language, being one of the languages of the Organisation for Security and Cooperation in Europe. It is the third most widely spoken first language in the European Union with 65 million native speakers, including Italian speakers in non-EU European countries and on other continents, the total number of speakers is around 85 million. Italian is the working language of the Holy See, serving as the lingua franca in the Roman Catholic hierarchy as well as the official language of the Sovereign Military Order of Malta. Italian is known as the language of music because of its use in musical terminology and its influence is also widespread in the arts and in the luxury goods market. Italian has been reported as the fourth or fifth most frequently taught foreign language in the world, Italian was adopted by the state after the Unification of Italy, having previously been a literary language based on Tuscan as spoken mostly by the upper class of Florentine society. Its development was influenced by other Italian languages and to some minor extent. Its vowels are the second-closest to Latin after Sardinian, unlike most other Romance languages, Italian retains Latins contrast between short and long consonants. As in most Romance languages, stress is distinctive, however, Italian as a language used in Italy and some surrounding regions has a longer history. What would come to be thought of as Italian was first formalized in the early 14th century through the works of Tuscan writer Dante Alighieri, written in his native Florentine. Dante is still credited with standardizing the Italian language, and thus the dialect of Florence became the basis for what would become the language of Italy. Italian was also one of the recognised languages in the Austro-Hungarian Empire. Italy has always had a dialect for each city, because the cities. Those dialects now have considerable variety, as Tuscan-derived Italian came to be used throughout Italy, features of local speech were naturally adopted, producing various versions of Regional Italian. Even in the case of Northern Italian languages, however, scholars are not to overstate the effects of outsiders on the natural indigenous developments of the languages
17.
French language
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French is a Romance language of the Indo-European family. It descended from the Vulgar Latin of the Roman Empire, as did all Romance languages, French has evolved from Gallo-Romance, the spoken Latin in Gaul, and more specifically in Northern Gaul. Its closest relatives are the other langues doïl—languages historically spoken in northern France and in southern Belgium, French was also influenced by native Celtic languages of Northern Roman Gaul like Gallia Belgica and by the Frankish language of the post-Roman Frankish invaders. Today, owing to Frances past overseas expansion, there are numerous French-based creole languages, a French-speaking person or nation may be referred to as Francophone in both English and French. French is a language in 29 countries, most of which are members of la francophonie. As of 2015, 40% of the population is in Europe, 35% in sub-Saharan Africa, 15% in North Africa and the Middle East, 8% in the Americas. French is the fourth-most widely spoken mother tongue in the European Union, 1/5 of Europeans who do not have French as a mother tongue speak French as a second language. As a result of French and Belgian colonialism from the 17th and 18th century onward, French was introduced to new territories in the Americas, Africa, most second-language speakers reside in Francophone Africa, in particular Gabon, Algeria, Mauritius, Senegal and Ivory Coast. In 2015, French was estimated to have 77 to 110 million native speakers, approximately 274 million people are able to speak the language. The Organisation internationale de la Francophonie estimates 700 million by 2050, in 2011, Bloomberg Businessweek ranked French the third most useful language for business, after English and Standard Mandarin Chinese. Under the Constitution of France, French has been the language of the Republic since 1992. France mandates the use of French in official government publications, public education except in specific cases, French is one of the four official languages of Switzerland and is spoken in the western part of Switzerland called Romandie, of which Geneva is the largest city. French is the language of about 23% of the Swiss population. French is also a language of Luxembourg, Monaco, and Aosta Valley, while French dialects remain spoken by minorities on the Channel Islands. A plurality of the worlds French-speaking population lives in Africa and this number does not include the people living in non-Francophone African countries who have learned French as a foreign language. Due to the rise of French in Africa, the total French-speaking population worldwide is expected to reach 700 million people in 2050, French is the fastest growing language on the continent. French is mostly a language in Africa, but it has become a first language in some urban areas, such as the region of Abidjan, Ivory Coast and in Libreville. There is not a single African French, but multiple forms that diverged through contact with various indigenous African languages, sub-Saharan Africa is the region where the French language is most likely to expand, because of the expansion of education and rapid population growth
18.
Greek language
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Greek is an independent branch of the Indo-European family of languages, native to Greece and other parts of the Eastern Mediterranean. It has the longest documented history of any living language, spanning 34 centuries of written records and its writing system has been the Greek alphabet for the major part of its history, other systems, such as Linear B and the Cypriot syllabary, were used previously. The alphabet arose from the Phoenician script and was in turn the basis of the Latin, Cyrillic, Armenian, Coptic, Gothic and many other writing systems. Together with the Latin texts and traditions of the Roman world, during antiquity, Greek was a widely spoken lingua franca in the Mediterranean world and many places beyond. It would eventually become the official parlance of the Byzantine Empire, the language is spoken by at least 13.2 million people today in Greece, Cyprus, Italy, Albania, Turkey, and the Greek diaspora. Greek roots are used to coin new words for other languages, Greek. Greek has been spoken in the Balkan peninsula since around the 3rd millennium BC, the earliest written evidence is a Linear B clay tablet found in Messenia that dates to between 1450 and 1350 BC, making Greek the worlds oldest recorded living language. Among the Indo-European languages, its date of earliest written attestation is matched only by the now extinct Anatolian languages, the Greek language is conventionally divided into the following periods, Proto-Greek, the unrecorded but assumed last ancestor of all known varieties of Greek. The unity of Proto-Greek would have ended as Hellenic migrants entered the Greek peninsula sometime in the Neolithic era or the Bronze Age, Mycenaean Greek, the language of the Mycenaean civilisation. It is recorded in the Linear B script on tablets dating from the 15th century BC onwards, Ancient Greek, in its various dialects, the language of the Archaic and Classical periods of the ancient Greek civilisation. It was widely known throughout the Roman Empire, after the Roman conquest of Greece, an unofficial bilingualism of Greek and Latin was established in the city of Rome and Koine Greek became a first or second language in the Roman Empire. The origin of Christianity can also be traced through Koine Greek, Medieval Greek, also known as Byzantine Greek, the continuation of Koine Greek in Byzantine Greece, up to the demise of the Byzantine Empire in the 15th century. Much of the written Greek that was used as the language of the Byzantine Empire was an eclectic middle-ground variety based on the tradition of written Koine. Modern Greek, Stemming from Medieval Greek, Modern Greek usages can be traced in the Byzantine period and it is the language used by the modern Greeks, and, apart from Standard Modern Greek, there are several dialects of it. In the modern era, the Greek language entered a state of diglossia, the historical unity and continuing identity between the various stages of the Greek language is often emphasised. Greek speakers today still tend to regard literary works of ancient Greek as part of their own rather than a foreign language and it is also often stated that the historical changes have been relatively slight compared with some other languages. According to one estimation, Homeric Greek is probably closer to demotic than 12-century Middle English is to modern spoken English, Greek is spoken by about 13 million people, mainly in Greece, Albania and Cyprus, but also worldwide by the large Greek diaspora. Greek is the language of Greece, where it is spoken by almost the entire population
19.
