Fibonacci, Leonardo approximately 1170-approximately 1240 [WorldCat Identities] The book of squares by Leonardo Fibonacci( Book ) 8 editions published between 1978 and 1988 in English and Undetermined and held by 21 WorldCat member libraries worldwide The Book of Squares by Fibonacci is a gem in the mathematical literature and one of the most important mathematical treatises written in the Middle Ages. It is a collection of theorems on indeterminate analysis and equations of second degree which yield, among other results, a solution to a problem proposed by Master John of Palermo to Leonardo at the Court of Frederick II. The book was dedicated and presented to the Emperor at Pisa in 1225. Dating back to the 13th century the book exhibits the early and continued fascination of men with our number system and the relationship among numbers with special properties such as prime numbers, squares, and odd numbers.

The faithful translation into modern English and the commentary by the translator make this book accessible to professional mathematicians and amateurs who have always been intrigued by the lure of our number system Pianography : prepared piano by Richard Bunger( ) 2 editions published in 1981 and held by 14 WorldCat member libraries worldwide Fibonacci, Leonardo by Cody Naeger Leonardo Pisano, or better known by his nickname Fibonacci, was born in Pisa which is in present day Italy. He was the son of Guilielmo and also belonged to the Bonacci family. His father was a representative of the merchants of Pisa who were trading in what is now present day Bejia. There are no records that show that Leonardo had any brothers or sisters which was probably due to his constant moving from place to place. For this reason also would explain why there are no records of Fibonacci to have a wife or children. Leonardo got most of his schooling in Northern Africa, and learned a lot of math from the Arabic traders that his father dealt with. The Holy Roman Emperor Frederick II was one of Fibonacci's biggest fans of his time. Frederick hired Fibonacci to help teach the people of Rome and to also be an accountant for a short time.

Fibonacci worked with his father in the merchant business for a few years, but he returned home to pursue his mathematical career. He never held a steady job; he was mainly busy with writing his many books. Fibonacci's accomplishments include introducing the decimal system into European culture, a more complex description of algorithm, and the Fibonacci series. The Fibonacci series is his most remembered accomplishment. The Fibonacci series starts with a problem like this ï¿½ a pair of rabbits are put in a field and, if rabbits take a month to become mature and then produce a new pair every month after that, how many pairs will there be in twelve months time?ï¿½ The series of numbers that are used to solve this are 1, 1, 2, 3, 5, 8, 13, 21, 34, 55ï¿½this is called the Fibonacci series. Leonardo is assumed to have died around 1240 at the age of about 70. There is no fact or proof that he did die at this time because the only thing to support this theory is that fact that recordings of his life stopped in 1240.

There is no proof to his death at this time or any other time at that which leaves the question of how or even if he died open. Fibonacci had a few oddities, which were he didn't refer to himself as Fibonacci because he was called this some 300yrs after his works, he used the name Bigollo sometimes which means good-for-nothing or a traveler, he hand wrote his 5 works: Liber Abbaci, Practica geometriae, Flos, Liber quadratorum, A letter to Master Theodorus. fUSION Anomaly. Fibonacci This nOde last updated December 30th, 2006 and is permanently morphing... (5 Caban (Earth) / 10 K'ank'in - 57/260 - 12.19.13.16.17) Fibonacci sequence noun The sequence of numbers, 1, 1, 2, 3, 5, 8, 13, . . . , in which each successive number is equal to the sum of the two preceding numbers. [After Leonardo Fibonacci (died c.

1250), Italian mathematician.] Fibonacci, Leonardo (fêbonät´chê), ; b. c.1170, d. after 1240; Italian mathematician, known also as Leonardo da Pisa. The Fibonacci SEQUENCE 0, 1, 1, 2, 3, 5, 8, 13, 21, … , in which each term is the sum of the two preceding terms, occurs in higher mathematics in various connections. Fibonacci numbers Fibonacci numbers (fib-e-nä'chê num`berz) noun In mathematics, an infinite series in which each successive integer is the sum of the two that precede it- for example, 1, 1, 2, 3, 5, 8, 13, 21, 34.... Fibonacci numbers are named for the thirteenth-century mathematician Leonardo Fibonacci. In computing, Fibonacci numbers are used to speed binary searches by repeatedly dividing a set of data into groups in accordance with successively smaller pairs of numbers in the Fibonacci sequence.

For example, a data set of 34 items would be divided into one group of 21 and another of 13. If the item being sought were in the group of 13, the group of 21 would be discarded, and the group of 13 would be divided into 5 and 8 ; the search would continue until the item was located. The ratio of two successive terms in the Fibonacci sequence converges on the Golden Ratio, a " magic number" that seems to represent the proportions of an ideal rectangle. The number describes many things, from the curve of a nautilus shell to the proportions of playing cards or, intentionally, the Parthenon, in Athens, Greece. Fibonacci, Leonardo Fibonacci, Leonardo or Leonardo of Pisa (1170?-1240?), Italian mathematician, who compiled and supplemented the mathematical knowledge of classical, Arabic, and Indian cultures, and contributed to algebra and number theory. Born in Pisa, Fibonacci was about 20 when he went to Algeria, where he began to learn Indian numerals and Arabic calculating methods.

Fibonacci used this experience to improve on the commercial computing techniques he knew and to extend the work of classical mathematical writers, such as Greek mathematicians Diophantus and Euclid. His writings on recreational mathematics became classic mental challenges and often involved the summation of recurrent series, such as the Fibonacci series. Science, 1202 Liber Abaci by Italian traveler-mathematician Leonardo Fibonacci (Leonardo da Pisa) introduces Europe to Arabic numerals from North Africa and the zero from India, making calculation much easier than with Roman numerals. First off, the system we use is not the Arabic system as many of us like to believe. It is the Hindu system. We refer to it as Arabic because Europe got the numerals from the Islamic world, which it sweepingly referred to as Arabic. The switch took place in the Middle Ages, propelled by a book by the mathematician Leonardo Fibonacci in which he discusses the merits of the Hindu numeral system. What you need to remember is that Islam was a more powerful culture, one that was more scientifically advanced than European civilizations after the fall of the Western Roman Empire. The Hindu numeral system promised the ability to understand Islamic mathematics. The Hindus also invented the number zero.

This was one of the greatest achievements in mathematical history. Leonardo of Pisa or Leonardo Pisano (c. 1175 - 1250), also known as Fibonacci, was an Italian mathematician and is best known for the invention of the Fibonacci numbers and his role in the introduction of the modern positional base-10 system for writing numbers to Europe. Leonardo's father Guilielmo (William) was nicknamed Bonacci ('good natured' or 'simple'). Leonardo was posthumously given the nickname Fibonacci (for filius Bonacci, son of Bonacci). William directed a trading post (by some accounts he was the consul for Pisa) in Bugia, North Africa (now Bejaia, Algeria), and as a young boy Leonardo traveled there to help him. There he learnt from the Arabic numeral system. Perceiving the superiority of these Arabic numerals, Fibonacci travelled throughout the Mediterranean world to study under the leading Arab mathematicians of the time , returning around 1200. In 1202, at age 27, he published what he had learned in Liber Abaci, or Book of Calculation.

