1.
Fibonacci number
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The Fibonacci sequence is named after Italian mathematician Leonardo of Pisa, known as Fibonacci. Liber Abaci introduced the sequence to European mathematics, although the sequence had been described earlier as Virahanka numbers in Indian mathematics. The sequence described in Liber Abaci began with F1 = 1. They are intimately connected with the golden ratio; for example, the closest rational approximations to the ratio are 2/1, 8/5.... Fibonacci numbers appear often in mathematics, so so that there is an entire journal dedicated to their study, the Fibonacci Quarterly. The Fibonacci sequence appears in Indian mathematics, in connection with Sanskrit prosody. Susantha Goonatilake writes that the development of the Fibonacci sequence "is attributed in part to Pingala, later being associated with Virahanka, Gopāla, Hemachandra". He dates Pingala before 450 BC. For variations of meters of two three being mixed, five happens. ... In this way, the process should be followed in all mātrā-vṛttas. The sequence is also discussed by Gopala and by the Jain scholar Hemachandra. Outside of India, the Fibonacci sequence first appears in the book Liber Abaci by Fibonacci. The puzzle that Fibonacci posed was: how many pairs will there be in one year? At the end of the first month, they mate, but there is still only 1 pair.
Fibonacci number
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A page of Fibonacci 's Liber Abaci from the Biblioteca Nazionale di Firenze showing (in box on right) the Fibonacci sequence with the position in the sequence labeled in Latin and Roman numerals and the value in Hindu-Arabic numerals.
Fibonacci number
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A tiling with squares whose side lengths are successive Fibonacci numbers
2.
Otto Fibonacci
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This article contains a list of minor characters in the American television series Prison Break. The listed characters are those who are played by guest stars. The characters are listed alphabetically by the name which appears in the episode credits. The "Pad Man" to fans, is the main antagonist in the series. He holds the rank of General. He appears only fleetingly in his first two seasons, at Sona. In his appearance in the season 4 premiere, he discovers that the man Michael was forced to break out of Sona, is a traitor. In "Sound", it is revealed to the viewers that the General's name is "Jonathan Krantz", as seen from the images of him. Learning that the General has one of the Scylla Cards, Michael's team plan an attack against his limo in "The Price". Due to the betrayal of team member Roland Glenn, the attack is not successful. Now knowing that Scylla is in danger, the General orders it to be puts increasing pressure on Wyatt to kill the brothers. He is tricked into thinking that Wyatt has killed the brothers, but decides to go ahead with moving Scylla anyway. He plays a large role in "Selfless", where he comes face to face for the first time. When he goes to confront Michael in the underground bunker, he is forced to hand over his card by Michael's team at gunpoint. Thinking it is useless without the other cards, he's shocked when Michael takes him hostage.
Otto Fibonacci
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Patricia Wettig, the actress who played Caroline Reynolds.
Otto Fibonacci
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John Billingsley played Terrence Steadman in the first season.
Otto Fibonacci
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Haywire in Season 1.
Otto Fibonacci
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Callie Thorne played Pamela Mahone.
3.
Pisa
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Pisa is a city in Tuscany, Central Italy, straddling the River Arno just before it empties into the Tyrrhenian Sea. It is the city of the Province of Pisa. Much of the city's architecture was financed as one of the Italian maritime republics. The origin of Pisa, is a mystery. Archaeological remains from the 5th century BC confirmed the existence of a city at the sea, trading with Greeks and Gauls. The presence of an Etruscan necropolis, discovered in 1991, confirmed its Etruscan origins. Ancient Roman authors referred as an old city. Strabo referred Pisa's origins after the fall of Troy. The maritime role of Pisa should have been already prominent if the ancient authorities ascribed to it the invention of the naval ram. Pisa took advantage of being the only port along the western coast from Genoa to Ostia. Pisa served against Ligurians, Gauls and Carthaginians. In 180 BC, it became a Roman colony as Portus Pisanus. In 89 BC, Portus Pisanus became a municipium. Emperor Augustus changed the name in Colonia Iulia obsequens. It is supposed that Pisa was founded on the shore.
Pisa
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Pisa
Pisa
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Coat of arms
Pisa
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Hypothetical map of Pisa in the 5th century AD
Pisa
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Hypothetical map of Pisa in the 11th century AD
4.
Mathematician
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A mathematician is someone who uses an extensive knowledge of mathematics in his/her work, typically to solve mathematical problems. Mathematics is concerned with numbers, data, quantity, structure, change. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. It was the Pythagoreans who coined the term "mathematics", 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 many works on applied mathematics. Mathematics in the Islamic world during the Middle Ages followed various modes of funding varied based primarily on scholars. 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 scholars 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 mathematicians 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.”
Mathematician
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Euclid (holding calipers), Greek mathematician, known as the "Father of Geometry"
Mathematician
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In 1938 in the United States, mathematicians were desired as teachers, calculating machine operators, mechanical engineers, accounting auditor bookkeepers, and actuary statisticians
Mathematician
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Archimedes, c. 287 – 212 BC
Mathematician
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Brahmagupta, c. 598 - 670
5.
Liber Abaci
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Liber Abaci is a historic book on arithmetic by Leonardo of Pisa, known later by his nickname Fibonacci. Liber Abaci was among the Western books to describe Hindu -- Arabic numbers traditionally described as "Arabic Numerals". By addressing the applications of mathematicians, it contributed to convincing the public of the superiority of the Hindu -- Arabic numeral system. The title of Liber Abaci means "The Book of Calculation". The second version of Liber Abaci was dedicated to Michael Scot in 1227 CE. No versions of the original 1202 CE book have been found. The first section introduces the Hindu -- Arabic system, including methods for converting between different representation systems. The second section presents calculations of profit and interest. The fourth section derives approximations, both geometrical, of irrational numbers such as square roots. The book also includes proofs in Euclidean geometry. Fibonacci's method of solving algebraic equations shows the influence of Abū Kāmil Shujāʿ ibn Aslam. There are three key differences between Fibonacci's notation and modern notation. We generally write a fraction to the right of the whole number to which it is added, for instance 2 3 for 7/3. Fibonacci instead would write the same fraction to i.e. 1 3 2. The notation was read to left.
Liber Abaci
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A page of the Liber Abaci from the Biblioteca Nazionale di Firenze showing (on right) the numbers of the Fibonacci sequence.
6.
Italians
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Italians are a nation and ethnic group native to Italy who share a common Italian culture, ancestry and speak the Italian language as a mother tongue. Italians have greatly contributed to science, arts, technology, cuisine, sports, jurisprudence and banking both abroad and worldwide. Italian people are generally known to clothing and family values. The term Italian has a history that goes back to pre-Roman Italy. Greek historian Dionysius of Halicarnassus states this account together with the legend that Italy was named after Italus, mentioned also by Aristotle and Thucydides. This period of unification was followed by one of conquest beginning with the First Punic War against Carthage. In the course of the century-long struggle against Carthage, the Romans conquered Sicily, Sardinia and Corsica. The final victor, was accorded the title of Augustus by the Senate and thereby became the first Roman emperor. Emperor Diocletian's administrative division of the empire into two parts in 285 provided only temporary relief; it became permanent in 395. In 313, churches thereafter rose throughout the empire. However, he also moved his capital to Constantinople greatly reducing the importance of the former. Romulus Augustulus, was deposed in 476 by a Germanic foederati general in Italy, Odoacer. His defeat marked the end of the western part of the Roman Empire. Odoacer ruled well after gaining control of Italy in 476. Then he was defeated by Theodoric, the king of another Germanic tribe, the Ostrogoths.
Italians
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Amerigo Vespucci, the notable geographer and traveller from whose name the word America is derived.
Italians
Italians
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Christopher Columbus, the discoverer of the New World.
Italians
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Laura Bassi, the first chairwoman of a university in a scientific field of studies.
7.