Hebrew
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Hebrew is a language native to Israel, spoken by over 9 million people worldwide, of whom over 5 million are in Israel. Historically, it is regarded as the language of the Israelites and their ancestors, the earliest examples of written Paleo-Hebrew date from the 10th century BCE. Hebrew belongs to the West Semitic branch of the Afroasiatic language family, Hebrew is the only living Canaanite language left, and the only truly successful example of a revived dead language. Hebrew had ceased to be a spoken language somewhere between 200 and 400 CE, declining since the aftermath of the Bar Kokhba revolt. Aramaic and to a lesser extent Greek were already in use as international languages, especially among elites and it survived into the medieval period as the language of Jewish liturgy, rabbinic literature, intra-Jewish commerce, and poetry. Then, in the 19th century, it was revived as a spoken and literary language, and, according to Ethnologue, had become, as of 1998, the language of 5 million people worldwide. After Israel, the United States has the second largest Hebrew-speaking population, with 220,000 fluent speakers, Modern Hebrew is one of the two official languages of the State of Israel, while premodern Hebrew is used for prayer or study in Jewish communities around the world today. Ancient Hebrew is also the tongue of the Samaritans, while modern Hebrew or Arabic is their vernacular. For this reason, Hebrew has been referred to by Jews as Leshon Hakodesh, the modern word Hebrew is derived from the word Ivri, one of several names for the Israelite people. It is traditionally understood to be a based on the name of Abrahams ancestor, Eber. This name is based upon the root ʕ-b-r meaning to cross over. Interpretations of the term ʕibrim link it to this verb, cross over, in the Bible, the Hebrew language is called Yәhudit because Judah was the surviving kingdom at the time of the quotation. In Isaiah 19,18 it is called the Language of Canaan, Hebrew belongs to the Canaanite group of languages. In turn, the Canaanite languages are a branch of the Northwest Semitic family of languages, according to Avraham ben-Yosef, Hebrew flourished as a spoken language in the Kingdoms of Israel and Judah during about 1200 to 586 BCE. Scholars debate the degree to which Hebrew was a vernacular in ancient times following the Babylonian exile. In July 2008 Israeli archaeologist Yossi Garfinkel discovered a ceramic shard at Khirbet Qeiyafa which he claimed may be the earliest Hebrew writing yet discovered, dating around 3000 years ago. The Gezer calendar also dates back to the 10th century BCE at the beginning of the Monarchic Period, classified as Archaic Biblical Hebrew, the calendar presents a list of seasons and related agricultural activities. The Gezer calendar is written in an old Semitic script, akin to the Phoenician one that through the Greeks, the Gezer calendar is written without any vowels, and it does not use consonants to imply vowels even in the places where later Hebrew spelling requires it
20.
Spanish language
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Spanish —also called Castilian —is a Romance language that originated in the Castile region of Spain, with hundreds of millions of native speakers around the world. It is usually considered the worlds second-most spoken native language after Mandarin Chinese and it is one of the few languages to use inverted question and exclamation marks. Spanish is a part of the Ibero-Romance group of languages, which evolved from several dialects of Vulgar Latin in Iberia after the collapse of the Western Roman Empire in the 5th century. Beginning in the early 16th century, Spanish was taken to the colonies of the Spanish Empire, most notably to the Americas, as well as territories in Africa, Oceania, around 75% of modern Spanish is derived from Latin. Greek has also contributed substantially to Spanish vocabulary, especially through Latin, Spanish vocabulary has been in contact from an early date with Arabic, having developed during the Al-Andalus era in the Iberian Peninsula. With around 8% of its vocabulary being Arabic in origin, this language is the second most important influence after Latin and it has also been influenced by Basque as well as by neighboring Ibero-Romance languages. It also adopted words from languages such as Gothic language from the Visigoths in which many Spanish names and surnames have a Visigothic origin. Spanish is one of the six languages of the United Nations. It is the language in the world by the number of people who speak it as a mother tongue, after Mandarin Chinese. It is estimated more than 437 million people speak Spanish as a native language. Spanish is the official or national language in Spain, Equatorial Guinea, speakers in the Americas total some 418 million. In the European Union, Spanish is the tongue of 8% of the population. Spanish is the most popular second language learned in the United States, in 2011 it was estimated by the American Community Survey that of the 55 million Hispanic United States residents who are five years of age and over,38 million speak Spanish at home. The Spanish Constitution of 1978 uses the term castellano to define the language of the whole Spanish State in contrast to las demás lenguas españolas. Article III reads as follows, El castellano es la lengua española oficial del Estado, las demás lenguas españolas serán también oficiales en las respectivas Comunidades Autónomas. Castilian is the official Spanish language of the State, the other Spanish languages as well shall be official in their respective Autonomous Communities. The Spanish Royal Academy, on the hand, currently uses the term español in its publications. Two etymologies for español have been suggested, the Spanish Royal Academy Dictionary derives the term from the Provençal word espaignol, and that in turn from the Medieval Latin word Hispaniolus, from—or pertaining to—Hispania
21.
German language
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German is a West Germanic language that is mainly spoken in Central Europe. It is the most widely spoken and official language in Germany, Austria, Switzerland, South Tyrol, the German-speaking Community of Belgium and it is also one of the three official languages of Luxembourg. Major languages which are most similar to German include other members of the West Germanic language branch, such as Afrikaans, Dutch, English, Luxembourgish and it is the second most widely spoken Germanic language, after English. One of the languages of the world, German is the first language of about 95 million people worldwide. The German speaking countries are ranked fifth in terms of publication of new books. German derives most of its vocabulary from the Germanic branch of the Indo-European language family, a portion of German words are derived from Latin and Greek, and fewer are borrowed from French and English. With slightly different standardized variants, German is a pluricentric language, like English, German is also notable for its broad spectrum of dialects, with many unique varieties existing in Europe and also other parts of the world. The history of the German language begins with the High German consonant shift during the migration period, when Martin Luther translated the Bible, he based his translation primarily on the standard bureaucratic language used in Saxony, also known as Meißner Deutsch. Copies of Luthers Bible featured a long list of glosses for each region that translated words which were unknown in the region into the regional dialect. Roman Catholics initially rejected Luthers translation, and tried to create their own Catholic standard of the German language – the difference in relation to Protestant German was minimal. It was not until the middle of the 18th century that a widely accepted standard was created, until about 1800, standard German was mainly a written language, in urban northern Germany, the local Low German dialects were spoken. Standard German, which was different, was often learned as a foreign language with uncertain pronunciation. Northern German pronunciation was considered the standard in prescriptive pronunciation guides though, however, German was the language of commerce and government in the Habsburg Empire, which encompassed a large area of Central and Eastern Europe. Until the mid-19th century, it was essentially the language of townspeople throughout most of the Empire and its use indicated that the speaker was a merchant or someone from an urban area, regardless of nationality. Some cities, such as Prague and Budapest, were gradually Germanized in the years after their incorporation into the Habsburg domain, others, such as Pozsony, were originally settled during the Habsburg period, and were primarily German at that time. Prague, Budapest and Bratislava as well as cities like Zagreb, the most comprehensive guide to the vocabulary of the German language is found within the Deutsches Wörterbuch. This dictionary was created by the Brothers Grimm and is composed of 16 parts which were issued between 1852 and 1860, in 1872, grammatical and orthographic rules first appeared in the Duden Handbook. In 1901, the 2nd Orthographical Conference ended with a standardization of the German language in its written form
22.
