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Leonardo de Pisa (Fibonacci)

History of Math- presentation
by

victoria golden

on 12 October 2012

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Transcript of Leonardo de Pisa (Fibonacci)

Leonardo de Pisa (Fibonacci) Fibonacci was able to gain knowledge about ancient mathematics from his travels with his father Education Fibonacci published a book called Liber Abaci, this was one of the earliest and most influential textbooks ever written in Europe Book of Calculation, Liber Abaci Born in Pisa, Italy Biography While studying in different Arabic countries, Leonardo realized how far behind Europe was in comparison (1175-1250) Leonardo's father was a Pisan businessman, who took Leonardo with him on business trips along the Mediterranean. A main source of his early education happened during his time in what is now Algeria. He learned his mathematics from different Arabic countries as well as China. His father pushed him to learn more and gain more knowledge European Mathematics It was his ingenious mind that decided to bring what he had learned from around the world back to Europe Before Fibonacci, there had not been an advance in European mathematics since the fall of the Roman Empire This book and Fibonacci are credited with bringing Arabic numerals (the numbers we use) to Europe In this book there are many different mathematical laws, principles, and problems 1st Problem: The Problems Liber Quadratorum, Book of Square Numbers, was another book he published and it dealt largely with indeterminate analysis He published Practica Geometriae, Practice of Geometry, which he worked incessantly on geometry and trigonometry Besides his first book, Liber Abaci, Leonardo published multiple other books Other Works In his book, Liber Abaci, Fibonacci discovered the famous sequence, known as the Fibonacci sequence This was one of the problems, in his book that utilized the Arabic numerals Rabbit Population Problem 1st Problem: Solutions During the reign of Emperor Frederick II of the Norman Kingdom of Sicily, Fibonacci was invited to the Emperor's court to participate in a mathematical tournament Fun Fact Three mathematical problems were assigned to the court Fibonacci was able to solve all three mathematical problems, while none of the other philosophers were able to solve any of the problems The Emperor was greatly impressed by Fibonacci and his mathematical abilities, thus there is a statue of him in a garden across the river Arno by the Leaning Tower of Pisa find a rational number x so that the quadratic expressions x²-5 and x²+5 represent a square of a rational number 2nd Problem: x=(41/12), since x²-5=(41/12)²-5 and x²+5=(41/12)²+5=(49/12)² This solution was later published in his book Liber Quadratorum "Fibonacci showed that the numbers a²-2ab-b², a²+b², a²+2ab-b² are in arithmetic progression. If a=5 and b=4, the common difference is 720 and the first and third squares are 41²-720=31² and 41²+720=49². Dividing by 12² led to the solution of the first of the tournament problem. This problem cannot be solved if 5 is replaced by 1, 2, 3 or 4. Fibonacci proved that if x and h are integers such that x²-h and x²+h are perfect squares, then h must be divisible by 24." 2nd Problem: Solutions determine a root of the cubic equation, x³+2x²+10x-20=0 3rd Problem: 'Three men possess a pile of money, their shares being 1/2, 1/3, 1/6. Each man takes some money from the pile until nothing is left. The first man returns 1/2 of what he took, the second 1/3 and the third 1/6. When the total so returned is divided equally among the men it is found that each then possesses what he is entitled to. How much money was in the original pile and how much did each man take from the pile?’ He found that no root of the equation can be formed in an irrational number, instead, he found an approximate decimal to represent the root x=1.3688081075 The solution was published in his book, Flos with some controversy since he never explained his thought process on completing the problem 3rd Problem: Solutions "Fibonacci solved this problem using a simple algebraic 3x. Before each person returned a third of the total returned, they owned (s/2)-x, (s/3)-x, (s/6)-x. Since these are the total amounts they owned after returning back 1/2, 1/3, 1/6 of what they had first taken, the total amounts first taken were 2((s/2)-x), (3/2)((s/3)-x), (6/5)((s/6)-x) so that the total amount is equal to s. This leads to 7s=47x and hence, the problem is indeterminate, he found 47 as the smallest answer. However, Fibonacci assumed that s=47 and x=7. Consequently, the amounts taken by the three persons from the original pile are 33, 13, 1. He proved problems like this in his book Liber Quadratorum Debnath, Lokenath. "A short history of the Fibonacci and golden numbers with their applications."International Journal of Mathematical Education in Science and Technology. 42. April (2011): 337-367. Sources: "Fibonachos"
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