Middle Ages
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In the history of Europe, the Middle Ages or medieval period lasted from the 5th to the 15th century. It merged into the Age of Discovery. The Middle Ages is the middle period of the three traditional divisions of Western history: classical antiquity, the medieval period, the modern period. The medieval period is itself subdivided into Late Middle Ages. Counterurbanisation, movement of peoples, which had begun in Late Antiquity, continued in the Early Middle Ages. The large-scale movements including Germanic peoples, formed new kingdoms in what remained of the Western Roman Empire. Although there were substantial changes in society and political structures, the break with classical antiquity was not complete. The Byzantine Empire remained a major power. In the West, most kingdoms incorporated the few extant Roman institutions. Monasteries were founded as campaigns to Christianise pagan Europe continued. The Franks, under the Carolingian dynasty, briefly established the Carolingian Empire during 9th century. The Crusades, first preached in 1095, were military attempts by Western European Christians to regain control of the Holy Land from Muslims. Kings became the heads of centralised nation states, reducing crime and violence but making the ideal of a unified Christendom more distant. Intellectual life was marked by a philosophy that emphasised joining faith by the founding of universities. Controversy, the Western Schism within the Catholic Church paralleled the interstate conflict, peasant revolts that occurred in the kingdoms.
Middle Ages
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The Cross of Mathilde, a crux gemmata made for Mathilde, Abbess of Essen (973–1011), who is shown kneeling before the Virgin and Child in the enamel plaque. The body of Christ is slightly later. Probably made in Cologne or Essen, the cross demonstrates several medieval techniques: cast figurative sculpture, filigree, enamelling, gem polishing and setting, and the reuse of Classical cameos and engraved gems.
Middle Ages
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A late Roman statue depicting the four Tetrarchs, now in Venice
Middle Ages
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Coin of Theodoric
Middle Ages
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Mosaic showing Justinian with the bishop of Ravenna, bodyguards, and courtiers
8.
Consul
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Consul was the title of one of the chief magistrates of the Roman Republic, subsequently a somewhat significant title under the Roman Empire. The title was also also revived in modern states, notably in the First French Republic. The relating adjective is consular, from the consularis. In modern terminology, a Consul is a type of diplomat. The American Heritage Dictionary defines consul as "an official appointed by a government to represent its interests there." Throughout most of southern France, a consul was an office roughly similar with English aldermen. The most prominent were those of Bordeaux and Toulouse, which came to be known as capitouls, respectively. The capitouls of Toulouse were granted transmittable nobility. In many other smaller towns the first consul, was the equivalent of a today, assisted by a variable number of secondary consuls and jurats. His main task was to collect tax. The Dukes of Gaeta often used also the title of "Consul" in its Greek form "Hypatos". The city-state of Genoa, unlike ancient Rome, bestowed the title of Consul on various state officials, not necessarily restricted to the highest. Among these were Genoese officials stationed in various Mediterranean ports, whose role included helping Genoese merchants and sailors in difficulties with the local authorities. This institution, with its name, is reflected in the modern usage of the word. In reality, Bonaparte, dominated his two colleagues and held supreme power, soon making himself Consul for life and eventually, in 1804, Emperor.
Consul
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A portrait of the three Consuls, Jean Jacques Régis de Cambacérès, Napoleon Bonaparte and Charles-François Lebrun (left to right)
9.
Bejaia
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Béjaïa, formerly Bougie and Bugia, is a Mediterranean port city on the Gulf of Béjaïa in Algeria; it is the capital of Béjaïa Province, Kabylia. Béjaïa is the largest principally Kabyle-speaking city in the Kabylie region of Algeria. The history of Béjaïa explains the diversity of the local population. Its inhabitants are mainly Berbers. All three of these geographic features are contained in the Gouraya National Park. The Soummam river runs past the town. Under French rule, it was formerly known under European names, such as Budschaja in German, Bugia in Italian, Bougie. It was an important town and the later Sitifensis. The son of a Pisan merchant, posthumously known as Fibonacci, there learned about Muslim mathematics and Hindu-Arabic numerals. He introduced modern mathematics into medieval Europe. In 1315, Raymond Lully died as a result of being stoned at Béjaïa, where, a few years before, Peter Armengaudius is reputed to have been hanged. After a Spanish occupation, the city was taken by the Ottoman Turks in 1555. For nearly three centuries, Béjaïa was a stronghold of the Barbary pirates. City landmarks include a casbah built by the Spanish in 1545. A picture of the Orientalist painter Maurice Boitel, who painted in the city for a while, can be found in the museum of Béjaïa.
Bejaia
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Béjaïa ⴱⴳⴰⵢⴻⵜ
Bejaia
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Monkey Peak (Pic des singes).
Bejaia
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The Western Roman empire, in the second century AD, during the reign of Hadrian. Saldae can be seen on the south coast of the Mediterranean
Bejaia
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Coin of the Hafsids, with ornamental Kufic script, from Béjaïa, 1249-1276.
10.
Almohad dynasty
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The Almohad Caliphate was a Moroccan Berber Muslim movement founded in the 12th century. The Almohad movement was started by Ibn Tumart among the Masmuda tribes of southern Morocco. The Almohads first established a Berber state in Tinmel in the Atlas Mountains in roughly 1120. They succeeded in governing Morocco by 1147 when Abd al-Mu ` al-Gumi declared Caliph. They then extended their power over all of the Maghreb by 1159. Al-Andalus followed the fate of North Africa and all Islamic Iberia was under Almohad rule by 1172. The Almohad movement originated with a Berber confederation of southern Morocco. At the time, Morocco, much of the rest of North Africa and Spain, was under the rule of the Almoravids, a Sanhaja Berber dynasty. Early in his life, Ibn Tumart went to Spain to pursue his studies, thereafter to Baghdad to deepen them. In Baghdad, Ibn Tumart attached himself to the theological school of al-Ash'ari, came under the influence of the teacher al-Ghazali. He soon developed his own system, combining the doctrines of various masters. Ibn Tumart represented a revolt against what he perceived as anthropomorphism in Muslim orthodoxy. His followers would become known as the al-Muwahhidun, meaning those who affirm the unity of God. He laid the blame for the latitude on the ruling dynasty of the Almoravids, whom he accused of obscurantism and impiety. His antics and fiery preaching led fed-up authorities to move him along from town to town.
Almohad dynasty
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The Almohads transferred the capital of Al-Andalus to Seville.
Almohad dynasty
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Flag
Almohad dynasty
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Almohads after 1212
Almohad dynasty
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La Giralda.
11.
North Africa
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North Africa or Northern Africa is the northernmost region of Africa. The United Nations definition of "North Africa" includes territories; Algeria, Egypt, Libya, Mauritania, Morocco, Sudan, Tunisia, Western Sahara. The countries of Algeria, Morocco, Tunisia, Libya are often collectively referred to as the Maghreb, the Arabic word for "sunset". Egypt lies to the encompasses part of West Asia, while Sudan is situated on the edge of the Sahel, to the south of Egypt. Egypt is a transcontinental country because of the Sinai Peninsula, which geographically lies in Western Asia. North Africa also includes a number of Spanish possessions. Madeira in the North Atlantic Ocean northwest of the African mainland are included in considerations of the region. North Africa is a major part of the Muslim world. They recede to the east, becoming a steppe landscape before meeting the Sahara desert, which covers more than 75 percent of the region. The sediments of the Sahara overlie an ancient plateau of crystalline rock, some of, more than billion years old. The Mediterranean coast are the main sources of fertile farming land. Woods such as cedar and cork, are grown. Typical Mediterranean crops, such as olives, figs, dates and fruits, also thrive in these areas. Most of the population in Egypt and Sudan live close to the river. Elsewhere, irrigation is essential to improve crop yields on the desert margins.
North Africa
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Market of Biskra in Algeria, 1899
North Africa
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Northern Africa (UN subregion)
North Africa
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The kasbah of Aït Benhaddou in Morocco
North Africa
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The first Roman emperor native to North Africa was Septimius Severus, born in Leptis Magna in present-day Libya.
12.
Algeria
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Algeria, officially the People's Democratic Republic of Algeria, is a sovereign state in North Africa on the Mediterranean coast. Most populous city is Algiers, located in the country's far north. With an area of 2,381,741 square kilometres, Algeria is the largest in Africa. The country is a semi-presidential republic consisting of 1,541 communes. Abdelaziz Bouteflika has been President since 1999. Berbers are generally considered to be the indigenous inhabitants of Algeria. Algeria is a middle power. Energy exports are the backbone of the economy. The national oil company, is the largest company in Africa. Algeria is the founding member of the Maghreb Union. The country's name derives from the city of Algiers. The city's name in turn derives from the Arabic al-Jazā ` a truncated form of the older Jazā ` ir Banī Mazghanna, employed by medieval geographers such as al-Idrisi. In the region of Ain Hanech, early remnants of hominid occupation in North Africa were found. Neanderthal tool makers produced hand axes in the Levalloisian and Mousterian styles similar to those in the Levant. Algeria was the site of the highest state of development of Middle Paleolithic Flake tool techniques.