Latin
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Latin is a classical language belonging to the Italic branch of the Indo-European languages. The Latin alphabet is derived from the Etruscan and Greek alphabets, Latin was originally spoken in Latium, in the Italian Peninsula. Through the power of the Roman Republic, it became the dominant language, Vulgar Latin developed into the Romance languages, such as Italian, Portuguese, Spanish, French, and Romanian. Latin, Italian and French have contributed many words to the English language, Latin and Ancient Greek roots are used in theology, biology, and medicine. By the late Roman Republic, Old Latin had been standardised into Classical Latin, Vulgar Latin was the colloquial form spoken during the same time and attested in inscriptions and the works of comic playwrights like Plautus and Terence. Late Latin is the language from the 3rd century. Later, Early Modern Latin and Modern Latin evolved, Latin was used as the language of international communication, scholarship, and science until well into the 18th century, when it began to be supplanted by vernaculars. Ecclesiastical Latin remains the language of the Holy See and the Roman Rite of the Catholic Church. Today, many students, scholars and members of the Catholic clergy speak Latin fluently and it is taught in primary, secondary and postsecondary educational institutions around the world. The language has been passed down through various forms, some inscriptions have been published in an internationally agreed, monumental, multivolume series, the Corpus Inscriptionum Latinarum. Authors and publishers vary, but the format is about the same, volumes detailing inscriptions with a critical apparatus stating the provenance, the reading and interpretation of these inscriptions is the subject matter of the field of epigraphy. The works of several hundred ancient authors who wrote in Latin have survived in whole or in part and they are in part the subject matter of the field of classics. The Cat in the Hat, and a book of fairy tales, additional resources include phrasebooks and resources for rendering everyday phrases and concepts into Latin, such as Meissners Latin Phrasebook. The Latin influence in English has been significant at all stages of its insular development. From the 16th to the 18th centuries, English writers cobbled together huge numbers of new words from Latin and Greek words, dubbed inkhorn terms, as if they had spilled from a pot of ink. Many of these words were used once by the author and then forgotten, many of the most common polysyllabic English words are of Latin origin through the medium of Old French. Romance words make respectively 59%, 20% and 14% of English, German and those figures can rise dramatically when only non-compound and non-derived words are included. Accordingly, Romance words make roughly 35% of the vocabulary of Dutch, Roman engineering had the same effect on scientific terminology as a whole
23.
Ballistics
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A ballistic body is a body with momentum which is free to move, subject to forces, such as the pressure of gases in a gun or a propulsive nozzle, by rifling in a barrel, by gravity, or by air drag. The earliest known ballistic projectiles were stones and spears, and the throwing stick. The oldest evidence of stone-tipped projectiles, which may or may not have been propelled by a bow, dating to c.64,000 years ago, were found in Sibudu Cave, present day-South Africa. The oldest evidence of the use of bows to shoot arrows dates to about 10,000 years ago and they had shallow grooves on the base, indicating that they were shot from a bow. The oldest bow so far recovered is about 8,000 years old, archery seems to have arrived in the Americas with the Arctic small tool tradition, about 4,500 years ago. The first devices identified as guns appeared in China around 1000 AD, and by the 12th century the technology was spreading through the rest of Asia, the word ballistics comes from the Greek βάλλειν ballein, meaning to throw. A projectile is any object projected into space by the exertion of a force, although any object in motion through space is a projectile, the term most commonly refers to a ranged weapon. Mathematical equations of motion are used to analyze projectile trajectory, examples of projectiles include balls, arrows, bullets, artillery shells, rockets, etc. Throwing is the launching of a projectile by hand, although some other animals can throw, humans are unusually good throwers due to their high dexterity and good timing capabilities, and it is believed that this is an evolved trait. Evidence of human throwing dates back 2 million years, the 90 mph throwing speed found in many athletes far exceeds the speed at which chimpanzees can throw things, which is about 20 mph. This ability reflects the ability of the shoulder muscles and tendons to store elasticity until it is needed to propel an object. A sling is a projectile weapon used to throw a blunt projectile such as a stone. A sling has a cradle or pouch in the middle of two lengths of cord. The sling stone is placed in the pouch, the middle finger or thumb is placed through a loop on the end of one cord, and a tab at the end of the other cord is placed between the thumb and forefinger. The sling is swung in an arc, and the tab released at a precise moment and this frees the projectile to fly to the target. A bow is a piece of material which shoots aerodynamic projectiles called arrows. A string joins the two ends and when the string is drawn back, the ends of the stick are flexed, when the string is released, the potential energy of the flexed stick is transformed into the velocity of the arrow. Archery is the art or sport of shooting arrows from bows, a catapult is a device used to launch a projectile a great distance without the aid of explosive devices — particularly various types of ancient and medieval siege engines
24.
Geometry
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Geometry is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. A mathematician who works in the field of geometry is called a geometer, Geometry arose independently in a number of early cultures as a practical way for dealing with lengths, areas, and volumes. Geometry began to see elements of mathematical science emerging in the West as early as the 6th century BC. By the 3rd century BC, geometry was put into a form by Euclid, whose treatment, Euclids Elements. Geometry arose independently in India, with texts providing rules for geometric constructions appearing as early as the 3rd century BC, islamic scientists preserved Greek ideas and expanded on them during the Middle Ages. By the early 17th century, geometry had been put on a solid footing by mathematicians such as René Descartes. Since then, and into modern times, geometry has expanded into non-Euclidean geometry and manifolds, while geometry has evolved significantly throughout the years, there are some general concepts that are more or less fundamental to geometry. These include the concepts of points, lines, planes, surfaces, angles, contemporary geometry has many subfields, Euclidean geometry is geometry in its classical sense. The mandatory educational curriculum of the majority of nations includes the study of points, lines, planes, angles, triangles, congruence, similarity, solid figures, circles, Euclidean geometry also has applications in computer science, crystallography, and various branches of modern mathematics. Differential geometry uses techniques of calculus and linear algebra to problems in geometry. It has applications in physics, including in general relativity, topology is the field concerned with the properties of geometric objects that are unchanged by continuous mappings. In practice, this often means dealing with large-scale properties of spaces, convex geometry investigates convex shapes in the Euclidean space and its more abstract analogues, often using techniques of real analysis. It has close connections to convex analysis, optimization and functional analysis, algebraic geometry studies geometry through the use of multivariate polynomials and other algebraic techniques. It has applications in areas, including cryptography and string theory. Discrete geometry is concerned mainly with questions of relative position of simple objects, such as points. It shares many methods and principles with combinatorics, Geometry has applications to many fields, including art, architecture, physics, as well as to other branches of mathematics. The earliest recorded beginnings of geometry can be traced to ancient Mesopotamia, the earliest known texts on geometry are the Egyptian Rhind Papyrus and Moscow Papyrus, the Babylonian clay tablets such as Plimpton 322. For example, the Moscow Papyrus gives a formula for calculating the volume of a truncated pyramid, later clay tablets demonstrate that Babylonian astronomers implemented trapezoid procedures for computing Jupiters position and motion within time-velocity space
25.