This book showed the practical importance of the new number system by applying it to commercial bookkeeping, conversion of weights and measures, the calculation of interests, money-changing, and numerous other applications. The book was enthusiastically received throughout educated Europe and had a profound impact on European thought. Leonardo became a guest of the Emperor Frederick II, who enjoyed mathematics and science. In 1240 the Republic of Pisa honoured Leonardo, under his alternative name of Leonardo Bigollo, by granting him a salary. Leonardo Fibonacci | ELECTRIC CAVES Leonardo Fibonacci This nOde last updated December 30th, 2006 and is permanently morphing… (5 Caban (Earth) / 10 K’ank’in – 57/260 – 12.19.13.16.17) Fibonacci sequence noun The sequence of numbers, 1, 1, 2, 3, 5, 8, 13, . . . , in which each successive number is equal to the sum of the two preceding numbers. [After Leonardo Fibonacci (died c.

1250), Italian mathematician.] Fibonacci, Leonardo (fêbonät´chê), ; b. c.1170, d. after 1240; Italian mathematician, known also as Leonardo da Pisa. The Fibonacci SEQUENCE 0, 1, 1, 2, 3, 5, 8, 13, 21, … , in which each term is the sum of the two preceding terms, occurs in higher mathematics in various connections. Fibonacci numbers Fibonacci numbers (fib-e-nä’chê num`berz) noun In mathematics, an infinite series in which each successive integer is the sum of the two that precede it- for example, 1, 1, 2, 3, 5, 8, 13, 21, 34…. Fibonacci numbers are named for the thirteenth-century mathematician Leonardo Fibonacci. In computing, Fibonacci numbers are used to speed binary searches by repeatedly dividing a set of data into groups in accordance with successively smaller pairs of numbers in the Fibonacci sequence.

For example, a data set of 34 items would be divided into one group of 21 and another of 13. If the item being sought were in the group of 13, the group of 21 would be discarded, and the group of 13 would be divided into 5 and 8 ; the search would continue until the item was located. The ratio of two successive terms in the Fibonacci sequence converges on the Golden Ratio, a “ magic number” that seems to represent the proportions of an ideal rectangle. The number describes many things, from the curve of a nautilus shell to the proportions of playing cards or, intentionally, the Parthenon, in Athens, Greece. Fibonacci, Leonardo Fibonacci, Leonardo or Leonardo of Pisa (1170?-1240?), Italian mathematician, who compiled and supplemented the mathematical knowledge of classical, Arabic, and Indian cultures, and contributed to algebra and number theory. Born in Pisa, Fibonacci was about 20 when he went to Algeria, where he began to learn Indian numerals and Arabic calculating methods.

Fibonacci used this experience to improve on the commercial computing techniques he knew and to extend the work of classical mathematical writers, such as Greek mathematicians Diophantus and Euclid. His writings on recreational mathematics became classic mental challenges and often involved the summation of recurrent series, such as the Fibonacci series. Science, 1202 Liber Abaci by Italian traveler-mathematician Leonardo Fibonacci (Leonardo da Pisa) introduces Europe to Arabic numerals from North Africa and the zero from India, making calculation much easier than with Roman numerals. First off, the system we use is not the Arabic system as many of us like to believe. It is the Hindu system. We refer to it as Arabic because Europe got the numerals from the Islamic world, which it sweepingly referred to as Arabic. The switch took place in the Middle Ages, propelled by a book by the mathematician Leonardo Fibonacci in which he discusses the merits of the Hindu numeral system. What you need to remember is that Islam was a more powerful culture, one that was more scientifically advanced than European civilizations after the fall of the Western Roman Empire. The Hindu numeral system promised the ability to understand Islamic mathematics. The Hindus also invented the number zero.

This was one of the greatest achievements in mathematical history. Leonardo of Pisa or Leonardo Pisano (c. 1175 – 1250), also known as Fibonacci, was an Italian mathematician and is best known for the invention of the Fibonacci numbers and his role in the introduction of the modern positional base-10 system for writing numbers to Europe. Leonardo’s father Guilielmo (William) was nicknamed Bonacci (‘good natured’ or ‘simple’). Leonardo was posthumously given the nickname Fibonacci (for filius Bonacci, son of Bonacci). William directed a trading post (by some accounts he was the consul for Pisa) in Bugia, North Africa (now Bejaia, Algeria), and as a young boy Leonardo traveled there to help him. There he learnt from the Arabic numeral system. Perceiving the superiority of these Arabic numerals, Fibonacci travelled throughout the Mediterranean world to study under the leading Arab mathematicians of the time , returning around 1200. In 1202, at age 27, he published what he had learned in Liber Abaci, or Book of Calculation.

This book showed the practical importance of the new number system by applying it to commercial bookkeeping, conversion of weights and measures, the calculation of interests, money-changing, and numerous other applications. The book was enthusiastically received throughout educated Europe and had a profound impact on European thought. Leonardo became a guest of the Emperor Frederick II, who enjoyed mathematics and science. In 1240 the Republic of Pisa honoured Leonardo, under his alternative name of Leonardo Bigollo, by granting him a salary. Fibonacci definition by Babylon’s free dictionary Wikipedia Dictionaries English Wikipedia - The Free Encyclopedia Leonardo Bonacci (c. 1170 – c. 1250)known as Fibonacci , and Leonardo of Pisa, Leonardo Pisano Bigollo, Leonardo Fibonacciwas an Italian mathematician, considered to be "the most talented Western mathematician of the Middle Ages". See more at Wikipedia.org... Mathematics & Dark Age | Armstrong Economics Mathematics & Dark Age Blog /Basic Concepts Posted Nov 8, 2015 by Martin Armstrong We tend to judge far too much by our own times. What cannot be overlooked is the lack of mathematics following the Dark Ages. When numbers were Roman numerals, calculation and bookkeeping were not supportive of international accounting.

Interestingly enough, as pornography enabled video streaming, it was gambling that gave birth to mathematics. Vices often inspire innovation. For example, the 1202 publication of “Liber Abaci” (Book of Abacus) by Leonardo Pisano or Bonacci of Pisa , known to most as Fibonacci (1170-1240 AD). When Fibonacci published his “Liber Abaci”, it introduced Hindu-Arabic numerals. This method allowed calculation that was not taught in schools and was unknown in Christian circles, except among a very small group of intellectuals who had access to translations ofthe Arab mathematician al-Khwarizmi (780-850 AD). Fibonacci’s “Liber Abaci” introduced vital concepts that enable banking to emerge. The first seven chapters dealt with notation’s introduction of the idea of a place value, whereas the position of a figure determined where it is a unit, such as 10, 100, 1000 and so on. He also introduced the use of numerals in arithmetical calculations. These techniques were groundbreaking for a culture that lost its identity with the fall of Rome.