Algeria
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Ancient Roman Empire ruins of Timgad. Street leading to the Arch of Trajan.
Algeria
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Flag
Algeria
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Ancient Roman theatre in Djémila
Algeria
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Numidia along with Egypt, Rome, and Carthage 200 BCE
13.
Mediterranean
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The sea is sometimes considered a part of the Atlantic Ocean, although it is usually identified as a separate body of water. The name Mediterranean is derived from the Latin mediterraneus, meaning "inland" or "in the middle of land". It covers an approximate area of 2.5 million km2, but its connection to the Atlantic is only 14 km wide. In oceanography, it is sometimes called the Eurafrican Mediterranean Sea or the European Mediterranean Sea to distinguish it from mediterranean seas elsewhere. The Mediterranean Sea has an average depth of 1,500 m and the deepest recorded point is 5,267 m in the Calypso Deep in the Ionian Sea. The sea is bordered on the north by Europe, the east by Asia, in the south by Africa. It is located between latitudes 30° and 46° N and longitudes 6° W and 36° E. Its west-east length, from the Strait of Gibraltar to the Gulf of Iskenderun, on the southwestern coast of Turkey, is approximately 4,000 km. The sea's average north-south length, from Croatia’s southern shore to Libya, is approximately 800 km. The Mediterranean Sea, including the Sea of Marmara, has a surface area of approximately 2,510,000 square km. The sea was an important route for merchants and travelers of ancient times that allowed for trade and cultural exchange between emergent peoples of the region. The history of the Mediterranean region is crucial to understanding the origins and development of many modern societies. In addition, Gaza Strip and the British Overseas Territories of Gibraltar and Akrotiri and Dhekelia have coastlines on the sea. The Ancient Greek name Mesogeios, is similarly from μέσο, "between" + γη, "land, earth"). It can be compared with the Ancient Greek name Mesopotamia, meaning "between rivers".
Mediterranean
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Circa the 6th century BCE: In ancient times the Mediterranean provided sources of food and local commerce and direct routes for trade and communications, colonisation, and war. Numerous cities and colonies were situated at its shores or within the basin: Greek (red) and Phoenician (yellow) colonies in antiquity; and other cities (grey), including the provincial "Rom".
Mediterranean
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Map of the Mediterranean Sea
Mediterranean
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With its highly indented coastline and large number of islands, Greece has the longest Mediterranean coastline.
Mediterranean
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The Battle of Lepanto, 1571, ended in victory for the European Holy League against the Ottoman Turks.
14.
Frederick II, Holy Roman Emperor
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Frederick II was a Holy Roman Emperor and King of Sicily in the Middle Ages, a member of the House of Hohenstaufen. His cultural ambitions, based in Sicily and stretching through Italy to Germany, even to Jerusalem, were enormous. However, his dynasty collapsed soon after his death. As such, he was King of Germany, of Burgundy. His other title was King of Jerusalem by virtue of marriage and his connection with the Sixth Crusade. Pope Gregory IX went so as to call him an Antichrist. Speaking six languages, Frederick was an avid patron of the arts. He played a major role in promoting literature through the Sicilian School of poetry. His Sicilian royal court from around 1220 to his death, saw the first use of a literary form of an Italo-Romance language, Sicilian. The poetry that emanated from the school had a significant influence on what was to become the modern Italian language. He was also the first king who explicitly outlawed trials by ordeal as they were considered irrational. After his death, the House of Hohenstaufen came to an end. Born near Ancona, Italy, Frederick was the son of the emperor Henry VI. He was known as the Apuliae. Some chronicles say that the forty-year-old Constance, gave birth to him in a public square in order to forestall any doubt about his origin.
Frederick II, Holy Roman Emperor
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Frederick II
Frederick II, Holy Roman Emperor
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The birth of Frederick II
Frederick II, Holy Roman Emperor
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Gold augustale of Emperor Frederik II, as King of Sicily 1198–1250.
Frederick II, Holy Roman Emperor
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Frederick II (left) meets Al-Kamil (right).
15.
Republic of Pisa
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The Republic of Pisa was a de facto independent state centered on the Tuscan city of Pisa during the late 10th and 11th centuries. During the High Middle Ages the city controlled a significant Mediterranean merchant fleet and navy. It expanded its influence in 1005. Pisa was with the Saracens, whose bases were in the Italian astersa, for control of the Mediterranean. In alliance with Genoa, Sardinia was captured with the defeat of the Saracen leader Mujāhid al - ` Āmirī. This victory gave supremacy in the Tyrrhenian Sea. When the Pisans subsequently ousted the Genoese from Sardinia, rivalry was born between the two maritime republics. Between 1035 Pisa went on to successfully defeat several rival towns in the Emirate of Sicily and conquer Carthage in North Africa. In 1051-1052 Admiral Jacopo Ciurini conquered Corsica, provoking more resentment from the Genoese. Roger declined due to other commitments. With no support, the Pisan attack against Palermo failed. The Pisan victory helped to consolidate its position in the Mediterranean. This was simply a confirmation of the present situation, because at the time the marquis of Tuscany had already been excluded from power. Pisa sacked the Zirid city of Mahdia in 1088. Four years later, Pisan and Genoese ships helped Alfonso VI of Castile force El Cid out of Valencia.
Republic of Pisa
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Map of Pisa in the 11th century
Republic of Pisa
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Flag
Republic of Pisa
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The Cathedral of Pisa was built during the Republic's heydays (11th and 12th century) and financed by the spoils and loot from the Sack of Mahdia (1087)
Republic of Pisa
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Relief of the seaport of Pisa on the Tower of Pisa
16.
National Central Library (Florence)
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The library was founded in 1714 when scholar Antonio Magliabechi bequeathed his entire collection of books, encompassing approximately 30,000 volumes, to the city of Florence. By 1743, it was required that a copy of every work published in Tuscany be submitted to the library. Originally known as the Magliabechiana, the library was opened to the public in 1747. Since 1870, the library has collected copies of all Italian publications. Before this, they were found in various rooms belonging to the Uffizi Gallery. The National Library System, located in the BNCF, is responsible for the automation of library services and the indexing of national holdings. Unfortunately, a major flood of the Arno River in 1966 damaged nearly one-third of the library's holdings, most notably its periodicals and Palatine and Magliabechi collections. The Restoration Center was subsequently established and may be credited with saving many of these priceless artifacts. However, much work remains to be done and some items are forever lost. Official website
National Central Library (Florence)
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The Library from Piazza dei Cavalleggeri
National Central Library (Florence)
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Arno river facade
National Central Library (Florence)
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The library beside Santa Croce
National Central Library (Florence)
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The distribution hall
17.
Place value
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Positional notation or place-value notation is a method of representing or encoding numbers. Positional notation is distinguished from other notations for its use of the same symbol for the different orders of magnitude. This greatly simplified arithmetic, leading to the rapid spread of the notation across the world. With the use of a point, the notation can be extended to include fractions and the numeric expansions of real numbers. The Babylonian system, base-60, was the first positional system developed, is still used today to count time and angles. The Hindu–Arabic numeral system, base-10, is the most commonly used system in the world today for most calculations. The base-10 system, likely motivated by counting with the ten fingers, is ubiquitous. Some continue to be used today. For example, it lacked a real 0 value. Zero was indicated by a space between sexagesimal numerals. By 300 BC, a symbol was co-opted as a placeholder in the same Babylonian system. In a tablet unearthed at Kish, the Bêl-bân-aplu wrote his zeros with three hooks, rather than two slanted wedges. The Babylonian placeholder was not a true zero because it was not used alone. Nor was it used at the end of a number. Thus numbers like 120, 3 and 180, 4 and 240, looked the same because the larger numbers lacked a final sexagesimal placeholder.
Place value
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Numeral systems
18.
