I’ve heard a lot about the amazing geometry of fibonacci and how it it’s supposed to be in all nature and that’s sacres geometry… But I simply don’t see it can some please explain me the hypes of it
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Fibonacci was a mathematician who published a book. The entire purpose of the book was to show how much easier it is to do mathematics using Arabic numerals, as opposed to Roman numerals. One example he gave was a simple list of numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89… et cetera. The sequence is formed by adding the two most recent numbers to get the next number.
Fibonacci was a mathematician who published a book. The entire purpose of the book was to show how much easier it is to do mathematics using Arabic numerals, as opposed to Roman numerals. One example he gave was a simple list of numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89… et cetera. The sequence is formed by adding the two most recent numbers to get the next number.
Fibonacci was a mathematician who published a book. The entire purpose of the book was to show how much easier it is to do mathematics using Arabic numerals, as opposed to Roman numerals. One example he gave was a simple list of numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89… et cetera. The sequence is formed by adding the two most recent numbers to get the next number.
In the Fibonacci sequence, each number is the sum of the two previous ones. It is helpful in computer science, for instance, for creating random numbers and sorting data. Natural examples include the spiral shapes of shells and galaxies.
In the Fibonacci sequence, each number is the sum of the two previous ones. It is helpful in computer science, for instance, for creating random numbers and sorting data. Natural examples include the spiral shapes of shells and galaxies.
In the Fibonacci sequence, each number is the sum of the two previous ones. It is helpful in computer science, for instance, for creating random numbers and sorting data. Natural examples include the spiral shapes of shells and galaxies.
There are multiple ways to define Fibonacci numbers:
– Set the first two to be 0 and 1, and every after as the sum of those two preceding it: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, … .
– The number of different ways to form a strip of fixed length by glueing strips of lengths 1 and 2 together.
– The number of binary (only 0 and 1 allowed) sequences with a fixed number of digits, and 1s must not be consecutive.
– Via Binet’s formula as ( φ^n – (-1/φ)^n ) / sqrt(5).
– [many more]
> how it it’s supposed to be in all nature and that’s sacres geometry…
That’s a myth at best, and a lie at worst. There are some very few instances where they somewhat appear, but those are one in a million things. None of the claims of golden ratios appearing within humans, plants or animals has ever withstood scrutiny, sqrt(2), 1.5 and sqrt(3) are just as probable and nonsensical.
Edit: spelling.
There are multiple ways to define Fibonacci numbers:
– Set the first two to be 0 and 1, and every after as the sum of those two preceding it: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, … .
– The number of different ways to form a strip of fixed length by glueing strips of lengths 1 and 2 together.
– The number of binary (only 0 and 1 allowed) sequences with a fixed number of digits, and 1s must not be consecutive.
– Via Binet’s formula as ( φ^n – (-1/φ)^n ) / sqrt(5).
– [many more]
> how it it’s supposed to be in all nature and that’s sacres geometry…
That’s a myth at best, and a lie at worst. There are some very few instances where they somewhat appear, but those are one in a million things. None of the claims of golden ratios appearing within humans, plants or animals has ever withstood scrutiny, sqrt(2), 1.5 and sqrt(3) are just as probable and nonsensical.
Edit: spelling.
There are multiple ways to define Fibonacci numbers:
– Set the first two to be 0 and 1, and every after as the sum of those two preceding it: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, … .
– The number of different ways to form a strip of fixed length by glueing strips of lengths 1 and 2 together.
– The number of binary (only 0 and 1 allowed) sequences with a fixed number of digits, and 1s must not be consecutive.
– Via Binet’s formula as ( φ^n – (-1/φ)^n ) / sqrt(5).
– [many more]
> how it it’s supposed to be in all nature and that’s sacres geometry…
That’s a myth at best, and a lie at worst. There are some very few instances where they somewhat appear, but those are one in a million things. None of the claims of golden ratios appearing within humans, plants or animals has ever withstood scrutiny, sqrt(2), 1.5 and sqrt(3) are just as probable and nonsensical.
Edit: spelling.
Not a lot of ELI5 answers, but some good history.
The Fibonacci sequence is a set of numbers with a distinct pattern (explained in other comments). What is important is that the ratio of one number to the one following it is always the same. (The second is always 1.618 times larger than the previous). That is called the golden ratio, and it is the golden ratio that is seen everywhere in nature.
If you’ve seen the image of rectangles that form into a spiral, this is what it means:
The small rectangle has sides with that exact ratio. The long side of that rectangle is the short side of the next, and that rectangle uses the golden ratio. The long side of that one is the short side of the next…. And so on. This creates a spiral pattern, and that pattern, in that ratio, happens all the time. Flowers, tree leaves, and animal shells for example. Always 1.618 times bigger than the previous part.
The number isn’t magical. 1.618 isn’t special. There is just a natural order to things, and we created a numerical system that happens to measure that order at that number.
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