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Fibonacci
Leonardo Bonacci ( – ), commonly known as Fibonacci, was an Italians, Italian mathematician from the Republic of Pisa, considered to be "the most talented Western mathematician of the Middle Ages". The name he is commonly called, ''Fibonacci'', is first found in a modern source in a 1838 text by the Franco-Italian mathematician Guglielmo Libri Carucci dalla Sommaja, Guglielmo Libri and is short for ('son of Bonacci'). However, even as early as 1506, Perizolo, a notary of the Holy Roman Empire, mentions him as "Lionardo Fibonacci". Fibonacci popularized the Hindu–Arabic numeral system, Indo–Arabic numeral system in the Western world primarily through his composition in 1202 of (''Book of Calculation'') and also introduced Europe to the sequence of Fibonacci numbers, which he used as an example in . Biography Fibonacci was born around 1170 to Guglielmo, an Italian merchant and customs official who directed a trading post in Béjaïa, Bugia, modern-day Béjaïa, Algeria ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fibonacci Number
In mathematics, the Fibonacci sequence is a Integer sequence, sequence in which each element is the sum of the two elements that precede it. Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers, commonly denoted . Many writers begin the sequence with 0 and 1, although some authors start it from 1 and 1 and some (as did Fibonacci) from 1 and 2. Starting from 0 and 1, the sequence begins : 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ... The Fibonacci numbers were first described in Indian mathematics as early as 200 BC in work by Pingala on enumerating possible patterns of Sanskrit poetry formed from syllables of two lengths. They are named after the Italian mathematician Leonardo of Pisa, also known as Fibonacci, who introduced the sequence to Western European mathematics in his 1202 book . Fibonacci numbers appear unexpectedly often in mathematics, so much so that there is an entire journal dedicated to their study, the ''Fibonacci Quarterly''. Appli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Liber Abaci
The or (Latin for "The Book of Calculation") was a 1202 Latin work on arithmetic by Leonardo of Pisa, posthumously known as Fibonacci. It is primarily famous for introducing both base-10 positional notation and the symbols known as Arabic numerals in Europe. Premise was among the first Western books to describe the Hindu–Arabic numeral system and to use symbols resembling modern "Arabic numerals". By addressing the applications of both commercial tradesmen and mathematicians, it promoted the superiority of the system and the use of these glyphs. Although the book's title is sometimes translated as "The Book of the Abacus", notes that it is an error to read this as referring to the abacus as a calculating device. Rather, the word "abacus" was used at the time to refer to calculation in any form; the spelling "abbacus" with two "b"s was, and still is in Italy, used to refer to calculation using Hindu-Arabic numerals, which can avoid confusion. The book describes methods o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formulas For Generating Pythagorean Triples
Besides Euclid's formula, many other formulas for generating Pythagorean triples have been developed. Euclid's, Pythagoras', and Plato's formulas Euclid's, Pythagoras' and Plato's formulas for calculating triples have been described here: The methods below appear in various sources, often without attribution as to their origin. Fibonacci's method Leonardo of Pisa () described this method for generating primitive triples using the sequence of consecutive odd integers 1,3,5,7,9,11,\ldots and the fact that the sum of the first terms of this sequence is n^2. If is the -th member of this sequence then n=(k+1)/2. Choose any odd square number from this sequence (k=a^2) and let this square be the -th term of the sequence. Also, let b^2 be the sum of the previous n-1 terms, and let c^2 be the sum of all terms. Then we have established that a^2+b^2=c^2 and we have generated the primitive triple . This method produces an infinite number of primitive triples, but not all of them. EXA ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Greedy Algorithm For Egyptian Fractions
In mathematics, the greedy algorithm for Egyptian fractions is a greedy algorithm, first described by Fibonacci, for transforming rational numbers into Egyptian fractions. An Egyptian fraction is a representation of an irreducible fraction as a sum of distinct unit fractions, such as . As the name indicates, these representations have been used as long ago as ancient Egypt, but the first published systematic method for constructing such expansions was described in 1202 in the '' Liber Abaci'' of Leonardo of Pisa (Fibonacci). It is called a greedy algorithm because at each step the algorithm chooses greedily the largest possible unit fraction that can be used in any representation of the remaining fraction. Fibonacci actually lists several different methods for constructing Egyptian fraction representations. He includes the greedy method as a last resort for situations when several simpler methods fail; see Egyptian fraction for a more detailed listing of these methods. The gre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hindu–Arabic Numeral System
The Hindu–Arabic numeral system (also known as the Indo-Arabic numeral system, Hindu numeral system, and Arabic numeral system) is a positional notation, positional Decimal, base-ten numeral system for representing integers; its extension to non-integers is the decimal, decimal numeral system, which is presently the most common numeral system. The system was invented between the 1st and 4th centuries by Indian mathematics, Indian mathematicians. By the 9th century, the system was adopted by Arabic mathematics, Arabic mathematicians who extended it to include fraction (mathematics), fractions. It became more widely known through the writings in Arabic of the Persian mathematician Al-Khwārizmī (''On the Calculation with Hindu Numerals'', ) and Arab mathematician Al-Kindi (''On the Use of the Hindu Numerals'', ). The system had spread to medieval Europe by the High Middle Ages, notably following Fibonacci's 13th century ''Liber Abaci''; until the evolution of the printing pre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Béjaïa