Numeral system
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The number the numeral represents is called its value. Such systems are, however, not the topic of this article. The most commonly used system of numerals is the Hindu–Arabic numeral system. Two Indian mathematicians are credited with developing it. Aryabhata of Kusumapura developed the place-value notation in the 5th century and a century later Brahmagupta introduced the symbol for zero. The Arabs adopted and modified it. The Arabs call the Hindu numeral system. The Arabs spread them with them. The Western world modified them and called them the Arabic numerals, as they learned from them. Hence the western system is the modified version of the Hindu numeral system developed in India. It also exhibits a great similarity to the Sanskrit–Devanagari notation, still used in India and neighboring Nepal. The simplest system is the unary system, in which every natural number is represented by a corresponding number of symbols. If the / is chosen, for example, seven would be represented by / / / / / / /. Tally marks represent one such system still in common use. The unary system is only useful for small numbers, although it plays an important role in theoretical computer science.
Numeral system
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Numeral systems
19.
Bookkeeping
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Bookkeeping is the recording of financial transactions, is part of the process of accounting in business. It is the only word in the English language with three consecutive groups of a repeating letter. Transactions include payments by an individual person or an organization/corporation. Bookkeeping is usually performed by a bookkeeper. A bookkeeper is a person who records the day-to-day financial transactions of a business. She is usually responsible for writing the daybooks, which contain records of purchases, payments. Babylonian records have been found dating back as far as 2600 B.C. written with a stylus on small slabs of clay. The term "waste book" was used in colonial America referring to bookkeeping. The purpose was to document daily transactions including receipts and expenditures. This was recorded in chronological order, the purpose was for temporary use only. The daily transactions would then be recorded in a daybook or account ledger in order to balance the accounts. The name "book" comes from the fact that once the book's data were transferred to the actual journal, the book could be discarded. The bookkeeping process primarily records the financial effects of transactions. In the normal course of business, a document is produced each time a transaction occurs. Sales and purchases usually have invoices or receipts.
Bookkeeping
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Portrait of the Italian Luca Pacioli, painted by Jacopo de' Barbari, 1495, (Museo di Capodimonte). Pacioli is regarded as the Father of Accounting and Bookkeeping.
20.
Abacus
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The use of the word abacus dates before 1387 AD, when a Middle English work borrowed the word from Latin to describe a sandboard abacus. The Latin word came from ἄβαξ abax which means something without base, improperly, any piece of rectangular board or plank. Alternatively, "drawing-board covered with dust". Greek ἄβαξ itself is probably a borrowing of a Northwest Semitic, perhaps word akin to Hebrew ʾābāq, "dust". The preferred plural of abacus is a subject of disagreement, with both abaci in use. The user of an abacus is called an abacist. Some scholars point to a character from the Babylonian cuneiform which may have been derived from a representation of the abacus. Archaeologists have found ancient disks of various sizes that are thought to have been used as counters. However, wall depictions of this instrument have not been discovered. During the Achaemenid Empire, around 600 BC the Persians first began to use the abacus. The earliest archaeological evidence for the use of the Greek abacus dates to the 5th BC. Also Demosthenes talked of the need to use pebbles for calculations too difficult for your head. The Greek abacus was a table of wood or marble, metal for mathematical calculations. This Greek abacus saw use in Achaemenid Persia, the Etruscan civilization, until the French Revolution, the Western Christian world. A tablet found in 1846 AD, dates back to 300 BC, making it the oldest counting board discovered so far.
Abacus
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A Chinese abacus
Abacus
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Calculating-Table by Gregor Reisch: Margarita Philosophica, 1503. The woodcut shows Arithmetica instructing an algorist and an abacist (inaccurately represented as Boethius and Pythagoras). There was keen competition between the two from the introduction of the Algebra into Europe in the 12th century until its triumph in the 16th.
Abacus
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Copy of a Roman abacus
Abacus
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Japanese soroban
21.
Banking
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A bank is a financial institution that accepts deposits from the public and creates credit. Lending activities can be performed either indirectly through capital markets. Due to their importance in the financial stability of a country, banks are highly regulated in most countries. Most nations have institutionalized a system known as fractional banking under which banks hold liquid assets equal to only a portion of their current liabilities. The oldest existing bank is Banca Monte dei Paschi di Siena, while the oldest existing merchant bank is Berenberg Bank. Banking began with the first prototype banks of merchants of the ancient world, which made grain loans to traders who carried goods between cities. This began in Assyria and Babylonia. Later, during the Roman Empire, lenders based in temples made loans and added two important innovations: they accepted deposits and changed money. Archaeology from this period in ancient China and India also shows evidence of money activity. The Bardi and Peruzzi families dominated banking in 14th-century Florence, establishing branches in other parts of Europe. One of the most famous Italian banks was the Medici Bank, set up by Giovanni di Bicci de' Medici in 1397. Banco di San Giorgio, was founded in 1407 at Genoa, Italy. Modern banking practices, including the issue of banknotes, emerged in the 17th and 18th centuries. Merchants started to store their gold with the goldsmiths of London, who charged a fee for that service. The goldsmith paid interest on these deposits.
Banking
–
The Bank of England, established in 1694.
Banking
–
Personal finance
Banking
–
Among many other things, the Code of Hammurabi from 1754 BC recorded interest-bearing loans.
Banking
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The sealing of the Bank of England Charter (1694).
22.
Accounting
–
Accounting or accountancy is the measurement, processing and communication of financial information about economic entities such as businesses and corporations. The modern field was established in 1494. Practitioners of accounting are known as accountants. The terms'accounting' and'financial reporting' are often used as synonyms. Accounting can be divided into several fields including financial accounting, management accounting, tax accounting. Accounting information systems are designed to support related activities. Accounting is facilitated by accounting organizations such as standard-setters, professional bodies. Financial statements are prepared in accordance with generally accepted accounting principles. As of 2012, "all major economies" have plans to adopt the International Financial Reporting Standards. The history of accounting is thousands of years old and can be traced to ancient civilizations. By the time of the Emperor Augustus, the Roman government had access to financial information. Accounting split into financial accounting and management accounting with the development of joint-stock companies. The last work on a double-entry system was published in Italy, by Luca Pacioli. The word "accountant" is derived from the French compter, also derived from the Italian and Latin word computare. Accountancy refers to the profession of an accountant, particularly in British English.
Accounting
–
Accounting
Accounting
–
Portrait of Luca Pacioli, painted by Jacopo de' Barbari, 1495, (Museo di Capodimonte).
23.
Irrational numbers
–
In mathematics, an irrational number is a real number that cannot be expressed as a ratio of integers, i.e. as a fraction. Therefore, irrational numbers, when written as decimal numbers, do not terminate, nor do they repeat. The same can be said for any irrational number. As a consequence of Cantor's proof that the real numbers are uncountable and the rationals countable, it follows that almost all real numbers are irrational. The first proof of the existence of irrational numbers is usually attributed to a Pythagorean, who probably discovered them while identifying sides of the pentagram. His reasoning is as follows: Start with an isosceles right triangle with side lengths of integers a, b, c. The ratio of the hypotenuse to a leg is represented by c:b. Assume a, b, c are in the smallest possible terms. By the Pythagorean theorem: c2 = a2+b2 = b2+b2 = 2b2. . Since c2 = 2b2, c2 is divisible by 2, therefore even. Since c2 is even, c must be even. Since c and b have no common factors, c is even, b must be odd. Since c is even, dividing c by 2 yields an integer. Let y be this integer.
Irrational numbers
–
The mathematical constant pi (π) is an irrational number that is much represented in popular culture.
24.
Prime numbers
–
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1, not a prime number is called a composite number. The property of being prime is called primality. A slow method of verifying the primality of a given n is known as trial division. It consists of testing whether n is a multiple of any integer between 2 and n. Algorithms much more efficient than trial division have been devised to test the primality of large numbers. Particularly fast methods are available for numbers of special forms, such as Mersenne numbers. As of January 2016, the largest known prime number has 22,338,618 decimal digits. There are infinitely many primes, as demonstrated by Euclid around 300 BC. There is no known simple formula that separates prime numbers from composite numbers. However, the distribution of primes, to say, the statistical behaviour of primes in the large, can be modelled. Many questions regarding prime numbers remain open, such as the prime conjecture. Such questions spurred the development of various branches of theory, focusing on algebraic aspects of numbers. Prime numbers give rise to various generalizations in mainly algebra, such as prime ideals. A natural number is called a prime number if it has exactly two positive divisors, 1 and the number itself.
