Fibonacci numbers

Fibonacci numbers for a long time fit into the history of mathematics. And it all started with the fact that Leonardo Fibonacci conducted research on rabbits. He wanted to calculate the rate of increase in their livestock, starting with two young individuals of different sexes. He drew a table of the growth of livestock, based on a pair of one-month-old age, a month later another heterosexual couple was born, then everything went on in the same order. If you try to make such a calculation yourself, starting at 0, and record the number of pairs of rabbits at the end of each month (in this calculation we do not take into account possible deaths), you get the so-called Fibonacci numbers: 0, 1, 1, 2, 3 , 5, 8, 13, 21, 34, 55, 89... This numerical sequence is called the "Fibonacci series" and continues to infinity.

Fibonacci numbers for a long time fit into the history of mathematics

Fibonacci numbers are very simple: each number is the sum of the two preceding numbers. A deeper look at the relationship between the numbers in the Fibonacci series shows that the further we move forward on the scale of numbers, the closer and closer to the "golden number" the ratio of each number to the next. Sometimes Fibonacci numbers are also considered for negative values, as a two-sided infinite sequence that satisfies the same recurrence relation.

Therefore, the Fibonacci numbers are closely related to "golden ratio", and this is reflected far beyond the limits of the world of mathematics and geometry created by man.

It turns out that the Fibonacci sequence was well known in ancient India, where it was applied in the metric sciences (prosody, in other words - versification), much earlier than it became known in Europe.

The greatest common divisor of two Fibonacci numbers is equal to the Fibonacci numbers with the index equal to the largest common index divisor.

Tools