Fibonacci illustrates practical problems on how to calculate profit margin, moneychanging, barter, conversion of weights and measures, partnerships, and last but not least, interest. He even introduced some geometry and algebra. This work was so earth-shattering, it became the topic of discussion and caught the attention of Holy Roman Emperor Frederick II (1215-1250 AD)(King of Sicily 1198-1250 AD). Fibonacci was given a test; the third problem was x3+2×2+10x=20 (modern notation). He solved the equation using the Babylonian method based upon sexagesimal fractions (base 60), which when translated into modern decimals is 1.3688081075. Fibonacci is strangely best known for his sequence derived from a pair of multiplying rabbits (1, I, 2, 3, 5, 8, 13, 21, 34, 55 .•.

) where the progression follows what has become known as the “golden ratio” 1.6180 that was discovered by the University of Glascow mathematician Robert Simson in 1753. The Arabs and the Jews were always highly educated and were not victims of the superstitions of the times. Thus, the knowledge of mathematics was highly restricted to these groups back then. Jews were not just moneylenders, but they had also been captains of ships where Christians were ignorant of mathematics. Therefore, Fibonacci opened the door for capitalism by first creating a knowledge base of mathematics by introducing the decimal system to Europe. Finally, the secrets of mathematics were starting to resurface from the Dark Ages. Knowledge seems to evaporate when going into a Dark Age. The question remains, what knowledge will evaporate this time if we go back that far? Geometry.Net - Scientists: Fibonacci Leonardo Fibonacci Leonardo: LEONARDO FIBONACCI  Mathematician.

Also known as Leonardo of Pisa,Fibonacci introduced to Europe and popularized the HinduArabic LEONARDO FIBONACCI Mathematician Also known as Leonardo of Pisa, Fibonacci introduced to Europe and popularized the Hindu-Arabic number system (also called the decimal system). He contributed greatly to number theory, and during his life published many important texts, including Liber abbaci Practica geometriae (1220) and Liber quadratorum (1225). He is also known for the Fibonacci Series, a numerical series found frequently in the natural world. In the sequence, each number is equal to the sum of the preceding two (1, 1, 2, 3, 5, 8, 13, 21 ...). For other explanations of terms and phrases from famous names, see our loop of Who's What? Slick and supercool examples and explanations Fibonacci Good text introduction to Fibonacci and his work Who Was Fibonacci? A brief bio that leads to a great all-around site on numbers Fibonacci An analysis that discusses the series' relationship to the Golden Ratio Birth: c. 1170 Birthplace: 2. Fibonacci Leonardo Pisano Fibonacci.

Leonardo Pisano is better known by his nickname Fibonacci.He was the son of Guilielmo and a member of the Bonacci family. ~history/Mathematicians/Fibonacci.html Born: 1170 in (probably) Pisa (now in Italy) Died: 1250 in (possibly) Pisa (now in Italy) Click the picture above to see two larger pictures Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Leonardo Pisano is better known by his nickname Fibonacci. He was the son of Guilielmo and a member of the Bonacci family. Fibonacci himself sometimes used the name Bigollo, which may mean good-for-nothing or a traveller. As stated in [1]:- Did his countrymen wish to express by this epithet their disdain for a man who concerned himself with questions of no practical value, or does the word in the Tuscan dialect mean a much-travelled man, which he was? Fibonacci was born in Italy but was educated in North Africa where his father, Guilielmo, held a diplomatic post.

His father's job was to represent the merchants of the Republic of Pisa who were trading in Bugia, later called Bougie and now called Bejaia. Bejaia is a Mediterranean port in northeastern Algeria. The town lies at the mouth of the Wadi Soummam near Mount Gouraya and Cape Carbon. Fibonacci was taught mathematics in Bugia and travelled widely with his father, recognising and the enormous advantages of the mathematical systems used in the countries they visited. Fibonacci writes in his famous book Liber abaci When my father, who had been appointed by his country as public notary in the customs at Bugia acting for the Pisan merchants going there, was in charge, he summoned me to him while I was still a child, and having an eye to usefulness and future convenience, desired me to stay there and receive instruction in the school of accounting. There, when I had been introduced to the art of the Indians' nine symbols through remarkable teaching, knowledge of the art very soon pleased me above all else and I came to understand it, for whatever was studied by the art in Egypt, Syria, Greece, Sicily and Provence, in all its various forms.

Translate this page fibonacci leonardo (1170-1240) Historique Fibonnaci (connu aussisous le nom de Leonard de Pise) est né à Pise mais rejoignit Liste de Mathématiciens Al Khwarizmi Apollonius de Perge Archimède Argand Jean Bezout Etienne Bombelli Rafaele Boole George Cardano Girolamo Cauchy Augustin Chasles Michel De Moivre Abraham De Morgan Augustus Del Ferro Scipione Descartes René Eratosthene Euclide Fermat Pierre Ferrari Ludovico Fibonacci Leonardo Galois Evariste Gauss Carl Germain Sophie Huygens Christiaan Leibniz Gottfried Pascal Blaise Peano Guiseppe Pythagore Tartaglia Nicolo Viete François Zenon d Elée Fibonacci Leonardo Historique : Si l'on note (u n ) la suite de Fibonacci, elle est définie par : u =0; u et u n = u n-1 +u n-2 pour tout n>2 La suite a les propriétés suivantes : u n et u n+1 sont premiers entre eux lim(u n /u n+1

 )=(racine(5)-1)/2 (nombre d'or) En Mathématiques, on parle également des suites de Fibonacci généralisées, définies par: u n =ru n-1 +su n-2 pour tout n>2 u =a; u =b avec a,b,r,s réels fixés.

Sources : Encyclopedia America Encarta 97 Liste par ordre alphabétique Translate this page nouvelle recherche, fibonacci leonardo Leonardo Fibonacci naît vers 1170 à Pise(Italie), alors ville commerçante dune grande puissance maritime. Leonar FIBONACCI Leonardo italien, 1170-1250 De son vrai nom Léonard de Pise, dit Fibonacci (signifiant "fils de Bonaccio"). Commerçant et grand voyageur. Dans son "Liber abaci", principalement consacré aux calculs commerciaux, il affine et résout des problèmes algébriques déjà rencontrés dans l'oeuvre du mathématicien Al Khwarizmi. Il fait grand usage des nombres "arabes" (système décimal positionnel) , du calcul fractionnaire et de la méthode de résolution des équations, dite de fausse position. Fibonacci publiera aussi un traité de géométrie, Practica geometriae , où il applique des méthodes algébriques à des problèmes géométriques.

Translate this page Leonardo Pisano Fibonacci. né à Pise 1170, probalement décédé en Italieen 1250. Leonardo Pisano est mieux connu sous son surnom Fibonacci. ~darras/site/fibo/fina.html Leonardo Pisano Fibonacci Leonardo Pisano est mieux connu sous son surnom Fibonacci. Liber abaci Liber abaci introduit la notation décimale arabo-hindoue de position et l'usage de chiffres "arabes" en Europe. Liber abaci Fibonacci Quarterly Les autres oeuvres importantes de Fibonacci sont Practica geometriae Liber quadratorum Mis practica geometriae fibonacci leonardo Fibonacci was born in Pisa Italy in 1175 AD Hewas also named Leonardo of Pisa. He traveled all over and when folder/fibonacci.htm Fibonacci Leonardo Fibonacci was born in Pisa Italy in 1175 A.D. He was also named Leonardo of Pisa. He traveled all over and when he came back to Europe he brought the Hindu-Arabic numbers back to Europe and it soon caught on.