Prime numbers
–
The number 12 is not a prime, as 12 items can be placed into 3 equal-size columns of 4 each (among other ways). 11 items cannot be all placed into several equal-size columns of more than 1 item each without some extra items leftover (a remainder). Therefore, the number 11 is a prime.
25.
Golden ratio
–
The figure on the right illustrates the geometric relationship. Its value is: φ = 1 + 2 = 1.6180339887.... The golden ratio is also called the golden mean or golden section. Other names mean ratio, medial section, divine proportion, divine section, golden proportion, golden cut, golden number. The golden ratio appears in some patterns including the spiral arrangement of leaves and other plant parts. Two quantities a and b are said to be in the golden φ if a + b a = a b = φ. One method for finding the value of φ is to start with the left fraction. Through substituting in b/a = 1 / φ, a + b a = 1 + b a = 1 + 1 φ. Therefore, 1 + φ = φ. Multiplying by φ gives φ + 1 = φ 2 which can be rearranged to φ 2 − φ − 1 = 0. Now the semicircle is drawn around the point B. The arising intersection E corresponds 2 φ. Up, the perpendicular on the line segment A E ¯ from the point D will be establish. The parallel F S ¯ to the line segment C M ¯, produces, as it were, the hypotenuse of the right triangle S D F. It is well recognizable, the triangle M S C are similar to each other.
Golden ratio
–
Michael Maestlin, first to publish a decimal approximation of the golden ratio, in 1597
Golden ratio
–
Line segments in the golden ratio
Golden ratio
–
Many of the proportions of the Parthenon are alleged to exhibit the golden ratio.
Golden ratio
–
The drawing of a man's body in a pentagram suggests relationships to the golden ratio.
26.
Camposanto Monumentale
–
The Campo Santo, also known as Camposanto Monumentale or Camposanto Vecchio, is a historical edifice at the northern edge of the Cathedral Square in Pisa, Italy. A legend claims that bodies buried in that ground will rot in just 24 hours. The term "monumental" serves to differentiate it from the later-established urban cemetery in Pisa. The building was the fourth and last one to be raised in the Cathedral Square. It was erected over the earlier ground. The construction of this Gothic cloister was begun in 1278 by the architect Giovanni di Simone. He died in 1284 when Pisa suffered a defeat in the naval battle of Meloria against the Genoans. The cemetery was only completed in 1464. The project changed during the construction. However we know that the original part was the western one, all the eastern part was the last to be built, finally closing the structure. The outer wall is composed of 43 blind arches. There are two doorways. The one on the right is crowned by a gracious Gothic tabernacle. It contains the Virgin Mary with Child, surrounded by four saints. It is the work from the second half of the 14th century by a follower of Giovanni Pisano.
Camposanto Monumentale
–
The Campo Santo
Camposanto Monumentale
–
Interior courtyard
Camposanto Monumentale
–
Interior hallway, pictured in 2012
Camposanto Monumentale
–
The Triumph of Death
27.
Piazza dei Miracoli
–
The square is sometimes called the Campo dei Miracoli. In 1987, the whole square was declared a UNESCO World Heritage Site. The heart of the Piazza del Duomo is the medieval cathedral of the Archdiocese of Pisa, dedicated to Santa Maria Assunta. The cathedral has two aisles on either side of the nave. The transept consists of three aisles. The church is known also as the archbishop of Pisa being a Primate since 1092. Its construction began by the architect Buscheto. It set the model for the Pisan Romanesque style of architecture. The mosaics of the interior, well as the pointed arches, show a strong Byzantine influence. Main doors were made in the workshops of Giambologna, replacing the original doors destroyed in a fire in 1595. The central door was of bronze, made around 1180 by Bonanno Pisano, while the other two were probably of wood. Above the doors are four rows of open galleries on top, statues of Madonna with Child and, on the corners, the Four evangelists. Also in the façade is found the tomb of Buscheto and an inscription about the foundation of the Cathedral and the victorious battle against the Saracens. The interior has a gilded ceiling and a frescoed dome. It was largely redecorated after a fire in 1595, which destroyed most of the Renaissance art works.
Piazza dei Miracoli
–
UNESCO World Heritage Site
Piazza dei Miracoli
–
Pisa Cathedral façade
Piazza dei Miracoli
–
Pisa Cathedral with the Leaning Tower of Pisa
Piazza dei Miracoli
–
Pisa Cathedral interior and Galileo's Lamp
28.
The Fibonaccis
–
The Fibonaccis were an American art rock band formed in 1981 in Los Angeles. The band consisted of songwriters John Dentino and Ron Stringer, Magie Song, later Tom Corey. The Fibonaccis were formed out of the Los Angeles art scene which included bands such as Wall of Voodoo, Oingo Boingo and Sparks. Lyrically, the band regularly explored esoteric subject matter ranging from serial killers to UFOs, presented in a satirical and surrealist fashion. The Fibonaccis released their EP in 1982, following up with a 12" single/EP, Tumor/Psycho/Slow Beautiful Sex, the next year. In 1984, the group independently filmed a video for an unreleased cover of Jimi Hendrix's "Purple Haze". Throughout their career, The Fibonaccis regularly contributed their music to independent film soundtracks. In 1986, the band collaborated on the score for the horror-comedy TerrorVision recording five tracks including the movie's theme song. Their song "Sergio Leone" was used for the closing credits of the previously unrecorded track "Art Life" was featured in 1987's Slam Dance. In 1987, the band released their sole studio LP, Its Discotheques on the Blue Yonder Sounds label. In explaining the reason for the LP's delay, the group said that various difficulties with record companies had plagued a more timely release. Their frustration over the album's recording, added with a lack of media recognition, led in 1988. In 1992, Restless Records released a 26-track retrospective of the band's work called Repressed - The Best of the Fibonaccis. To celebrate the release of the album, The Fibonaccis performed a one-off reunion show on November 19, 1992, their final public performance. Following The Fibonaccis' disbandment, John Dentino has recently been working on independent documentary films.
The Fibonaccis
–
The Fibonaccis, circa 1982. Left to right: Berardi, Dentino, Corey and Song.
29.
Surveying
–
Surveying or land surveying is the technique, profession, science of determining the terrestrial or three-dimensional position of points and the distances and angles between them. A land surveying professional is called a land surveyor. Surveyors work with elements of geometry, trigonometry, regression analysis, physics, engineering, the law. They use equipment like total stations, robotic total stations, GPS receivers, retroreflectors, 3D scanners, radios, handheld tablets, digital levels, surveying software. Surveying has been an element in the development of the human environment since the beginning of recorded history. The planning and execution of most forms of construction require it. It is also used in transport, the definition of legal boundaries for land ownership. It is an important tool for research in scientific disciplines. Basic surveyance has occurred since humans built the first large structures. The prehistoric monument at Stonehenge was set out by prehistoric surveyors using geometry. In ancient Egypt, a rope stretcher would use simple geometry to re-establish boundaries after the annual floods of the Nile River. The almost perfect squareness and north-south orientation of the Great Pyramid of Giza, built c. 2700 BC, affirm the Egyptians' command of surveying. The Groma instrument originated in Mesopotamia. The mathematician Liu Hui described ways of measuring distant objects in his work Haidao suanjing or The Sea Island Mathematical Manual, published in 263 AD. The Romans recognized land surveyors as a profession.
Surveying
–
A surveyor at work with an infrared reflector used for distance measurement.
Surveying
–
Table of Surveying, 1728 Cyclopaedia
Surveying
–
A map of India showing the Great Trigonometrical Survey, produced in 1870
Surveying
–
A German engineer surveying during the First World War, 1918
30.
