The Golden Ratio and the Fibonacci Numbers defined
The History of the Golden Ratio
The History of Fibonacci
Mathematical Properties of the Golden Ratio
Constructing a Golden Rectangle
The Secret of the Golden Ratio
The Golden Ratio and Beauty...
The History of the Fibonacci Sequence
Fibonacci's full name was Leonardo of Pisa, or Leonardo Pisano. Sometimes he used his nickname Bigollo which probably means good for nothing or a traveler. He was born in 1175 in a place called Pisa in Italy.
His father, Guilielmo, one of the merchants of the Republic of Pisa, traded in Bugia (now is called Bejaja) which is a Mediterranean port in northeastern Algeria. During his journey with his father in North Africa, he had gained a lot of valuable mathematical systems that were popular used in the countries they visited.
After 15 years, he ended his long travel and retuned to his hometown, where he began writing books based on his foundation of mathematics. The copies of Fibonacci's hand-written books that we fortunately have are Liber abaci (1202), Practica geometricae (1220), Flos (1225), and Liber quadratorum. Although some of his books about commercial arithmetic, irrational numbers are lost.
In his Liber abaci, the Fibonacci numbers was frist introduced. It became one of the reasons for which Fibonacci is best remembered today. Liber quadratorum is Fibonacci's most impressive piece of work in which he first notes that square numbers can be contracted as sums of odd numbers, describing an inductive construction by using the formula 2 + (2n+1) = (n+1)2. Fibonacci also proved many other interesting number theories. Such as there is no x, y such that x^2 + y^2 and x^2 - y^2 are both squares and x^4 - y^4 cannot be a square. Fibonacci's work of number theoy was unknown during the Middle ages, and we actually find the same results appearing in the work of Maurolico, three hundred years later.