We use the Hindu-Arabic number system today becuase it is based on 10 and has a symbol for zero. Leonardo wrote many books. His most famous book is Liber Abaci. In the book he uses the Hindu-Arabic number system. This book was a book on calculating but also had things such as linear and quadratic equations. The book also contains the rabbit problem. It is a very popular problem which shows the golden ratio. No copies of his book survived but a copy of the 1228 version does still exsist. Fibonacci died somewhere circa 1240 and no one really knows how. There is a statue remembering him in a cemetary next to the catherdral in Pisa.

3 : 2 = 2 Prime 7 : 13 = 13 Prime 11 : 89 = 89 Prime 13 : 233 = 233 Prime 17 : 1597 = 1597 Prime 23 : 28657 = 28657 Prime 29 : 514229 = 514229 Prime 43 : 433494437 = 433494437 Prime 47 : 2971215073 = 2971215073 Prime 83 : 99194853094755497 = 99194853094755497 Prime Bibliography Leonardo Fibonacci. by Naomi Brodersen. Leonardo Leonardo Fibonacciwas born in Pisa and is sometimes known as Leonardo of Pisa.

When Leonardo Fibonacci by Naomi Brodersen Leonardo Fibnonacci was a famous Italian mathematitian who lived from 1170-1240 A.D. He helped introduce the Hindu-Arabic numbers (0,1,2,3,4,5,6,7,8,9,) into Western Europe. When he was a boy, he traveled widely on business in the Middle East with his father. While traveling he learned a lot about Greek and Arabic mathematics. Fiobonacci was also introduced to many different mathematical ideas used throughout the world. He put these ideas into books so people could learn them without having to travel as he had. Leonardo Fibonacci was born in Pisa and is sometimes known as Leonardo of Pisa. When he was young he joined his father in a Pisan colony called Bujaia (now dern Bougie Algeria) where he began studying mathematics. One of Fibonacci's greatest works was a book called Liber Abasi. He published this book in 1202. It was revised in 1228. Liber Abasi means book of the abacus. In this book Fibonacci explained methods of arithmetic, applications to commercial problems, and many other mathematical methods.

One of the methods in his book eventually became the Roman numeral system. Some other books Leonardo Fibonacci wrote were Practicia geometriae (1220), Liber quadratorum (1225), and Flos (about 1225). This mathematician discovered a sequence of numbers called the Fibonacci Sequence or Fibonacci Numbers. This sequence contains the numbers 1,1,2,3,5,8,13,..... Each number after the first two numbers equals the sum of the two numbers before it. Here's an example: 1+1=2, 1+2=3, 2+3=5, 5+3=8, 8+5=13... Leonardo Fibonacci also was the first person to discover the Golden Rectangle, Golden Ratio and the Golden Spiral. Leonardo Fibonacci's sequence, rectangle ratio and spiral have been used and studied people by people all over the world. University of Virginia Fibonacci fibonacci leonardo Fibonacci Universityof Michigan Fibonacci ItalianAmerican Website Fibonacci. Back to. ~mm97106/math/fibo/fibo.htm Do you believe in Fibonacci Numbers ? Andrew's Fibonacci Dreams LEONARDO FIBONACCI.

Leonardo Fibonacci was born in Pisa, Italy, around 1175. LeonardoFibonacci was the gratest European mathematician of the Middle Ages. LEONARDO FIBONACCI Leonardo Fibonacci was born in Pisa, Italy, around 1175. His father was Guilielmo Bonacci, a secretary of the Republic of Pisa.His father was also a customs officer for the North African city of Bugia. Some time after 1192. Bonacci brought his son with him to Bugia.Guilielmo wanted for Leonardo to become a merchant and so arranged for his instruction in calculational techniques, escpecially those involving the Hindu - Arabic numerals which had not yet been introduced into Europe.Since Fibonacci was the son of a merchant, he was able go travel freely all over the Byzantine Empire. Merchants at the time were immuned, so they were allowed to move about freely. This allowed him to visit many of the area's centers of trade. While he was there, he was able to learn both the mathematics of the scholars and the calculating schemes in popular use, at the time.

Fibonacci writes in his famous book Liber abaci When my father, who had been appointed by his country as public notary in the customs at Bugia acting for the Pisan merchants going there, was in charge, he summoned me to him while I was still a child, and having an eye to usefulness and future convenience, desired me to stay there and receive instruction in the school of accounting. There, when I had been introduced to the art of the Indians' nine symbols through remarkable teaching, knowledge of the art very soon pleased me above all else and I came to understand it, for whatever was studied by the art in Egypt, Syria, Greece, Sicily and Provence, in all its various forms $12.95 per page! Leonardo fibonacci leonardo Fibonacci was born in Pisa,Italy around 1175 to Guilielmo Bonacci. Leonardos father Leonardo Fibonacci. Leonardo Fibonacci was an Italian mathematicianwho lived between 11701240. He travelled a lot on business with Leonardo Fibonacci Leonardo Fibonacci was an Italian mathematician who lived between 1170-1240.

He travelled a lot on business with his father and was exposed to many different mathematical techniques used throughout the world. Fibonacci collected these ideas in books, for people to learn without having to travel as he had. His writings introduced Arabic numerals into European mathematics. Fibonacci also made significant contributions to mathematics himself, in number theory and on recursive sequences. He is most famous for the Fibonacci sequence, in which each number is the sum of the previous two. Last modified February 25, 1997 by the Windows Team The source of this material is Windows to the Universe , at Leonardo Fibonacci. Leonardo Fibonacci, sometimes known as Leonardo of Pisa,is renowned for creating the series of numbers that bear his name. Leonardo Fibonacci Leonardo Fibonacci, sometimes known as Leonardo of Pisa, is renowned for creating the series of numbers that bear his name. He also helped introduce the Hindu-Arabic numeral system into Europe. He was born in Pisa, Italy in about 1175 to Guilielmo Bonacci who was a merchant who helped begin the Pisan trading colony in Bugia in 1192. Some time after this Fibonacci travelled with his father, who intended Fibonacci to become a merchant, around the Middle East.

His father arranged for him to learn about calculation related with the Hindu-Arabic numeral system which had not been introduced into Europe at that time. Eventually, Bonacci enlisted his son to help carry out business for the Pisan republic and sent him on trips to Egypt, Syria, Greece, Sicily, and Provence. Fibonacci used some of this time to learn more about the Hindu-Arabic system of which he wrote in five books. In about 1200 Leonardo went back to Pisa where he worked on his own mathematical compositions. After 25 years he had produced many works but after this virtually nothing is known of Leonardo's life. He died around 1240. Leonardo Fibonacci By Crystal Gaudio. Leonardo Fibonacci was a twelfth centurymathematician born near the year 1180 into the privileged class of Pisa. Leonardo Fibonacci By Crystal Gaudio Leonardo Fibonacci was a twelfth century mathematician born near the year 1180 into the privileged class of Pisa. His father Bonacci was a Pisan business and government official.