Measurement
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Measurement is the assignment of a number to a characteristic of an object or event, which can be compared with other objects or events. The scope and application of a measurement is dependent on the context and discipline. Measurement is a cornerstone of quantitative research in many disciplines. Historically, many measurement systems existed for the varied fields of human existence to facilitate comparisons in these fields. Often these were achieved by local agreements between trading partners or collaborators. Since the 18th century, developments progressed towards unifying, widely accepted standards that resulted in the modern International System of Units. This system reduces all physical measurements to a mathematical combination of seven base units. The science of measurement is pursued in the field of metrology. The measurement of a property may be categorized by the following criteria: uncertainty. They enable unambiguous comparisons between measurements. The type or level of measurement is a taxonomy for the methodological character of a comparison. For example, two states of a property may be compared by preference. The type is commonly not explicitly expressed, but implicit in the definition of a measurement procedure. The magnitude is the numerical value of the characterization, usually obtained with a suitably chosen measuring instrument. An uncertainty represents the systemic errors of the procedure; it indicates a level in the measurement.
Measurement
–
A typical tape measure with both metric and US units and two US pennies for comparison
Measurement
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A baby bottle that measures in three measurement systems, Imperial (U.K.), U.S. customary, and metric.
Measurement
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Four measuring devices having metric calibrations
31.
Area
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Area is the quantity that expresses the extent of a two-dimensional figure or shape, or planar lamina, in the plane. Surface area is its analog on the two-dimensional surface of a three-dimensional object. It is the two-dimensional analog of the volume of a solid. The area of a shape can be measured by comparing the shape to squares of a fixed size. A shape with an area of three square metres would have the same area as three such squares. In mathematics, the area of any other shape or surface is a dimensionless real number. There are well-known formulas for the areas of simple shapes such as triangles, rectangles, circles. Using these formulas, the area of any polygon can be found by dividing the polygon into triangles. For shapes with curved boundary, calculus is usually required to compute the area. Indeed, the problem of determining the area of plane figures was a major motivation for the historical development of calculus. For a solid shape such as a sphere, cylinder, the area of its boundary surface is called the surface area. Area plays an important role in modern mathematics. In analysis, the area of a subset of the plane is defined using Lebesgue measure, though not every subset is measurable. In general, area in higher mathematics is seen as a special case of volume for two-dimensional regions. It can be proved that such a function exists.
Area
–
A square metre quadrat made of PVC pipe.
Area
–
The combined area of these three shapes is approximately 15.57 squares.
32.
Volume
–
Volume is the quantity of three-dimensional space enclosed by a closed surface, for example, the space that a substance or shape occupies or contains. Volume is often quantified numerically using the cubic metre. Three mathematical shapes are also assigned volumes. Circular shapes can be easily calculated using arithmetic formulas. Volumes of a complicated shape can be calculated by integral calculus if a formula exists for the shape's boundary. Two-dimensional shapes are assigned zero volume in the three-dimensional space. The volume of a solid can be determined by fluid displacement. Displacement of liquid can also be used to determine the volume of a gas. The combined volume of two substances is usually greater than the volume of one of the substances. However, sometimes one substance dissolves in the combined volume is not additive. In geometry, volume is expressed by means of the volume form, is an important global Riemannian invariant. In thermodynamics, volume is a conjugate variable to pressure. Any unit of length gives a corresponding unit of volume: the volume of a cube whose sides have the given length. For example, a cubic centimetre is the volume of a cube whose sides are one centimetre in length. In the International System of Units, the standard unit of volume is the cubic metre.
Volume
–
A measuring cup can be used to measure volumes of liquids. This cup measures volume in units of cups, fluid ounces, and millilitres.
33.
Geometry
–
Geometry is a branch of mathematics concerned with questions of shape, size, relative position of figures, 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 for dealing with lengths, areas, volumes. Geometry began to see elements of mathematical science emerging in the West as early as the 6th century BC. By the 3rd BC, geometry was put into an axiomatic form by Euclid, whose treatment, Euclid's Elements, set a standard for many centuries to follow. Geometry arose independently with texts providing rules for geometric constructions appearing as early as the 3rd century BC. Islamic scientists expanded on them during the Middle Ages. By the 17th century, geometry had been put on a solid analytic footing by mathematicians such as René Descartes and Pierre de Fermat. Since then, into modern times, geometry has expanded into non-Euclidean geometry and manifolds, describing spaces that lie beyond the normal range of human experience. While geometry has evolved significantly throughout the years, there are some general concepts that are less fundamental to geometry. These include the concepts of points, lines, planes, surfaces, curves, as well as the more advanced notions of manifolds and topology or metric. Contemporary geometry has many subfields: Euclidean geometry is geometry in its classical sense. The educational curriculum of the majority of nations includes the study of points, lines, planes, angles, triangles, congruence, similarity, solid figures, circles, analytic geometry. Euclidean geometry also has applications in computer science, various branches of modern mathematics. Differential geometry uses techniques of linear algebra to study problems in geometry.
Geometry
–
Visual checking of the Pythagorean theorem for the (3, 4, 5) triangle as in the Chou Pei Suan Ching 500–200 BC.
Geometry
–
An illustration of Desargues' theorem, an important result in Euclidean and projective geometry
Geometry
–
Geometry lessons in the 20th century
Geometry
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A European and an Arab practicing geometry in the 15th century.
34.
Diophantine equation
–
In mathematics, a Diophantine equation is a polynomial equation, usually in two or more unknowns, such that only the integer solutions are sought or studied. A linear Diophantine equation is an equation between two sums of monomials of degree zero or one. An exponential Diophantine equation is one in which exponents on terms can be unknowns. Diophantine problems have fewer equations than unknown variables and involve finding integers that work correctly for all equations. In more technical language, they define an algebraic curve, algebraic surface, or more general object, ask about the lattice points on it. The mathematical study of Diophantine problems that Diophantus initiated is now called Diophantine analysis. Proof: If d is this greatest common divisor, Bézout's identity asserts the existence of integers e and f such that ae + bf = d. If c is a multiple of d, then c = dh for some integer h, is a solution. For every pair of integers x and y, the greatest common d of a and b divides ax + by. Thus, if the equation has a solution, then c must be a multiple of d. Finally, given two solutions such that ax1 + by1 = ax2 + by2 = c, one deduces that u + v = 0. Therefore, x2 = x1 + kv and y2 = y1 − ku, which completes the proof. The system to be solved may thus be rewritten as B = UC. If this condition is fulfilled, the solutions of the given system are V, where hk+1... hn are arbitrary integers. Hermite normal form may also be used for solving systems of linear Diophantine equations.
Diophantine equation
–
Finding all right triangles with integer side-lengths is equivalent to solving the Diophantine equation.
35.
Congruum
–
In number theory, a congruum is the difference between successive square numbers in an arithmetic progression of three squares. The problem is the problem of finding squares in arithmetic progression and their associated congrua. When this equation is satisfied, both sides of the equation equal the congruum. Fibonacci solved the congruum problem together with their associated arithmetic progressions. According to this formula, each congruum is four times the area of a Pythagorean triangle. For instance, the 96 is a congruum, since it is the difference between each pair of the three squares 4, 100, 196. The few congrua are: 24, 96, 120, 216, 240, 336, 384, 480, 600, 720.... Fibonacci did not give a satisfactory proof of this fact. The result is now known as Fermat's right triangle theorem. Leonhard Euler proved, that there is no sequence of four squares in arithmetic progression. The problem may be solved by choosing two distinct positive integers m and n; then the number 4mn is a congruum. The other two squares may be found by adding or subtracting the congruum. Additionally, produces another congruum, whose progression of squares is multiplied by the same factor. All solutions arise in one of these two ways. The congruum itself is four times the area of the same Pythagorean triangle.
Congruum
–
The two right triangles with leg and hypotenuse (7,13) and (13,17) have equal third sides of length √120. The square of this side, 120, is a congruum: it is the difference between consecutive values in the arithmetic progression of squares 7 2, 13 2, 17 2. Equivalently, the two annuli between the three yellow circles have equal areas, π times the congruum.
36.