Bologna
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Bologna is the largest city of the Emilia-Romagna Region in Northern Italy. It is the seventh most populous city in Italy, located in the heart of an area of about one million. The first settlements back to at least 1000 BC. The city has been a centre, first under the Etruscans. Home to the oldest university in the world, University of Bologna, founded in 1088, Bologna is also an important transportation crossroad for the roads and trains of Northern Italy, where many important mechanical, electronic and nutritional industries have their headquarters. According to the most recent data gathered by the European Regional Economic Growth Index of 2009, Bologna is the first Italian city, Bologna is home to numerous prestigious cultural, economic and political institutions as well as one of the most impressive trade fair districts in Europe. In 2000 it was declared European capital of culture and in 2006, the city of Bologna was selected to participate in the Universal Exposition of Shanghai 2010 together with 45 other cities from around the world. Bologna is also one of the wealthiest cities in Italy, often ranking as one of the top cities in terms of quality of life in the country, after a long decline, Bologna was reborn in the 5th century under Bishop Petronius. According to legend, St. Petronius built the church of S. Stefano. After the fall of Rome, Bologna was a stronghold of the Exarchate of Ravenna in the Po plain. In 728, the city was captured by the Lombard king Liutprand, the Germanic conquerors formed a district called addizione longobarda near the complex of S. Stefano. Charlemagne stayed in this district in 786, traditionally said to be founded in 1088, the University of Bologna is widely considered to be the first university. The university originated as a centre of study of medieval Roman law under major glossators. It numbered Dante, Boccaccio and Petrarca among its students, the medical school is especially famous. In the 12th century, the families engaged in continual internecine fighting. Troops of Pope Julius II besieged Bologna and sacked the artistic treasures of his palace, in 1530, in front of Saint Petronio Church, Charles V was crowned Holy Roman Emperor by Pope Clement VII. Then a plague at the end of the 16th century reduced the population from 72,000 to 59,000, the population later recovered to a stable 60, 000–65,000. However, there was also great progress during this era, in 1564, the Piazza del Nettuno and the Palazzo dei Banchi were built, along with the Archiginnasio, the centre of the University
26.
Charles de Brosses
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Charles de Brosses, comte de Tournay, baron de Montfalcon, seigneur de Vezins et de Prevessin, was a French writer of the 18th century. Because he opposed the power of the king, he was exiled twice. He wrote numerous papers on topics concerning ancient history, philology and linguistics, some of which were used by Denis Diderot. De Brosses published five books, Lettres sur létat actuel de la ville souterraine dHerculée et sur les causes de son ensevelissement sous les ruines du Vésuve and this contains a list of archeological discoveries from the excavation of Herculaneum, including some ancient inscriptions in the Oscan language. Histoire des navigations aux terres australes, contenant ce que lon sait des moeurs et des productions des contrées découvertes jusquà ce jour. It proved extremely useful to James Cook with respect to the discovery of Australia in 1770, and contains what may be the first occurrence of the words Polynésie and Australasie. It has been written that it is this book which convinced the French explorer Louis-Antoine de Bougainville, then a soldier in Canada, to become a sailor and, in his own terms, do something great. Du culte des dieux fétiches ou Parallèle de lancienne religion de lEgypte avec la religion actuelle de Nigritie and this provides a materialistic theory of the origin of religion, and represents one of the first theoretical works in the discipline of ethno-anthropology. Notably it contains the first historical occurrence of the word fétichisme, later borrowed by Karl Marx in 1842, traité de la formation méchanique des langues et des principes physiques de létymologie. This provides a theory of the origin and the evolution of language. It had an influence on Condillacs Grammaire and an important role in the birth of a scientific conception of language. This is a French translation of Sallust’s Historia, partially restored with the help of ancient fragments, De Brosses is also remembered for his posthumously published letters, LItalie il y a cent ans, ou Lettres écrites dItalie à quelques amis en 1739 et 1740. This book is a collection of cultured, witty, open-minded letters and it was loved by Alexander Pushkin and Stendhal. The first English translation of Du culte des dieux fétiches will be published in The Returns of Fetishism, Charles De Brosses and the Afterlives of an Idea in June 2017. Works by or about Charles de Brosses at Internet Archive Charles de Brosses, Du culte des Dieux Fétiches, traité de la formation méchanique des langues, in CTLF Corpus des Textes Linguistiques Fondamentaux, Paris-Lyon,2006
27.
Ramiro Rampinelli
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Ramiro Rampinelli, born Lodovico Rampinelli, was an Italian mathematician and physicist. He was a monk in the Olivetan Order and he had a decisive influence on the spread of mathematical analysis, algebra and mathematical physics in the best universities of Italy. He is one of the best known Italian scholars in the field of mathematics of the first half of the 18th century. He was born in Brescia into the noble Rampinelli family and educated by the Jesuits and he studied first at the University of Bologna, where he was a disciple of Gabriele Manfredi, and took his monastic vows on 1 November 1722 at San Michele in Bosco. In 1727, after a stay at the Monastery of St. Helen in Venice. In 1731 he was in Rome for a year, spending time with Celestino Galiani and Antonio Leprotti and he then returned to the University of Bologna in 1733, to teach mathematics. Here he completed his Istituzioni Fisiche con il metodo analitico, in 1740, after a stay at the monastery of St. In 1747, the Senate of Milan appointed him to the chair in Mathematics and Physics at the University of Pavia and this work on optics was to have been followed by Trigonometria and Applicazione dei principi matematici alla fisica pratica, but Rampinelli suffered a stroke on 10 April 1758. After a short period of recuperation in Brescia, he returned to the monastery of San Vittore al Corso in Milan and he dedicated himself willingly to others benefit, and of benefits received, an indelible, grateful memory was preserved. Giornale de Letterati, Rome,1760 F. Torricelli, de Vita Rampinelli Epistola. in Lectiones Opticae. Nuova raccolta di opuscoli scientifici e filosofici, elogi de Bresciani per dottrina eccellenti nel secolo XVIII. Memorie appartenenti alla vita ed agli studi di P. Frisi, elogio storico di Donna M. G. Agnesi Milanese. Biographisch-literarisches Handwörterbuch zur Geschichte der exakten Wissenschaften, del movimento intellettuale nella provincia di Brescia. Linsegnamento fisico matematico a Pavia alle soglie delletà Teresiana, in Economia, istituzioni, cultura in Lombardia nelletà di M. Teresa
28.
Olivetans
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The Olivetans, or the Order of Our Lady of Mount Olivet, are a monastic order formally recognised in 1344. They have formed the Olivetan Congregation within the Benedictine Confederation since 1960 and they initially lived as hermits in the savage waste of Accona. The building of the monastery began with the approbation of the foundation charter by Guido Tarlati. The name Olivetan comes from the name of the original hermitage. The monastery later known as Monte Oliveto Maggiore to distinguish it from successive foundations at Florence, San Gimignano, Naples. It is still the mother house of the order or congregation, see Monte Oliveto Maggiore for the main article on the monastery. After the arrival of a number of new followers, the nascent community adopted the Rule of St. Benedict and was recognised by Pope Clement VI in 1344. Despite modern myths surrounding the prophesies attributed to Catholic mystic Saint Malachy, while it is true that the Olivetan congregation is considered a branch of the Benedictine order, the same can be said of the many other monastic congregations that follow the Rule of St. Benedict. The Olivetan monks rule Bec Abbey in France, as well as houses in England, USA, Italy, Brazil, Guatemala, Israel. La spiritualità dellantico monachesimo alle origini di Monte Oliveto, in Giancarlo Andenna / Mirko Breitenstein / Gert Melville, internationalen Kongresses des Italienisch-deutschen Zentrums für Vergleichende Ordensgeschichte. Münster / Hamburg / Berlin / London, LIT2005, 443-461, Monte Oliveto Maggiore Order of St. Benedict This article incorporates text from a publication now in the public domain, Herbermann, Charles, ed. article name needed
29.