Because of his elevated status, Fibonacci attended public school and studied the "seven liberal arts": grammar (Latin), rhetoric, logic, geometry, astronomy, music and arithmetic. During Fibonacci's life, Pisa participated in the Commercial Revolution of the twelfth and thirteenth centuries, out of a Roman port that continued operation through the Dark Ages. Pisa was a site of extensive commercial activity requiring calculation on an abacus and recording with Roman numerals. After his formal public education, Fibonacci followed his father to North Africa, Bugia to continue his business education. There he discovered the long established HinduArabic numerals similar to what we use today. The numerals consisted of symbols 1-9 and the extraordinary concept of zero. Fibonacci was responsible for introducing the HinduArabic numerals to Western Europe in his publication Liber abaci (Book of the Abacus) . Fibonacci was also responsible for introducing the Arab method of balancing income and expenditure in the double-entry system of bookkeeping. Another section of Liber abaci calculated the progeny of a single pair of rabbits. Through systematic calculations involving logic and consistency, the "Fibonacci Sequence" was created.

In subsequent months, the number of paired rabbits would theoretically continue as follows: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89...or u Leonardo Pisano Fibonacci. Leonardo Pisano Fibonacci (11701228). About Fibonaccilife it is known a little. Even the exact date of his birth is obscure. Leonardo Pisano Fibonacci The "Middle Ages" in our consciousness associate with the concept of inquisition orgy, campfires, on which witches and heretics are incinerated, and crusades for "the body of God". The science in those times obviously was not "in a center of society attention". In these conditions appearance of the mathematical book "Liber abaci" ("the book about an abacus"), written in 1202 by the Italian mathematician Leonardo Pisano (by the nickname of Fibonacci) was the relevant event in the "scientific life of society". Who was Fibonacci? And why his mathematical works are so important for the West-European mathematics? To answer these questions it is necessary to reproduce the historical epoch, in which Fibonacci lived and worked.

One of the most interesting persons of the Crusades epoch, a harbinger of the Renaissance epoch, was the emperor Fridrich Gogenstaufen, an apprentice of the Sicilian Arabs and an admirer of the Arabian culture. At his palace in Pisa the greatest European mathematician of the Middle Ages Leonardo Pisano (by the nickname of Fibonacci that means the son of Bonacci) lived and worked. Leonardo Pisano Fibonacci (1170-1228) About Fibonacci life it is known a little. Even the exact date of his birth is obscure. It is supposed, that Fibonacci was born in the eighth decade of the 12th century (presumptively in 1170). His father was a merchant and a government official, the representative of the new class of the businessmen generated by the "Commercial Revolution". In that time the city of Pisa was one of the largest commercial Italian centers actively cooperating with the Islam East, and Fibonacci's father traded in one of the trading posts, founded by Italians on the northern coast of Africa. Due to this circumstance he can give his son, the future mathematician Fibonacci, good mathematical education in one of the Arabian educational institutions. Leonardo Pisano Fibonacci.

Born 1170 Died 1250. Leonardo Pisanois better known by his nickname Fibonacci. He was the son 1000+ images about Fibonacci - Math Night on Pinterest | Mathematicians, Mona lisa and Golden ratio Pinterest • The world’s catalog of ideas Fibonacci - Math Night Math Night celebration, November 2013. Great opportunity to celebrate awesome mathematician and promote a Positive Math Culture. We did kid friendly, rabbit and bee problems, Fibonacci in Nature, Pascal's triangle, Golden Rectangle mosaic, Your Birthday in Roman Numerals and lots of games. 48 Pins15 Followers · May 9, 2014 · Nikolai Ivanovich Lobachevsky (1792 – 1856) The man who with his discovery bought a paradigm shift in the geometrical thinking that assisted Einstein to build the mathematical equations necessary to explain the space curvature due to gravity is Nikolai Ivanovich Lobachevsky. Although, this new geometry, called the non-Euclidean geometry, was independently developed by Carl Friedrich Gauss, Janos Bolyai, and Labachevsky, it was Labachevsky who published the his discoveries fir...st.

Nikolai Lobachevsky was born on 2nd December, 1792 in Gorki, Russia. His father, Ivan Maksimovich was clerk. In 1800, Nikolai with his two brothers and mother moved with to Kazan, where he his schooling, and later graduated in mathematics and physics from the university of Kazan in 1812. For Lobachevsky, the beginnings of an alternative geometry, other than the conventional Euclidean geometry, occurred when he, like many others in the past attempted to prove the fifth postulate of Euclid that states that for a given line, and an external point, there is only one line passing through this external point that is in parallel to the original given line. Since he too failed in proving this postulate, he turned into building an another geometry that does not require this fifth postulate of Euclid. In his construction, it is possible to have multiple lines passing through this external point and still parallel to the original given line. This geometry also called the hyperbolic geometry in which the sum of the angles of a triangle is less than 180 degrees expresses the equations of space and gravity.

Other than geometry, Lobachevsky contributed to algebra, infinite series, and theory of integration. Gauss, who highly valued Lobachevsky mathematical work later assisted him to secure a position at the Academy of Science, Gottingen. Later in life, he faced severe financial situation and health wise, he started deteriorating in eye sight and became totally blind. He died on February 24th, 1856. · April 30, 2014 · John Napier (1550 – 1617) Not only for his contribution to logarithms, a method that enabled others to perform faster arithmetic, Napier is also known for providing a transcendental function that has fascinated mathematicians for centuries. Born in 1550 in Edinburgh, Scotland, John Napier, a member of an aristocratic family (his father, Archibald Napier, Knighted in 1565) received his early education at home and went on to study at the St. Andrew’s University in 1563. Soon a...fter his mother’s death thereafter, his passion shifted to theology that remained his interest throughout his life.

Although he attributes all his mathematical discoveries as theological, to the world he is remembered as a mathematician. Records indicate that he traveled widely in Europe, and continued education at Paris. However, he returned to Scotland to occupy himself in looking after the estates. He was a talented innovator and invented several agricultural methods. Being a staunch protestant, he was involved in the religious controversies happening at that time and even published a work opposing the spread of Roman Catholicism. His invention of logarithms as a method that simplifies multiplication to additions is called the Napier logarithm and is one of the most fascinating tools in mathematics. His first public discourse on logarithms appeared in Mirifici logarithmorum canonis description (Description of the marvelous canon of logarithms) in 1614. Since Napier logarithm was slightly different than the current version, one major problem was his definition of the logarithm of one is not zero. It was desirable to have the logarithm of one as zero to allow the interpretation of logarithm as the inverse of exponentiation. However, later Henry Briggs communicated to Napier to have the logarithms to base 10, so as to allow the logarithm of one to zero.