Euclid's Elements
–
Euclid's Elements is a mathematical and geometric treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt circa 300 BC. It is a collection of definitions, postulates, mathematical proofs of the propositions. The books cover the ancient Greek version of elementary number theory. It is the oldest extant axiomatic deductive treatment of mathematics. It has proven instrumental in the development of logic and modern science. According to Proclus, the term "element" was used to describe a theorem that helps furnishing proofs of many other theorems. The element in the Greek language is the same as letter. This suggests that theorems in the Elements should be seen as standing as letters to language. Euclid's Elements has been referred to as the most influential textbook ever written. Scholars believe that the Elements is largely a collection of theorems proven by other mathematicians, supplemented by some original work. The Heiberg manuscript, is from a Byzantine workshop around 900 and is the basis of modern editions. Papyrus Oxyrhynchus 29 only contains the statement of one proposition. Although known to, for instance, Cicero, no record exists of the text having been translated prior to Boethius in the fifth or sixth century. The Arabs received the Elements around 760; this version was translated into Arabic under Harun al Rashid circa 800. The Byzantine scholar Arethas commissioned the copying of the extant Greek manuscripts of Euclid in the late ninth century.
Euclid's Elements
–
The frontispiece of Sir Henry Billingsley's first English version of Euclid's Elements, 1570
Euclid's Elements
–
A fragment of Euclid's "Elements" on part of the Oxyrhynchus papyri
Euclid's Elements
–
An illumination from a manuscript based on Adelard of Bath 's translation of the Elements, c. 1309–1316; Adelard's is the oldest surviving translation of the Elements into Latin, done in the 12th-century work and translated from Arabic.
Euclid's Elements
–
Euclidis – Elementorum libri XV Paris, Hieronymum de Marnef & Guillaume Cavelat, 1573 (second edition after the 1557 ed.); in-8, 350, (2)pp. THOMAS-STANFORD, Early Editions of Euclid's Elements, n°32. Mentioned in T.L. Heath's translation. Private collection Hector Zenil.
37.
Fibonacci numbers in popular culture
–
The Fibonacci numbers, in the golden ratio, are a popular theme in culture. They have been mentioned in novels, films, songs. The numbers have also been used in the creation of music, architecture. Stock traders frequently look to the "Fibonacci retracement" when predicting future share prices. The sequence has been used in the design of a building, the Core, near St Austell, Cornwall, England. In 21, the first seven numbers in the Fibonacci Sequence are drawn in icing on Ben's cake. 21, is left out. Ben and Miles quickly figure it out. Along with golden spiral, the Fibonacci sequence is mentioned in Darren Aronofsky's independent film Pi. They are used to find the name of God. In The Da Vinci Code, the numbers are used to unlock a safe. They are also placed out in a message to indicate that the message is also out of order. In Mr. Magorium's Wonder Emporium, Magorium hires accountant Henry Weston after an interview in which he demonstrates knowledge of Fibonacci numbers. In Death Note: the World, genius boy Near is seen arranging sugar cubes in a Fibonacci sequence. In a strip of Frazz by Jef Mallett, a student are discussing her knitted hat.
Fibonacci numbers in popular culture
–
Chimney of Turku Energia, Turku, Finland featuring Fibonacci sequence in 2m high neon lights. By Italian artist Mario Merz for an environmental art project (1994)
Fibonacci numbers in popular culture
–
Martina Schettina: Fibonaccis Dream, 2008, 40 x 40 cm
38.
Keith Devlin
–
Keith J. Devlin is a British mathematician and popular science writer. Since 1987 he has lived in the United States. He has American-British citizenship. He is a commentator on National Public Radio's Weekend Edition Saturday, where he is known as "The Math Guy." As of 2012, he is the author of over 80 research articles. Several of his books are aimed at an audience of the general public. Springer. 1984. ISBN 3-540-13258-9. Logic and Information. Cambridge University Press. 1991. ISBN 0-521-49971-2. The Joy of Sets: Fundamentals of Contemporary Set Theory. Springer.
Keith Devlin
–
Keith Devlin (2011)
39.
MS Word
–
Microsoft Word is a word processor developed by Microsoft. Word was first released under the name Multi-Tool Word for Xenix systems. Commercial versions of Word are licensed as a component of Microsoft Office, Windows RT or the discontinued Microsoft Works suite. Microsoft Word Viewer and Office Online are freeware editions of Word with limited features. In 1981, Microsoft hired Charles Simonyi, the first GUI word processor, developed at Xerox PARC. Simonyi started work on a processor called Multi-Tool Word and soon hired Richard Brodie, a former Xerox intern, who became the primary software engineer. Microsoft announced Multi-Tool Word for Xenix and MS-DOS in 1983. Its name was soon simplified to Microsoft Word. Microsoft demonstrated Word running on Windows. Unlike most MS-DOS programs at the time, Microsoft Word was designed to be used with a mouse. Word was not initially popular, since its interface was different from the leading word processor at the time, WordStar. However, Microsoft steadily improved the product, releasing versions 2.0 over the next six years. In 1985, Microsoft ported Word to Mac OS. Following the precedents of LisaWrite and MacWrite, Word for Mac OS added true WYSIWYG features. Word fulfilled a need for a processor, more capable than MacWrite.
MS Word
–
Microsoft Office Word 2013 on Windows 8
40.
International Standard Book Number
–
The International Standard Book Number is a unique numeric commercial book identifier. An ISBN is assigned to each variation of a book. For example, an e-book, a hardcover edition of the same book would each have a different ISBN. The ISBN is 13 digits long if assigned after 1 January 2007, 10 digits long if assigned before 2007. The method of assigning an ISBN varies from country to country, often depending on how large the publishing industry is within a country. The initial ISBN configuration of recognition was generated based upon the 9-digit Standard Book Numbering created in 1966. The 10-digit ISBN format was published in 1970 as international standard ISO 2108. The International Standard Serial Number, identifies periodical publications such as magazines; and the International Standard Music Number covers for musical scores. The ISBN configuration of recognition was generated in 1967 in the United Kingdom by Emery Koltay. The 10-digit ISBN format was published as international standard ISO 2108. The United Kingdom continued to use the 9-digit SBN code until 1974. The ISO on-line facility only refers back to 1978. An SBN may be converted by prefixing the digit "0". This can be converted to ISBN 0-340-01381-8; the digit does not need to be re-calculated. Since 1 ISBNs have contained 13 digits, a format, compatible with "Bookland" European Article Number EAN-13s.
International Standard Book Number
–
A 13-digit ISBN, 978-3-16-148410-0, as represented by an EAN-13 bar code
41.
Yale School of Management
–
The Yale School of Management is the graduate business school of Yale University and is located on Whitney Avenue in New Haven, Connecticut, United States. Beginning in the 2017-2018 school year, the school will launch a one-year Master of Management Studies degree in Systemic Risk. The School has 86 full-time faculty members, the dean is Edward A. Snyder. The School conducts research in leadership, behavioral economics, operations management, marketing, entrepreneurship, other areas. The EMBA program offers focused study in sustainability. Beginning in the 1950s, Yale University started to expand coursework offerings in management. In 1971, Yale University received a donation establishing a program in management from Frederick W. Beinecke, PhB 1909. Two years later, the Yale Corporation approved the establishment of a School of Organization and Management. Arriving in 1976, the first class of the two-year program that awarded a master's degree in public and private management attended the campus on Hillhouse Avenue. Thereafter in 1999, the School discontinued the MPPM degree. In 2006 it introduced its team-taught "Integrated Curriculum" for all MBA students. An inaugural conference entitled "Business + Society: Leadership in an Increasingly Complex World" marked the opening of the new campus. The three-day conference examined major trends transforming markets and organizations around the world. Edward P. Evans Hall houses technology-enabled classrooms, student and meeting spaces organized around an enclosed courtyard. The Master of Advanced Management program is a one-year program based at SOM's New Haven campus for business students from Global Network for Advanced Management schools.
Yale School of Management
–
Yale SOM Logo
Yale School of Management
Yale School of Management
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Founders Hall, the school's former main building
Yale School of Management
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Steinbach Hall, a mansion formerly used by the school on Hillhouse Avenue
42.
Wikisource
–
Wikisource is an online digital library of free content textual sources on a wiki, operated by the Wikimedia Foundation. The project's aims are to host all forms of free text, in many languages, translations. Originally conceived as an archive to store important historical texts, it has expanded to become a general-content library. The project officially began under the name Project Sourceberg. It received its own domain name seven months later. It is also cited by organisations such as the National Archives and Records Administration. Verification was initially made offline, or by trusting the reliability of digital libraries. Now works are supported by online scans via the ProofreadPage extension, which ensures the accuracy of the project's texts. Each representing a specific language, now only allow works backed up with scans. While the bulk of its collection are texts, Wikisource as a whole hosts other media, to audio books. Some Wikisources allow user-generated annotations, subject to the specific policies of the Wikisource in question. Wikisource's early history included the move to language subdomains in 2005. The original concept for Wikisource was as storage for important historical texts. These texts were intended to support Wikipedia articles, as an archive in its own right. The collection was initially focused on important cultural material, distinguishing it from other digital archives such as Project Gutenberg.
