Фибоначчи

8φ = 8 × 1.618034.
= 12.94427.
= 13 (rounded)

What is the Fibonacci sequence?

From its origins to its significance, almost every popular notion about the famous Fibonacci sequence is wrong.

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The seeds in a sunflower exhibit a golden spiral, which is tied to the Fibonacci sequence. (Image credit: belterz/Getty Images)

• Who discovered it?
• Why is it important?
• Are there real-life examples?

The Fibonacci sequence is a series of numbers in which each number is the sum of the two that precede it. Starting at 0 and 1, the first 10 numbers of the sequence look like this: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and so on forever. The Fibonacci sequence can be described using a mathematical equation: Xn+2= Xn+1 + Xn

People claim there are many special properties about the numerical sequence, such as the fact that it is “nature’s secret code” for building perfect structures, like the Great Pyramid at Giza or the iconic seashell that likely graced the cover of your school mathematics textbook. But much of that is incorrect and the true history of the series is a bit more down-to-earth.

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Golden Ratio

And here is a surprise. When we take any two successive (one after the other) Fibonacci Numbers, their ratio is very close to the Golden Ratio «φ» which is approximately 1.618034.

In fact, the bigger the pair of Fibonacci Numbers, the closer the approximation. Let us try a few:

B / A

We don’t have to start with 2 and 3, here I randomly chose 192 and 16 (and got the sequence 192, 16,208,224,432,656, 1088, 1744, 2832, 4576, 7408, 11984, 19392, 31376, . ):

B / A
192
16
7408
11984
11984
19392

It takes longer to get good values, but it shows that not just the Fibonacci Sequence can do this!

Формула послідовності Фібоначчі

Наприклад:

F ₂ = F ₁ + F ₀ = 1 + 0 = 1

F ₃ = F ₂ + F ₁ = 1 + 1 = 2

F ₄ = F ₃ + F ₂ = 2 + 1 = 3

F ₅ = F ₄ + F ₃ = 3 + 2 = 5

Источники:

https://www.livescience.com/37470-fibonacci-sequence.html&rut=1ff5ff70da779552a19184e8022d3b1357225e0d693ec7f5f7f1ab0ea1feb8b7
https://en.wikipedia.org/wiki/Fibonacci_sequence&rut=968d85b5c46cfec30a9b37f0132a6957963c5e2c476722770876cd0788e891e0
https://www.mathsisfun.com/numbers/fibonacci-sequence.html&rut=e3032982d8704ec5ed3259f239346294bf2496769f651bcb5e904adb2629a1d2
https://www.rapidtables.org/uk/math/number/fibonacci.html&rut=2a7b5c6e8056bba3991288a840342bc35253fcd9910980b9f2b34195b156f2df