Leonhard Euler
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He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion of a mathematical function. He is also known for his work in mechanics, fluid dynamics, optics, astronomy, Euler was one of the most eminent mathematicians of the 18th century, and is held to be one of the greatest in history. He is also considered to be the most prolific mathematician of all time. His collected works fill 60 to 80 quarto volumes, more than anybody in the field and he spent most of his adult life in Saint Petersburg, Russia, and in Berlin, then the capital of Prussia. A statement attributed to Pierre-Simon Laplace expresses Eulers influence on mathematics, Read Euler, read Euler, Leonhard Euler was born on 15 April 1707, in Basel, Switzerland to Paul III Euler, a pastor of the Reformed Church, and Marguerite née Brucker, a pastors daughter. He had two sisters, Anna Maria and Maria Magdalena, and a younger brother Johann Heinrich. Soon after the birth of Leonhard, the Eulers moved from Basel to the town of Riehen, Paul Euler was a friend of the Bernoulli family, Johann Bernoulli was then regarded as Europes foremost mathematician, and would eventually be the most important influence on young Leonhard. Eulers formal education started in Basel, where he was sent to live with his maternal grandmother. In 1720, aged thirteen, he enrolled at the University of Basel, during that time, he was receiving Saturday afternoon lessons from Johann Bernoulli, who quickly discovered his new pupils incredible talent for mathematics. In 1726, Euler completed a dissertation on the propagation of sound with the title De Sono, at that time, he was unsuccessfully attempting to obtain a position at the University of Basel. In 1727, he first entered the Paris Academy Prize Problem competition, Pierre Bouguer, who became known as the father of naval architecture, won and Euler took second place. Euler later won this annual prize twelve times, around this time Johann Bernoullis two sons, Daniel and Nicolaus, were working at the Imperial Russian Academy of Sciences in Saint Petersburg. In November 1726 Euler eagerly accepted the offer, but delayed making the trip to Saint Petersburg while he applied for a physics professorship at the University of Basel. Euler arrived in Saint Petersburg on 17 May 1727 and he was promoted from his junior post in the medical department of the academy to a position in the mathematics department. He lodged with Daniel Bernoulli with whom he worked in close collaboration. Euler mastered Russian and settled life in Saint Petersburg. He also took on a job as a medic in the Russian Navy. The Academy at Saint Petersburg, established by Peter the Great, was intended to improve education in Russia, as a result, it was made especially attractive to foreign scholars like Euler
30.
Infinitesimal calculus
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Calculus is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations. It has two branches, differential calculus, and integral calculus, these two branches are related to each other by the fundamental theorem of calculus. Both branches make use of the notions of convergence of infinite sequences. Generally, modern calculus is considered to have developed in the 17th century by Isaac Newton. Today, calculus has widespread uses in science, engineering and economics, Calculus is a part of modern mathematics education. A course in calculus is a gateway to other, more advanced courses in mathematics devoted to the study of functions and limits, Calculus has historically been called the calculus of infinitesimals, or infinitesimal calculus. Calculus is also used for naming some methods of calculation or theories of computation, such as calculus, calculus of variations, lambda calculus. The ancient period introduced some of the ideas that led to integral calculus, the method of exhaustion was later discovered independently in China by Liu Hui in the 3rd century AD in order to find the area of a circle. In the 5th century AD, Zu Gengzhi, son of Zu Chongzhi, indian mathematicians gave a non-rigorous method of a sort of differentiation of some trigonometric functions. In the Middle East, Alhazen derived a formula for the sum of fourth powers. He used the results to carry out what would now be called an integration, Cavalieris work was not well respected since his methods could lead to erroneous results, and the infinitesimal quantities he introduced were disreputable at first. The formal study of calculus brought together Cavalieris infinitesimals with the calculus of finite differences developed in Europe at around the same time, pierre de Fermat, claiming that he borrowed from Diophantus, introduced the concept of adequality, which represented equality up to an infinitesimal error term. The combination was achieved by John Wallis, Isaac Barrow, and James Gregory, in other work, he developed series expansions for functions, including fractional and irrational powers, and it was clear that he understood the principles of the Taylor series. He did not publish all these discoveries, and at this time infinitesimal methods were considered disreputable. These ideas were arranged into a calculus of infinitesimals by Gottfried Wilhelm Leibniz. He is now regarded as an independent inventor of and contributor to calculus, unlike Newton, Leibniz paid a lot of attention to the formalism, often spending days determining appropriate symbols for concepts. Leibniz and Newton are usually credited with the invention of calculus. Newton was the first to apply calculus to general physics and Leibniz developed much of the used in calculus today
31.
Mathematical analysis
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Mathematical analysis is the branch of mathematics dealing with limits and related theories, such as differentiation, integration, measure, infinite series, and analytic functions. These theories are studied in the context of real and complex numbers. Analysis evolved from calculus, which involves the elementary concepts and techniques of analysis, analysis may be distinguished from geometry, however, it can be applied to any space of mathematical objects that has a definition of nearness or specific distances between objects. Mathematical analysis formally developed in the 17th century during the Scientific Revolution, early results in analysis were implicitly present in the early days of ancient Greek mathematics. For instance, a geometric sum is implicit in Zenos paradox of the dichotomy. The explicit use of infinitesimals appears in Archimedes The Method of Mechanical Theorems, in Asia, the Chinese mathematician Liu Hui used the method of exhaustion in the 3rd century AD to find the area of a circle. Zu Chongzhi established a method that would later be called Cavalieris principle to find the volume of a sphere in the 5th century, the Indian mathematician Bhāskara II gave examples of the derivative and used what is now known as Rolles theorem in the 12th century. In the 14th century, Madhava of Sangamagrama developed infinite series expansions, like the power series and his followers at the Kerala school of astronomy and mathematics further expanded his works, up to the 16th century. The modern foundations of analysis were established in 17th century Europe. During this period, calculus techniques were applied to approximate discrete problems by continuous ones, in the 18th century, Euler introduced the notion of mathematical function. Real analysis began to emerge as an independent subject when Bernard Bolzano introduced the definition of continuity in 1816. In 1821, Cauchy began to put calculus on a firm logical foundation by rejecting the principle of the generality of algebra widely used in earlier work, instead, Cauchy formulated calculus in terms of geometric ideas and infinitesimals. Thus, his definition of continuity required a change in x to correspond to an infinitesimal change in y. He also introduced the concept of the Cauchy sequence, and started the theory of complex analysis. Poisson, Liouville, Fourier and others studied partial differential equations, the contributions of these mathematicians and others, such as Weierstrass, developed the -definition of limit approach, thus founding the modern field of mathematical analysis. In the middle of the 19th century Riemann introduced his theory of integration, the last third of the century saw the arithmetization of analysis by Weierstrass, who thought that geometric reasoning was inherently misleading, and introduced the epsilon-delta definition of limit. Then, mathematicians started worrying that they were assuming the existence of a continuum of numbers without proof. Around that time, the attempts to refine the theorems of Riemann integration led to the study of the size of the set of discontinuities of real functions, also, monsters began to be investigated
32.
Algebra
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Algebra is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols, as such, it includes everything from elementary equation solving to the study of abstractions such as groups, rings, and fields. The more basic parts of algebra are called elementary algebra, the abstract parts are called abstract algebra or modern algebra. Elementary algebra is generally considered to be essential for any study of mathematics, science, or engineering, as well as such applications as medicine, abstract algebra is a major area in advanced mathematics, studied primarily by professional mathematicians. Elementary algebra differs from arithmetic in the use of abstractions, such as using letters to stand for numbers that are unknown or allowed to take on many values. For example, in x +2 =5 the letter x is unknown, in E = mc2, the letters E and m are variables, and the letter c is a constant, the speed of light in a vacuum. Algebra gives methods for solving equations and expressing formulas that are easier than the older method of writing everything out in words. The word algebra is used in certain specialized ways. A special kind of object in abstract algebra is called an algebra. A mathematician who does research in algebra is called an algebraist, the word algebra comes from the Arabic الجبر from the title of the book Ilm al-jabr wal-muḳābala by Persian mathematician and astronomer al-Khwarizmi. The word entered the English language during the century, from either Spanish, Italian. It originally referred to the procedure of setting broken or dislocated bones. The mathematical meaning was first recorded in the sixteenth century, the word algebra has several related meanings in mathematics, as a single word or with qualifiers. As a single word without an article, algebra names a broad part of mathematics, as a single word with an article or in plural, an algebra or algebras denotes a specific mathematical structure, whose precise definition depends on the author. Usually the structure has an addition, multiplication, and a scalar multiplication, when some authors use the term algebra, they make a subset of the following additional assumptions, associative, commutative, unital, and/or finite-dimensional. In universal algebra, the word refers to a generalization of the above concept. With a qualifier, there is the distinction, Without an article, it means a part of algebra, such as linear algebra, elementary algebra. With an article, it means an instance of some abstract structure, like a Lie algebra, sometimes both meanings exist for the same qualifier, as in the sentence, Commutative algebra is the study of commutative rings, which are commutative algebras over the integers
33.
