Fibonacci Numbers

In Pisa in 1223, Emperor Frederick II of Swabia, was happy to attend a single tournament between ABAC and algorithms, armed only with paper, pen and abacus . In fact, the race proved that the method positional Indian learned from the Arabs could calculate faster than any schedule. The test was: “How many pairs of rabbits can be obtained in one year (except in cases of death) on the assumption that each pair give birth to another pair every month and that younger couples are able to reproduce only the second month of life? “. A Pisano, Leonardo, said Bigollo, also known as father of” fill Bonacci “or Fibonacci won the race. Son of a civilian use for trade in the Mediterranean, Leonardo lived in Arab countries as a child and learned the principles of algebra, calculus, from the masters of Algiers, which had been entrusted by his father, an expert accountant.

Leonard gave the test an answer so fast as to even suspect that the tournament was rigged: At the end of the first month you have the first pair and a torque generated by this and by the end of the second month you add a third pair, but there are two more torque, so that the second pair began to build,bringing the bill to 5 pairs, and so on. The argument continues with the following scale: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393 … With this trick it was easy for the Fibonacci find the correct answer.Each new number is not the sum of the two preceding it. This is the first logical progression of mathematics! This series, now known as the “Fibonacci numbers” has certain properties (the most important of which is that if any number of the series is squared, this is equal to the product of the number that precedes and what follows it, increased or decreased by one unit) that allow you to build some puzzling tricks. Example: 21 2 = (13 * 34) -1 = 441 and 89 2 = (55 * 144) +1 = 7921 Later that exercising mercatura, Leonardo traveled to Syria, Egypt, Greece, knowing the greatest Muslim mathematecians . From these experiences arose the Liber Abaci, a colossal Treaty opened up the mysteries of the nine West “figures” and the Indian sign unknown to the Greeks and Latins, “quod zephirum appellantur arabic, which is a number like a breath of empty Wind: zefito precisely zefr, or zero.
Source:scienceray.com