Together with Briggs, Napier worked out the logarithmic tables until his death in 1617. Another popular invention of Napier is the so called the Napier bones, a set of iron rods which, when arranged in a special pattern could read out the product of numbers. · April 20, 2014 · Lazare Carnot (1753 – 1823) It is rare to attain fame both as a scientist and a politician, but, Lazare Carnot is notably famous for his contribution to mechanical engineering by applying mathematical analysis methods – majorly calculus and politically named as ‘Organizer of Victory’ in the wars of French revolution. Born on 13th May, 1753 in Nolay France, Lazare Carnot, was the son of a Lawyer, initially trained for a military career shifted focus to learn mathematics, mecha...nics and physics. He started with writing on topics like mathematics and military strategy. In 1791, he started his political career winning a seat at legislative assembly. He advocated giving chance to those who were talented. Later when the war broke, he was employed in the military services.

For his commitment and loyalty he was appointed as the minister of war that he later resigned due to differences of opinion. It was at this point, Carnot returned to his scientific interests serving various commissions on investigating French military inventions. He notably worked on providing the abstract definition of a machine, especially the concept that power can be transmitted without any loss. His writings on pure mathematics, covering the subject of calculus were published in several languages and thus received wider circulation. His book on the science of geometric motion attempted to connect his mechanical studies and geometry. Carnot being a patriot volunteered to aid Napoleon, however when the monarch was dethroned he had to flee France, and started his new life in Magdeburg, Germany until he died 2nd August 1823. · April 4, 2014 · Aryabhata 1 (476—550) Not much is known about Aryabhata, who was later named Aryabhata 1 to distinguish from another great mathematician with the same name born 4 centuries later. Aryabhata contributed largely to the development of number system and number theory when the rest of the world, especially, Europe was wrapped with ignorance.

Believed to be born in Kusumaputra, a city in India, that later became the center of mathematical learning. Aryabhata wrote 2 treatises in hi...s life. The first, The Aryabhatiya in 499, when he was 23 years old, and the second is unknown and lost. In Aryabhatia, he exposed 3 sections: mathematics, time and planetary motions, and sphere. The mathematics section contains 66 mathematical rules without proof, covering arithmetic, algebra, planar and spherical trigonometry, spherical geometry. Some advance chapters have quadratic equations, infinite series, and table of sines. Aryabhata greatest contribution to mathematics a number system with a place value. The advantage of place value is that large numbers could be written and manipulated with fewer alphabets. It is the construction of this system from which the number zero originated. His work on algebra was mostly connected to linear equations with integer coefficients arising mostly in astronomical calculations employed by him. In another, Aryabhata improved the approximation for pi, accurate to 8 decimal places. In geometry, he gave formulas to calculate the area of triangles and circles, although the volume of sphere and pyramid he formulated was incorrect.

In astronomy, he had formulations to predict the lunar and solar eclipses. Aryabhata’s influence to the later mathematicians and astronomers was enormous. His contributions, given the mathematical and astronomical knowledge around his time is significant. · March 28, 2014 · Joseph – Louis Lagrange (1736 – 1813) Born on 25th January, 1736 in Turin, Italy as the eldest of 11 children, Joseph Louis Lagrange is often described as the last great mathematician of the 18th century. His major contributions are his mechanistic description of the universe and exact mathematical formulations of the laws governing motion and mechanics. Intended for a career in law, he switched to physics when he started to read and develop interest in this subject. He commu...nicated his first results on the calculus of variation to Leonhard Euler at the age of 19. Calculus of variation is a branch of mathematical analysis with an objective to minimize or maximize a certain function. The novel method introduced by Lagrange was so impressive that Euler immediately started using it to every optimization problem.

Thereafter, the popularity of Lagrange grew and soon he was appointed as Professor in the Royal Artillery school in Turin. Lagrange applied his newly developed method to mechanics and started producing brilliant results. It was during this time he developed the method of integration by parts, a method well known to every college student today. In mechanics, he mathematically formulated the laws of celestial motion, including for the moon, for which he won several outstanding prizes from the Academy of Sciences in Paris. Another well known formulation of Lagrange is the principle of least action. The principle of least action states that a moving object chooses a path that consumes the least energy. In summary, all mathematicians of his time like Jean D’ Alembert and Pierre-Simon Laplace recognized the excellent quality and originality of his work that many of them wanted to secure and offer him a position at their respective universities. Finally, he took the vacant position left by Euler at Berlin Institute of Sciences. There he was named the director with no teaching duties. He was fully payed with the only job of doing research on mathematics. This period of Lagrange is considered as a second scientific period of his life.

Here at Berlin, he continued the work of Euler, mostly, algebra, number theory and integration of differential equations. Many of his contributions to these subjects are still applicable in solving many scientific and engineering problems. While in Berlin, he married his cousin, but unfortunately was childless for 16 years, until her death. Later he moved to Paris and married again. He spent his later life in teaching and participating in standardizing weights and measurements. He died on April 11th, 1813 in Paris. His contribution to mechanics of heavenly bodies is highly valued to an extend that sometimes it is called Lagrangian mechanics. · March 21, 2014 · Christiaan Huygens (1629 – 1695) Born between the time of two mathematicians – Rene Descartes, and Issac Newton, Christiaan Huygens was one of the mathematical geniuses of Europe. He contributed majorly to the topics like theory of light, mechanics, geometry and astronomy. Christiaan Huygens was born in The Hague, The Netherlands, on 14th April, 1629 to a wealthy family who served the royal house.

His father, Constantijn Huygens educated both his sons in music, literature, ma...thematics and mechanics. Christiaan Huygens showed his constructional abilities, and intellect quite early in life that he built a lathe at the age of 13. In 1645, he attended the University of Leiden to study Mathematics and Law. At the University he taught himself the works of Rene Descartes and Pierre De Fermat, and researched on the mechanics of falling bodies. Returning home after his graduation, he started working on mathematics, especially on algebraic equations and probability theory. Christiaan Huygens was one of the founders of probability theory. On algebraic geometry, he worked on the problem of the quadrature of the circle, also called the squaring of the circle, an ancient problem that requires a construction of a square equal in area to a given circle with compass and ruler alone. This problem, although has been proven to be unsolvable (in 1882: Lindemann–Weierstrass theorem) for the reason that pi, is a transcendental number, Huygens provided an approximate solution to the quadrature of the circle problem. Huygens also contributed considerably to natural science.

Very gifted with hands, he grinded lens for building telescopes of high quality with which he could observe the rings of Saturn. With a microscope, he built, he observed several micro-organisms including bacteria. In 1656, he built the pendulum clock to observe time in higher accuracy that was much needed for navigation and astronomy. In mechanics, the derived the laws of descent along the inclined planes and in the process, he derived the value of acceleration due to the gravity on earth to be 9.8 meters per second squared. While investigating on the wave theory of light, he explained reflection and refraction with his perception that light moved as series of shock waves. One of the most interesting fact about Huygens is that he never believed in the Newtonian concept of force and critically opposed it. Being very conservative to newer mathematical techniques like calculus (evolving at this time from the work of Leibnitz and Newton), he applied older geometrical methods to the problems. Huygens never married and mostly dedicated his life to the advancement and understanding of nature. He was an expert in applying mathematical methods to practical problems. He died on 8th July, 1695.