Finite difference method
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Today, FDMs are the dominant approach to numerical solutions of partial differential equations. First, assuming the function whose derivatives are to be approximated is properly-behaved, by Taylors theorem, we can create a Taylor Series expansion f = f + f ′1. H n + R n, where n. denotes the factorial of n, the error in a methods solution is defined as the difference between the approximation and the exact analytical solution. To use a finite difference method to approximate the solution to a problem and this is usually done by dividing the domain into a uniform grid. Note that this means that finite-difference methods produce sets of numerical approximations to the derivative. An expression of general interest is the truncation error of a method. Typically expressed using Big-O notation, local truncation error refers to the error from an application of a method. That is, it is the quantity f ′ − f i ′ if f ′ refers to the exact value, the remainder term of a Taylor polynomial is convenient for analyzing the local truncation error. Using the Lagrange form of the remainder from the Taylor polynomial for f, N +1, where x 0 < ξ < x 0 + h, the dominant term of the local truncation error can be discovered. For example, again using the formula for the first derivative. 2, and with some algebraic manipulation, this leads to f − f i h = f ′ + f ″2, a final expression of this example and its order is, f − f i h = f ′ + O. This means that, in case, the local truncation error is proportional to the step sizes. The quality and duration of simulated FDM solution depends on the discretization equation selection, the data quality and simulation duration increase significantly with smaller step size. Therefore, a balance between data quality and simulation duration is necessary for practical usage. Large time steps are useful for increasing speed in practice. However, time steps which are too large may create instabilities, the von Neumann method is usually applied to determine the numerical model stability. For example, consider the differential equation u ′ =3 u +2. The last equation is an equation, and solving this equation gives an approximate solution to the differential equation
34.
Charles Bossut
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Charles Bossut was a French mathematician and confrère of the Encyclopaedists. He was born at Tartaras, Loire, and died in Paris,1768 member of Académie des sciences OConnor, John J. Robertson, Edmund F. Charles Bossut, MacTutor History of Mathematics archive, University of St Andrews. This article incorporates text from a now in the public domain, Wood, James. London and New York, Frederick Warne
35.
Paris
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Paris is the capital and most populous city of France. It has an area of 105 square kilometres and a population of 2,229,621 in 2013 within its administrative limits, the agglomeration has grown well beyond the citys administrative limits. By the 17th century, Paris was one of Europes major centres of finance, commerce, fashion, science, and the arts, and it retains that position still today. The aire urbaine de Paris, a measure of area, spans most of the Île-de-France region and has a population of 12,405,426. It is therefore the second largest metropolitan area in the European Union after London, the Metropole of Grand Paris was created in 2016, combining the commune and its nearest suburbs into a single area for economic and environmental co-operation. Grand Paris covers 814 square kilometres and has a population of 7 million persons, the Paris Region had a GDP of €624 billion in 2012, accounting for 30.0 percent of the GDP of France and ranking it as one of the wealthiest regions in Europe. The city is also a rail, highway, and air-transport hub served by two international airports, Paris-Charles de Gaulle and Paris-Orly. Opened in 1900, the subway system, the Paris Métro. It is the second busiest metro system in Europe after Moscow Metro, notably, Paris Gare du Nord is the busiest railway station in the world outside of Japan, with 262 millions passengers in 2015. In 2015, Paris received 22.2 million visitors, making it one of the top tourist destinations. The association football club Paris Saint-Germain and the rugby union club Stade Français are based in Paris, the 80, 000-seat Stade de France, built for the 1998 FIFA World Cup, is located just north of Paris in the neighbouring commune of Saint-Denis. Paris hosts the annual French Open Grand Slam tennis tournament on the red clay of Roland Garros, Paris hosted the 1900 and 1924 Summer Olympics and is bidding to host the 2024 Summer Olympics. The name Paris is derived from its inhabitants, the Celtic Parisii tribe. Thus, though written the same, the name is not related to the Paris of Greek mythology. In the 1860s, the boulevards and streets of Paris were illuminated by 56,000 gas lamps, since the late 19th century, Paris has also been known as Panam in French slang. Inhabitants are known in English as Parisians and in French as Parisiens and they are also pejoratively called Parigots. The Parisii, a sub-tribe of the Celtic Senones, inhabited the Paris area from around the middle of the 3rd century BC. One of the areas major north-south trade routes crossed the Seine on the île de la Cité, this place of land and water trade routes gradually became a town
36.
Lucasian Professor of Mathematics
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The Lucasian Chair of Mathematics is a mathematics professorship in the University of Cambridge, England, its holder is known as the Lucasian Professor. The post was founded in 1663 by Henry Lucas, who was Cambridge Universitys Member of Parliament from 1639–1640, the current and 19th Lucasian Professor is Michael Cates, succeeding Michael Green now retired, starting from 1 July 2015. The previous holder of the post was the theoretical physicist Michael Green who was a fellow in Clare Hall at the University of Cambridge. He was appointed in October 2009, succeeding Stephen Hawking, who retired in September 2009, in the year of his 67th birthday. Hawking and Green now hold the position of Emeritus Lucasian Professor of Mathematics, kevin Knox and Richard Noakes, From Newton to Hawking, A History of Cambridge Universitys Lucasian Professors of Mathematics ISBN 0-521-66310-5
37.
University of Cambridge
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The University of Cambridge is a collegiate public research university in Cambridge, England, often regarded as one of the most prestigious universities in the world. Founded in 1209 and given royal status by King Henry III in 1231, Cambridge is the second-oldest university in the English-speaking world. The university grew out of an association of scholars who left the University of Oxford after a dispute with the townspeople, the two ancient universities share many common features and are often referred to jointly as Oxbridge. Cambridge is formed from a variety of institutions which include 31 constituent colleges, Cambridge University Press, a department of the university, is the worlds oldest publishing house and the second-largest university press in the world. The university also operates eight cultural and scientific museums, including the Fitzwilliam Museum, Cambridges libraries hold a total of around 15 million books, eight million of which are in Cambridge University Library, a legal deposit library. In the year ended 31 July 2015, the university had an income of £1.64 billion. The central university and colleges have an endowment of around £5.89 billion. The university is linked with the development of the high-tech business cluster known as Silicon Fen. It is a member of associations and forms part of the golden triangle of leading English universities and Cambridge University Health Partners. As of 2017, Cambridge is ranked the fourth best university by three ranking tables and no other institution in the world ranks in the top 10 for as many subjects. Cambridge is consistently ranked as the top university in the United Kingdom, the university has educated many notable alumni, including eminent mathematicians, scientists, politicians, lawyers, philosophers, writers, actors, and foreign Heads of State. Ninety-five Nobel laureates, fifteen British prime ministers and ten Fields medalists have been affiliated with Cambridge as students, faculty, by the late 12th century, the Cambridge region already had a scholarly and ecclesiastical reputation, due to monks from the nearby bishopric church of Ely. The University of Oxford went into suspension in protest, and most scholars moved to such as Paris, Reading. After the University of Oxford reformed several years later, enough remained in Cambridge to form the nucleus of the new university. A bull in 1233 from Pope Gregory IX gave graduates from Cambridge the right to teach everywhere in Christendom, the colleges at the University of Cambridge were originally an incidental feature of the system. No college is as old as the university itself, the colleges were endowed fellowships of scholars. There were also institutions without endowments, called hostels, the hostels were gradually absorbed by the colleges over the centuries, but they have left some indicators of their time, such as the name of Garret Hostel Lane. Hugh Balsham, Bishop of Ely, founded Peterhouse, Cambridges first college, the most recently established college is Robinson, built in the late 1970s
38.