Wikisource
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The original Wikisource logo
Wikisource
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Screenshot of wikisource.org home page
Wikisource
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::: Original text
Wikisource
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::: Action of the modernizing tool
43.
University of St Andrews
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The University of St Andrews is a British public research university in St Andrews, Fife, Scotland. It is the oldest of the four ancient universities of Scotland and the third oldest university in the English-speaking world. St Andrews was founded between 1413, when the Avignon Antipope Benedict XIII issued a papal bull to a small group of Augustinian clergy. St Andrews is made up including 18 academic schools organised into four faculties. The university occupies historic and modern buildings located throughout the town. The academic year is divided into Candlemas. In time, over one-third of the town's population is either a staff student of the university. It is ranked behind Oxbridge. The Times Higher Education World Universities Ranking names St Andrews among the world's Top 50 universities for Social Sciences, Arts and Humanities. St Andrews has the highest student satisfaction amongst all multi-faculty universities in the United Kingdom. St Andrews has affiliated faculty, including eminent mathematicians, scientists, theologians, politicians. Six Nobel Laureates are amongst St Andrews' alumni and former staff: two in Chemistry and Physiology or Medicine, one each in Peace and Literature. A charter of privilege was bestowed by the Bishop of Henry Wardlaw, on 28 February 1411. King James I of Scotland confirmed the charter of the university in 1432. Subsequent kings supported the university with King James V "confirming privileges of the university" in 1532.
University of St Andrews
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College Hall, within the 16th century St Mary's College building
University of St Andrews
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University of St Andrews shield
University of St Andrews
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St Salvator's Chapel in 1843
University of St Andrews
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The "Gateway" building, built in 2000 and now used for the university's management department
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Linda Hall Library
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It is the "largest independently funded public library of science, engineering and technology in the world." Established through the philanthropy of Linda and Herbert F. Hall, of the Hall-Bartlett Grain Co. the library has achieved global recognition and stature. The library's William N. Deramus III Cosmology Theater shows images of the cosmos from the Hubble Space Telescope and NASA science missions. These images are delivered to the library with daily updates that provide the library with new content for visitors. The library's collection numbers over million items. The library's distinguished History of Science Collection contains more than 10,000 volumes, including first editions of many landmarks of technology. Some of the oldest books in the collection date back to the fifteenth century. Online Tycho Brahe's 1632 Astronomicall Coniectur Georg Joachim Rheticus's Narratio Prima. Nicolaus Copernicus, De revolutionibus coelestium. Leonhard Fuchs, De historia stirpium. Galileo Galilei, Sidereus nuncius. Francis Bacon, Instauratio magna. Isaac Newton, Philosophiae naturalis mathematica. Georges Buffon, Histoire naturelle. Charles Darwin, On the Origin of Species.
Linda Hall Library
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Linda Hall Library Main Reading Room
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Virtual International Authority File
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The Virtual International Authority File is an international authority file. It operated by the Online Computer Library Center. The project was initiated by the US Library of Congress. The aim is to link the national authority files to a virtual authority file. In this file, identical records from the different sets are linked together. The data are available for research and data exchange and sharing. Reciprocal updating uses the Open Archives Initiative protocol. The file numbers are incorporated into Wikidata. VIAF's clustering algorithm is run every month. Integrated Authority File International Standard Name Identifier Wikipedia's authority control template for articles Official website
Virtual International Authority File
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Screenshot 2012
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Integrated Authority File
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The Integrated Authority File or GND is an international authority file for the organisation of personal names, subject headings and corporate bodies from catalogues. It is used mainly increasingly also by archives and museums. The GND is managed with various regional library networks in German-speaking Europe and other partners. The GND falls under the Creative Commons Zero license. The GND specification provides a hierarchy of high-level sub-classes, useful in library classification, an approach to unambiguous identification of single elements. It also comprises an ontology intended for knowledge representation in the semantic web, available in the RDF format.
Integrated Authority File
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GND screenshot
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Union List of Artist Names
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The Union List of Artist Names is an online database using a controlled vocabulary currently containing around 293,000 names and other information about artists. Names in ULAN may include given names, pseudonyms, variant spellings, names that have changed over time. Among these names, one is flagged as the preferred name. The focus of each ULAN record is an artist. Currently there are around 120,000 artists in the ULAN. In the database, each record is identified by a unique numeric ID. Linked to each artist record are names, related artists, sources for the data, notes. The scope is global. The ULAN associated information about artists. Artists may be either groups of individuals working together. Artists in the ULAN generally represent creators involved in the production of visual arts and architecture. Some performance artists are included. Some donors are included as well. In 1987 the Getty created a department dedicated to distributing terminology. The ULAN changes via contributions from the user community and editorial work of the Getty Vocabulary Program.
Union List of Artist Names
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Contents
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National Library of Australia
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In 2012 -- 2013, the National Library collection comprised an additional 15,506 metres of manuscript material. In 1901, a Commonwealth Parliamentary Library was established to serve the newly formed Federal Parliament of Australia. From its inception the Commonwealth Parliamentary Library was driven to development of a truly national collection. The present building was opened in 1968. The building was designed by the architectural firm of Bunning and Madden. The foyer is decorated in marble, with stained-glass windows by Mathieu Matégot. In 2012–2013 the Library collection comprised 6,496,772 items, with an estimated additional 2,325,900 items held in the manuscripts collection. The Library's collections of Australiana have developed into the nation's single most important resource of materials recording the cultural heritage. Australian writers, illustrators are actively sought and well represented -- whether published in Australia or overseas. Approximately 92.1 % of the Library's collection is discoverable through the online catalogue. The Library has digitized over 174,000 items from its collection and, where possible, delivers these directly across the Internet. The Library maintains an Internet-accessible archive of selected Australian websites called the Pandora Archive. The Library has particular collection strengths in the performing arts, including dance. The Library's considerable collections of general rare book materials, as well as world-class Asian and Pacific collections which augment the Australiana collections. The print collections are further supported by extensive microform holdings.
National Library of Australia
National Library of Australia
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National Library of Australia as viewed from Lake Burley Griffin, Canberra
National Library of Australia
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The original National Library building on Kings Avenue, Canberra, was designed by Edward Henderson. Originally intended to be several wings, only one wing was completed and was demolished in 1968. Now the site of the Edmund Barton Building.
National Library of Australia
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The library seen from Lake Burley Griffin in autumn.
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Fibonacci
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Fibonacci popularized the Hindu–Arabic numeral system to the Western World primarily through his composition in 1202 of Liber Abaci. He also introduced Europe to the sequence of Fibonacci numbers, which he used as an example in Liber Abaci. Fibonacci was born for Pisa. Guglielmo directed a post in North Africa. It was in Bugia that he learned about the Hindu -- Arabic system. Fibonacci travelled extensively around the Mediterranean coast, meeting with many merchants and learning about their systems of doing arithmetic. He soon realised the many advantages of the Hindu-Arabic system. In 1202, he completed the Liber Abaci which popularized Hindu–Arabic numerals in Europe. Fibonacci became a guest of Emperor Frederick II, who enjoyed mathematics and science. It has been estimated to be between 1250, most likely in Pisa. In the Liber Abaci, Fibonacci introduced the so-called modus Indorum, today known as Hindu-Arabic numerals. The book advocated place value. The book was well-received throughout educated Europe and had a profound impact on European thought. No copies of the 1202 edition are known to exist. The book also discusses irrational numbers and prime numbers.
Fibonacci
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Portrait by an unknown artist
Fibonacci
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A page of Fibonacci's Liber Abaci from the Biblioteca Nazionale di Firenze showing (in box on right) the Fibonacci sequence with the position in the sequence labeled in Roman numerals and the value in Hindu-Arabic numerals.
Fibonacci
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19th century statue of Fibonacci in Camposanto, Pisa.