· December 5, 2013 · Euclid of Alexandria (325 BC – 265 BC) Born between the times of Plato and Archimedes, Euclid collected and organized all the mathematical knowledge that was scattered around in Greece and complied one of the greatest work of all times which now is known as Euclid Elements. Euclid Elements is a composition of 13 chapters. Most of the chapters were concerning geometry for which he started with postulates and axioms that were taken for granted. An example of these is the existe...nce of points, lines and circles. From there he wrote propositions that were carefully and sequentially laid down such that the each validity of each statement was sought from the previous validated ones. Most of the geometry learnt at school geometry and used in daily life is Euclidean geometry and is deduced from the first three postulates stated in the Euclid Elements. The fifth postulate relating to the definition of a parallel line remained a notorious one for at least several centuries. The reason for this was that every mathematician after Euclid tried to deduce the fifth postulate from the previous ones and eventually failed.

This resulted in the formation of geometry that was not Euclidean, and thus the birth of non-Euclidean geometry. An example to differentiate Euclidean from non-Euclidean is the difference in the sum of angles of a triangle. In Euclidean geometry, the sum of the triangles is always 180 degrees, while in non-Euclidean it is either less or greater than 180 degrees. To give a rough estimate of the knowledge covered in Euclid Elements, Book I treat geometry of points, lines, triangles, squares and parallelograms, including the proposition of the Pythagoras theorem. Book II is about transformation of areas, Book III about the intersection of circles, Book IV is on inscribing rectilinear figures into circles and thus to astronomy, Book V on propositions which mathematicians consider an elegant work and a great contribution to mathematics and Book VI on proposition applied to similar figures. Book VII – IX are on numbers like prime numbers, greatest common divisors, etc., and Book X on irrationals. The last books were mostly on the geometry of solids like cones, spheres, parallelepipeds, pyramids, etc.

As stated earlier, Euclid’s contribution to mathematics is his collective compositions of mathematical works in Euclid Elements. He set out by providing rigorous proofs in a sequential and logical order that initiated mathematicians to provide a standardized way of writing and proving mathematical conjectures. The parallel postulate and the theory of proportion are considered his best shares to the mathematical world. · November 18, 2013 · Pierre de Fermat (1601 – 1665) A 16th century mathematician of high class who contributed majorly to number theory, calculus and probability. His research into properties of primes and divisibility of numbers encouraged later mathematicians like Gauss, and Euler to contribute further in the field of number theory. Born in Beaumont-Lomagne, France on August 20th, 1601, to a prosperous merchant – Dominique Fermat, and Claire de Long, a noble woman, Fermat enjoyed high social st...atus and chose a profession of law. He later ascended to the highest councils of the parliament, and then to the president of the chamber. Fermat although enjoyed the fame as a mathematician always showed unwillingness towards publishing his results.

In 1636, Fermat completed a mathematical work on solids and planes where he introduced the use of algebra to describe the geometry. This work very similar to the work of Rene Descartes – The Geometrie in 1637, the issue of first discoverer is not resolved. In his work on solids and planes, Fermat demonstrated the use of geometry to solve algebraic equations. One his main contributions was to introduce the concept of dimension and thus relating the number of spatial dimensions to a number of unknown variables (thus x, y, z to 3 dimensions, for example). Another was a method to determine the maximum and minimum of curves that essentially involved in the method of derivatives. Thus Fermat came close to the foundations of calculus. However, as earlier said, Fermat was reluctant to publish his results and for this reason, many of his discoveries lay unknown with some of them were re-discovered by later mathematicians and were attributed to their names. Fermat is mostly known for his contributions to number theory. However, again most of the results were either written along the margin of his book or as letters to his friends.

One famous example is the Fermat’s theorem which states that there are no integer solutions for x, y, z for the equation x^n + y^n = z^n, where n is greater than 2. Fermat states this theorem in one of his reading material without stating any proof, however with a remark that the theorem is true and the margin does not have enough writing space to hold the proof. This problem – Fermat’s theorem, kept mathematicians busy for next 400 years, only to be proved by Andrew Wiles in 1994. In the later years, Fermat did not keep contact with any mathematicians and was forgotten. However, later 19th century mathematicians like Gauss and Euler acknowledged his work, and continued to produce many results inspired from Fermat work. · Niels Hendrik Abel (1802 – 1829) Abel, a Norwegian mathematician, had a short life of just 26 years but left behind a wealth of mathematical work that most mathematicians would have achieved in a lifetime.

Born to Soren Abel and Ane Marie Simonson on 5 August 1802, Abel was a marginal student at school in Oslo, Norway, until the arrival of new mathematics teacher Bernt Holmboe. Together they started reading the works of Euler and other French mathematicians. Soon Abel got in...terested in the theory of algebraic equations. The theory of algebraic equations mostly deals with finding solutions to polynomials as a function of its coefficients. An example is the second degree polynomial, ax^2 + bx + c = 0, where the solution x for x = (-b +/- (b^ - 4ac)^0.5)/2a. Solutions to polynomials greater than 4 were known at the time of Abel, and mathematicians were actively attempting to find solutions for polynomial of degree 5 (quintic equation). Abel attempted the quintic equation, but failed in his first attempt. However, the effort introduced him to another important field of mathematics, the theory of elliptic functions. Theory of elliptical functions and elliptical integrals are the studies on the arc length of an ellipse and are majorly used in number theory, and differential equations.

Abel had a brief stint at the University of Sweden to complete his degree and later to Denmark. However due to financial struggle he returned back to Oslo. Back home, he attempted the solution for the quintic equation again, but this time to prove that a radical expression for the solution (briefly said, no solution as a function of the polynomial coefficients). He sent out these results and sadly there was no intended reaction, including Gauss, one of the prominent mathematicians of those times. From then on Abel continued to work on generalizing the Euler’s work on elliptical integrals. This masterpiece although was sent for publication was never published. However, it was published after his death. Back home, Abel’s health was deteriorating and further on due to severe cold he fell ill and died of tuberculosis on April 26, 1829. Posthumously, the French academy of sciences awarded the Grand Prix to Abel. · November 11, 2013 · Leonardo Fibonacci (1170 – 1240) Member of Bonacci family, Leonardo Fibonacci was born in year 1170 in Pisa, Italy, to Guglielmo Bonacci.