Francis Maseres
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Francis Maseres was an English lawyer. He is known as general of the Province of Quebec, judge, mathematician, historian, member of the Royal Society. Francis Maseres was born in London on 15 December 1731 and his parents were Magdalene du Pratt du Clareau and Peter Abraham Maseres, physician. The Maseres family were French Protestants who left France after the revocation of Edict of Nantes in 1685 and he had a brother, named Peter. He studied in Rev. Richard Wooddesons School in Kingston-upon-Thames, then entered Clare College, Cambridge, where he obtained a Bachelor of Arts and he entered the Inner Temple to study law in 1750, and was admitted to the bar in 1758. He was sworn in office on 26 September 1766 and exercised his functions until the autumn of 1769, in March 1768, the Carleton government requested of him a report on the reform of the provinces law system. He submitted his report in February 1769, upon his return to London, he continued to take interest in American colonial affairs. In an essay published in 1770, he recommended that the colonies be represented as quickly as possible in the House of Commons and he was elected member of the Royal Society of London in 1771 and made cursitor baron of the exchequer in August 1773. He was elected judge of sheriff’s court in London in 1780. He espoused the cause of Pierre du Calvet who intended to bring governor Frederick Haldimand before the courts for violating the British constitution and this translation was valuable for British mathematics, but Maseres also influenced British mathematics negatively by attacking calculus and other advanced mathematical methods. He died unmarried at his house of Reigate on 19 May 1824. A Dissertation On the Use of the Negative Sign in Algebra, London, 1777–1779 Charles-Louis de Secondat, baron de Montesquieu, Francis Masères, transl. A View of the English Constitution, by the late Baron de Montesquieu. Being a Translation of the Sixth Chapter of the Eleventh Book of his Celebrated Treatise, Intitled LEsprit des loix, London, by William Hales. To Which is Added a Second Edition of The Moderate Reformer. London,1794 The Principles of Algebra by William Frend, London,1796 The Doctrine of Permutations and Combinations, London,1795 Tracts on the Resolution of Affected Algebräick Equations by Dr. Halleys, Mr. London,1809 The History of the Parliament of England. J. OConnor et E F Robertson, Francis Maseres, in the sit of the School of Mathematics and Statistics University of St Andrews, June 2004 Ville de Montréal. American Philosophical Society and Yale University,2002 Francis Masères - Portraits of Statisticians, in the site of the Mathematics Department of York University,15 July 2008
39.
Maria Theresa
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Maria Theresa Walburga Amalia Christina was the only female ruler of the Habsburg dominions and the last of the House of Habsburg. She was the sovereign of Austria, Hungary, Croatia, Bohemia, Transylvania, Mantua, Milan, Lodomeria and Galicia, by marriage, she was Duchess of Lorraine, Grand Duchess of Tuscany and Holy Roman Empress. She started her 40-year reign when her father, Emperor Charles VI, Charles VI paved the way for her accession with the Pragmatic Sanction of 1713 and spent his entire reign securing it. Upon the death of her father, Saxony, Prussia, Bavaria, Prussia proceeded to invade the affluent Habsburg province of Silesia, sparking a nine-year conflict known as the War of the Austrian Succession, and subsequently conquered it. Maria Theresa would later try to reconquer Silesia during the Seven Years War. Of the sixteen, ten survived to adulthood and she had eleven daughters and five sons. She criticised and disapproved of many of Josephs actions, Maria Theresa understood the importance of her public persona and was able to simultaneously evoke both esteem and affection from her subjects. However, she refused to allow religious toleration and contemporary travelers thought her regime was bigoted and superstitious. As a young monarch who fought two wars, she believed that her cause should be the cause of her subjects. The dowager empresses, her aunt Wilhelmine Amalia of Brunswick-Lüneburg and grandmother Eleonor Magdalene of the Palatinate-Neuburg, were her godmothers and her father was the only surviving male member of the House of Habsburg and hoped for a son who would prevent the extinction of his dynasty and succeed him. Thus, the birth of Maria Theresa was a disappointment to him. Charles sought the other European powers approval for disinheriting his nieces and they exacted harsh terms, in the Treaty of Vienna, Great Britain demanded that Austria abolish the Ostend Company in return for its recognition of the Pragmatic Sanction. France, Spain, Saxony-Poland, Bavaria and Prussia later reneged, little more than a year after her birth, Maria Theresa was joined by a sister, Maria Anna, and another one, named Maria Amalia, was born in 1724. The portraits of the family show that Maria Theresa resembled Elisabeth Christine. The Prussian ambassador noted that she had blue eyes, fair hair with a slight tinge of red, a wide mouth. Unlike many other members of the House of Habsburg, neither Maria Theresas parents nor her grandparents were closely related to each other, Maria Theresa was a serious and reserved child who enjoyed singing and archery. She was barred from riding by her father, but she would later learn the basics for the sake of her Hungarian coronation ceremony. The imperial family staged opera productions, often conducted by Charles VI and her education was overseen by Jesuits
40.
Pope Benedict XIV
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Pope Benedict XIV, born Prospero Lorenzo Lambertini, served as the Pope of the Catholic Church from 17 August 1740 to his death in 1758. Perhaps one of the greatest scholars in Christendom, yet overlooked, he promoted scientific learning, the baroque arts, reinvigoration of Thomism. In terms of the governance of the Papal States, he reduced taxation, a scholar, he laid the groundwork for the present Vatican Museum. Horace Walpole described him as a priest without insolence or interest, a prince without favorites, Lambertini was born into a noble family of Bologna to Marcello Lambertini and Lucrezia Bulgarini, the third of five children. At the time of his birth, Bologna was the second largest city in the Papal States, at the age of thirteen, he began attending the Collegium Clementianum in Rome, where he studied rhetoric, Latin, philosophy, and theology. During his studies as a man, he often studied the works of St. Thomas Aquinas. While he enjoyed studying at Collegium Clementianum, the bent of his mind was well towards ecclesiastical and civil law, soon after, in 1694 at the age of nineteen, he received the degree of Doctor of Sacred Theology and Doctor Utriusque Juris. On the death of Innocent XII, he was made an advocate by Clement XI. Lambertini was consecrated a bishop in Rome, in the Pauline Chapel of the Vatican Palace, on 16 July 1724, the co-consecrators were Giovanni Francesco Nicolai, titular Archbishop of Myra, and Nicola Maria Lercari, titular Archbishop of Nazianzus. He was made Bishop of Ancona in 1727 and he was created a cardinal in pectore, his name being published on 30 April 1728, and was subsequently made the Cardinal-Priest of Santa Croce in Gerusalemme on 10 May 1728. He also served as the Archbishop of Bologna, after the death of Pope Clement XII, Lambertini attended the papal conclave to choose a successor. It would last for six months, at first Cardinal Ottoboni, dean of the Sacred College, was favored to be elected, but a number of cardinals were opposed to this on account of the cardinal being protector of France. This appears to have assisted his cause for winning the election, which benefited from his reputation for deep learning, gentleness, wisdom. On 17 August 1740 he was elected in the evening and took his new name of Benedict XIV in honour of Pope Benedict XIII. He managed to overcome most of these problems — the Holy Sees disputes with the Kingdom of Naples, Sardinia, Spain, Venice and he had a very active papacy, reforming the education of priests, the calendar of feasts of the Church, and many papal institutions. Perhaps the most important act of Benedict XIVs pontificate was the promulgation of his famous laws about missions in the two bulls, Ex quo singulari and Omnium solicitudinum and this question was especially pressing in the case of an ancestor known not to have been a Christian. The choice of a Chinese translation for the name of God had also been debated since the early 17th century, Benedict XIV denounced these practices in these two bulls. The consequence of this was many of these converts left the Church
41.