Béjaïa ( ; , , ), formerly known as Bougie and Bugia, is a Mediterranean seaport, port city and communes of Algeria, commune on the Gulf of Béjaïa in Algeria; it is the capital of Béjaïa Province. Geography Location Béjaïa owes its existence to its port, which also makes it prosperous. It is located in a sickle-shaped bay protected from the swell of offshore winds (northwest facing) by the advance of Cape Carbon (to the west of the city). The city is backed by :fr:Yemma Gouraya, Mount Gouraya located in a northwest position. This port site, in one of the most beautiful bays of the Maghreb and Mediterranean coast, is dominated in the background by the Babor Mountains, Babors mountain range. Another advantage is that the city is the outlet of the Soummam River, Soummam valley, a geographical corridor facing southwest. However, since the time when the city was a capital, there has been a divorce between the city and the region (Kabylia) linked to the difficulty of secur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Congruum
In number theory, a congruum (plural ''congrua'') is the difference between successive square numbers in an arithmetic progression of three squares. The congruum problem is the problem of finding squares in arithmetic progression and their associated congrua. It can be formalized as a Diophantine equation. Fibonacci solved the congruum problem by finding a parameterized formula for generating all congrua, together with their associated arithmetic progressions. According to this formula, each congruum is four times the area of a Pythagorean triangle, a right triangle whose sides are integers. Congrua are also closely connected with congruent numbers, the areas of right triangles whose sides are rational numbers. Every congruum is a congruent number, and every congruent number is a congruum multiplied by the square of a rational number. Fibonacci claimed without proof that it is impossible for a congruum to be a square number. This was later proven by Pierre de Fermat as Fermat's r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Of Palermo
John of Palermo () was a translator of mathematical works from Arabic to Latin who lived in Palermo, Sicily. He worked in the court of Emperor Frederick II. John had been introduced into the court of Frederick II through the mathematician Domenico Ispano. John is mentioned by Leonardo Fibonacci in his ''Liber quadratorum'' (1225) and several problems from Arab texts by Omar Khayyam Ghiyāth al-Dīn Abū al-Fatḥ ʿUmar ibn Ibrāhīm Nīshābūrī (18 May 1048 – 4 December 1131) (Persian language, Persian: غیاث الدین ابوالفتح عمر بن ابراهیم خیام نیشابورﻯ), commonly known as Omar ... were posed to Fibonacci. Some court documents mention a Johannes de Panormo who is thought to be the same person. John translated an Arab manuscript, possibly by Ibn al-Haytham, on the parabola into Latin as the ''De duabus lineis semper approximantibus sibi invicem et nunquam concurrentibus''. John as noted as a "notarius" and there are indications that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Italians
Italians (, ) are a European peoples, European ethnic group native to the Italian geographical region. Italians share a common Italian culture, culture, History of Italy, history, Cultural heritage, ancestry and Italian language, language. Their predecessors differ regionally, but generally include populations such as the Etruscan civilization, Etruscans, Rhaetians, Ligurians, Adriatic Veneti, Magna Graecia, Ancient Greeks and Italic peoples, including Latins (Italic tribe), Latins, from which Roman people, Romans emerged and helped create and evolve the modern Italian identity. Legally, Italian nationality law, Italian nationals are citizens of Italy, regardless of ancestry or nation of residence (in effect, however, Italian nationality law, Italian nationality is largely based on ''jus sanguinis'') and may be distinguished from ethnic Italians in general or from people of Italian descent without Italian citizenship and ethnic Italians living in territories adjacent to the I ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pisa
Pisa ( ; ) is a city and ''comune'' (municipality) in Tuscany, Central Italy, straddling the Arno just before it empties into the Ligurian Sea. It is the capital city of the Province of Pisa. Although Pisa is known worldwide for the Leaning Tower of Pisa, the city contains more than twenty other historic churches, several medieval palaces, and bridges across the Arno. Much of the city's architecture was financed from its history as one of the Italian maritime republics. The city is also home to the University of Pisa, which has a history going back to the 12th century, the Scuola Normale Superiore di Pisa, founded by Napoleon in 1810, and its offshoot, the Sant'Anna School of Advanced Studies.Scuola Superiore Sant'Anna di Pisa Information statistics History ...
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Frederick II, Holy Roman Emperor
Frederick II (, , , ; 26 December 1194 – 13 December 1250) was King of Sicily from 1198, King of Germany from 1212, King of Italy and Holy Roman Emperor from 1220 and King of Jerusalem from 1225. He was the son of Emperor Henry VI, Holy Roman Emperor, Henry VI of the Hohenstaufen dynasty (the second son of Emperor Frederick Barbarossa) and Queen Constance I of Sicily of the Hauteville dynasty. Frederick was one of the most powerful figures of the Middle Ages and ruled a vast area, beginning with Sicily and stretching through Italy all the way north to Germany. Viewing himself as a direct successor to the Roman emperors of antiquity, he was Holy Roman Emperor, Emperor of the Romans from his papal coronation in 1220 until his death; he was also a claimant to the title of King of the Romans from 1212 and unopposed holder of that monarchy from 1215. As such, he was King of Germany, King of Italy, of Italy, and King of Burgundy, of Burgundy. At the age of three, he was crowned King ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Keith Devlin
Keith James Devlin (born 16 March 1947) is a British mathematician and popular science writer. Since 1987 he has lived in the United States. He has dual British-American citizenship.Curriculum vitae Profkeithdevlin.com, accessed 3 February 2014. Education He was born and grew up in England, in Kingston upon Hull, where he attended Greatfield Estate, Kingston upon Hull#Schools, Greatfield High School. Devlin earned a BSc (special) in mathematics at King's College London in 1968, and a mathematics PhD in logic at the University of Bristol in 1971 under the supervision of Frederick Rowbottom.Career Later he got a position as a scientific assistant in mathematics at the University of Oslo, Norway, from August till December 1972. In 1974 he became a scientific assist ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