He was nicknamed Bigollo meaning loafer (who does not work) for the reason that people of the town took his mathematical work lightly. Fibonacci’s father was a trader and more often young Fibonacci was asked to accompany his father to learn the trade. In one such occasion, his father had to lead a trading commission in Algeria and Fibonacc...i had to accompany his father. Thus Leonardo received his learning instructions from Arab teachers. It was from the Arab teachers, Fibonacci encountered the Indian numerals. These numbers were symbolic and had 10 distinct symbols. By appropriately placing the digits any number could be represented with these symbols. This appropriate placements to represent any number is the place value system introduced by Brahmagupta (598 – 665). Until this time, the Europeans merchants used the roman numerals and was not efficient in adding or multiplying large numbers. On his return to his native land, Fibonacci spent the next 25 years in introducing, improving the usage of this Indian numeric system to European merchants. He complied these works in Liber abbaci – a profound manuscript that focused on computation, in 1202. Liber abbaci had four portions.

In the first portion he discussed about Arab numerals, finger calculations and introduced Indian numerals. The second portion was more dedicated to merchants and thus contained information and method s for calculating wages, measurement of quantities and exchange rules for currencies. The third portion contained puzzles and mathematical riddles. It is here he introduced the famous problem of rabbits and their off springs to which the solution is the famous Fibonacci sequence. The fourth section dealt with calculation of radicals and several approximation for pi. He also extensively worked on practical application of geometry and these works were compiled in his another manuscript – Practica Geometriae (Practice of geometry) in 1220. In summary, Fibonacci played a central role in the advancement of mathematics in Europe. His introduction of Indian numerals to the west was crucial to advance the science of calculation. · November 8, 2013 · John Venn (1834 – 1920) English mathematician born on August 4th, 1834 at Hull, England who contributed to majorly to logic and probability. For studies he attended Cambridge and after his education started lecturing at his college.

For his contribution to mathematics he was elected as a fellow of Cambridge and retained his fellowship whole of his life. He was a fellow of the Royal Society as well. Venn is famously know for the Venn diagrams representing union and intersecti...on of a set of objects. Although the use of geometry to represent sets and logic had been used by the mathematicians in the past, including Euler (Eulerian Circles), these diagrams became very popular after Venn. He wrote several texts on the subject of logic and probability. He very much criticized the work of George Boole for using algebra in expressing and manipulating logic. While developing probability theory he described the chance of an event as the limiting ratio of number of times the event occurred in the past. Venn died on April 4th, 1923 in Cambridge. His geometrical representation of logic and its application to probability is one of the noteworthy contribution and is used even today to impart training in logic and set theory at elementary levels. · November 6, 2013 · Brahmagupta (598 – 665) One of the earliest Indian mathematician and astronomer from Rajasthan, India, who contributed very much to the advancement of mathematics.

Son of Jinsugupta, Brahmagupta composed his first work – Brahmasphutasiddhata, on mathematics and astronomy when he was 30 years old. His second, and last work – Khandakhadyaka, mostly astronomy, was composed in 665. Brahmagupta’ s good understanding of the number system help him discover the number ‘zero’ without ...which realizing numbers beyond 9 would need additional symbols other than 0 until 9. He also introduced the concept of negative numbers, and properties of numbers with which he showed that the product of a negative number and a positive number is a negative number. With his place value system concept he showed how large numbers can be multiplied. Thus the numbering system, as we all use today, is based on the concept developed by Brahmagupta. Brahmagupta described methods to find the square root of a number and is similar in principle to the method of Newton-Raphson used in finding the roots of an algebraic equation. He also described rules to compute the squares, cubes and consecutive series. In geometry he showed ways to calculate the area of a quadrilateral. His works influenced many later Indian mathematicians like Bhaskara II.

Considering that there was not any mathematical development in Europe, his contribution to mathematics is commendable. · October 31, 2013 · George Boole (1815 – 1864) George Boole, son of a poor cobbler John Boole, was born in 1815 at Lincoln, England. His father who had a natural inclination towards mathematics tutored George Boole. Due to poverty, George Boole was not able to pursue higher education. To support himself and his family George Boole started teaching mathematics at his home town. In his spare time he educated himself the work – Principia (Mathematical Principles of Natural Philosophy) of Newton, ...and started contributing regularly to the Cambridge mathematics journal and to the Royal society. At the times of Boole, the various fields of mathematics like probability, set theory, differential equations, etc., were seen as independent areas of study. A disagreement in one field could not be resolved with an aide of another field. Most of these disagreements were philosophical in kind and there was not a well-defined mathematical system to verify the truth. An arithmetic capable to express logical thoughts and thus verify the truths was devised by Boole.

This arithmetic is what we know today as Boolean arithmetic. Boole’s other mathematical writings were in the areas of finite differences and differential equations. So intellectual were his discoveries in these subjects that without any formal degree he was appointed as Professor of mathematics at the Queen’s college of Cork, Ireland. It was at this time he extended the arithmetic (Boolean arithmetic) to define the operator rules to invent the algebra of logic. He used this newly formed algebra in combination with set theory to describe multiplication, addition and subtraction laws of probability. He put together all these works in – Investigation of the laws of thought, which is one of the most important legacies of Boole. He was awarded doctoral degrees from the Universities of Dublin and Oxford and was elected to the Royal society. Unable to cover himself from rain while walking towards his lecture hall, beginning with a fever, ended up with excessive fluid accumulation in his lungs and finally death on 8th December, 1864. · October 29, 2013 · Georg Cantor (February 19?

1845 – Jan 6, 1918) Born to rich German parents on February 19 (debatable) 1845 in Saint Petersburg, Russia, Georg Cantor was a brilliant mathematician who discovered set theory. Set theory, today as fundamental theory, is used in several branches of mathematics, like algebra, statistics, probability, and even in advance mathematics like topology (the branch of mathematics dealing with shapes and spaces). At the age of 6, Cantor moved to Germany, an...d graduated from the University of Zurich, Germany. He continued to work on mathematics, and produced brilliant results in the field of number theory. After completing his doctoral degree in mathematics, he became a full time professor at the University of Halle and continued to hold the position for the rest of his life. Being bought up in a very religious Christian family (father was a Protestant, while his mother was a Catholic), Cantor had a very religious view to Mathematics. He discoveries and most importantly about the number system having more than one kind of infinities was attributed to God. His proved the existence of infinities of more than one kind and proved that the number of real numbers is larger than the number of natural numbers.

In attempting to prove these truths, he laid a strong foundation to set theory and their principles. However, the descriptions of having more than one infinities irked many mathematicians including Henri Poincaré, and his own teacher Leopold Kronecker. They openly ridiculed his work, and referred to his ideas as a ‘grave disease’ poisoning the younger generation. These strong oppositions did not favour in getting him a position at the prestigious University of Berlin that he wished all his life. One of the major problems with his descriptions was that it was counter intuitive and shook the very basis of then classical view of mathematics and the notion of numbers. However, later in time (beginning of the 20th century), his work started gaining acceptance and he was made the honorary member of the several mathematical societies. The Royal society with its Sylvester Medal, the highest laurels in mathematics, honoured Cantor in 1904. By then, Cantor, a subject of intense laughter of the past hit depression and eventually died at the psychiatric clinic of University of Halle on January 6th, 1918.

Question: What was the pseudonym of the mathematician Leonardo Bonacci (1170-1240)?
Answer: Fibonacci