Jacopo Riccati
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Jacopo Francesco Riccati was an Venetian mathematician and jurist from Venice. He is best known for having studied the equation which bears his name, Riccati was educated first at the Jesuit school for the nobility in Brescia, and in 1693 he entered the University of Padua to study law. He received a doctorate in law in 1696, encouraged by Stefano degli Angeli to pursue mathematics, he studied mathematical analysis. Riccati received various offers, but declined them in order to devote his full attention to the study of mathematical analysis on his own. Peter the Great invited him to Russia as president of the St. Petersburg Academy of Sciences and he was also invited to Vienna as an imperial councilor and was offered a professorship at the University of Padua. He was often consulted by the Senate of Venice on the construction of canals, some of his work on multinomials was included by Maria Gaetana Agnesi, at Riccatis request, in the book on integral calculus of her Analytical Institutions. The Riccati equation is named after him and his father, Conte Montino Riccati, came from a noble family who owned land near Venice. His mother was from the powerful Colonna family and his father died in 1686, when Riccati was only ten, leaving the youth a handsome estate. Jacopos son, Vincenzo Riccati, a Jesuit, followed his fathers footsteps, a second son, Giordano Riccati was the first to measure the ratio of Youngs moduli of metals—predating the better known Thomas Young by 25 years. Jacopo Riccati was named honorary Academician of the Academy of Sciences of the Institute of Bologna in 1723, oConnor, John J. Robertson, Edmund F. Jacopo Riccati, MacTutor History of Mathematics archive, University of St Andrews
42.
Witch of Agnesi
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In mathematics, the Witch of Agnesi, sometimes called the Witch of Maria Agnesi is the curve defined as follows. Starting with a circle, a point O on the circle is chosen. For any other point A on the circle, the secant line OA is drawn, the point M is diametrically opposite to O. The line OA intersects the tangent of M at the point N, the line parallel to OM through N, and the line perpendicular to OM through A intersect at P. As the point A is varied, the path of P is the Witch of Agnesi, the curve is asymptotic to the line tangent to the fixed circle through the point O. Suppose the point O is the origin, and that M is on the positive y-axis, suppose the radius of the circle is a. Then the curve has Cartesian equation y =8 a 3 x 2 +4 a 2, note that if a = 1/2, then this equation becomes rather simple, y =1 x 2 +1. This is the derivative of the arctangent function. Parametrically, if θ is the angle between OM and OA, measured clockwise, then the curve is defined by the equations x =2 a tan θ, y =2 a cos 2 θ = a vercosin . Another parameterization, with θ being the angle between OA and the x-axis, increasing anti-clockwise is x =2 a cot θ, y =2 a sin 2 θ = a versin , the following properties can be derived from integral calculus. The area between the witch and the asymptote at O is four times the area of the fixed circle, the centroid of this region is ill-defined, as the first moment with respect to x is ill-defined. The centroid of the circle is located at. The volume of revolution of the Witch of Agnesi, about its asymptote, is 4π2a3, the curve was studied by Pierre de Fermat in 1630. In 1703, Guido Grandi gave a construction for the curve, in 1748, Maria Gaetana Agnesi published her summation treatise Instituzioni analitiche ad uso della gioventù italiana, in which the curve was named according to Grandi, versiera. Coincidentally, the contemporary Italian word avversiera or versiera, derived from Latin adversarius, cambridge professor John Colson mistranslated the name of the curve thus. Different modern works about Agnesi and about the curve suggest slightly different guesses how exactly this mistranslation happened, struik mentions that, The word is derived from Latin vertere, to turn, but is also an abbreviation of Italian avversiera, female devil. Some wit in England once translated it witch, and the pun is still lovingly preserved in most of our textbooks in English language. The curve had already appeared in the writings of Fermat and of others, the curve is type 63 in Newtons classification
43.
Pierre de Fermat
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He made notable contributions to analytic geometry, probability, and optics. He is best known for his Fermats principle for light propagation and his Fermats Last Theorem in number theory, Fermat was born in the first decade of the 17th century in Beaumont-de-Lomagne, France—the late 15th-century mansion where Fermat was born is now a museum. He was from Gascony, where his father, Dominique Fermat, was a leather merchant. Pierre had one brother and two sisters and was almost certainly brought up in the town of his birth, there is little evidence concerning his school education, but it was probably at the Collège de Navarre in Montauban. He attended the University of Orléans from 1623 and received a bachelor in law in 1626. In Bordeaux he began his first serious mathematical researches, and in 1629 he gave a copy of his restoration of Apolloniuss De Locis Planis to one of the mathematicians there, there he became much influenced by the work of François Viète. In 1630, he bought the office of a councillor at the Parlement de Toulouse, one of the High Courts of Judicature in France and he held this office for the rest of his life. Fermat thereby became entitled to change his name from Pierre Fermat to Pierre de Fermat, fluent in six languages, Fermat was praised for his written verse in several languages and his advice was eagerly sought regarding the emendation of Greek texts. He communicated most of his work in letters to friends, often little or no proof of his theorems. In some of these letters to his friends he explored many of the ideas of calculus before Newton or Leibniz. Fermat was a trained lawyer making mathematics more of a hobby than a profession, nevertheless, he made important contributions to analytical geometry, probability, number theory and calculus. Secrecy was common in European mathematical circles at the time and this naturally led to priority disputes with contemporaries such as Descartes and Wallis. Anders Hald writes that, The basis of Fermats mathematics was the classical Greek treatises combined with Vietas new algebraic methods, Fermats pioneering work in analytic geometry was circulated in manuscript form in 1636, predating the publication of Descartes famous La géométrie. This manuscript was published posthumously in 1679 in Varia opera mathematica, in these works, Fermat obtained a technique for finding the centers of gravity of various plane and solid figures, which led to his further work in quadrature. Fermat was the first person known to have evaluated the integral of power functions. With his method, he was able to reduce this evaluation to the sum of geometric series, the resulting formula was helpful to Newton, and then Leibniz, when they independently developed the fundamental theorem of calculus. In number theory, Fermat studied Pells equation, perfect numbers, amicable numbers and it was while researching perfect numbers that he discovered Fermats little theorem. Fermat developed the two-square theorem, and the polygonal number theorem, although Fermat claimed to have proved all his arithmetic theorems, few records of his proofs have survived