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Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers, ... created by drawing circular arcs ... as n-Step Fibonacci numbers. [66 ...
Draw a line segment then turn 90° to the left if k is even; Draw a line segment then Turn 90° to the right if k is odd; If the digit is 1: Draw a line segment and stay straight; To a Fibonacci word of length (the n th Fibonacci number) is associated a curve made of segments.
Hosoya's triangle or the Hosoya triangle (originally Fibonacci triangle; OEIS: A058071) is a triangular arrangement of numbers (like Pascal's triangle) based on the Fibonacci numbers. Each number is the sum of the two numbers above in either the left diagonal or the right diagonal.
In the Fibonacci sequence, each number is the sum of the previous two numbers. Fibonacci omitted the "0" and first "1" included today and began the sequence with 1, 2, 3, ... . He carried the calculation up to the thirteenth place, the value 233, though another manuscript carries it to the next place, the value 377.
F, also called the Fibonacci factorial, where n is a nonnegative integer, is defined as the product of the first n positive Fibonacci numbers, i.e. !:= =,, where F i is the i th Fibonacci number, and 0! F gives the empty product (defined as the multiplicative identity, i.e. 1).
The Fibonacci sequence manifests in the number of spiral arms at a unique spot on the Mandelbrot set, mirrored both at the top and bottom. This distinctive location demands the highest number of iterations of for a detailed fractal visual, with intricate details repeating as one zooms in. [42]
The infinite Fibonacci word is a morphic word, generated in {0,1}* by the endomorphism 0 → 01, 1 → 0. [9] The nth element of a Fibonacci word, , is 1 if the Zeckendorf representation (the sum of a specific set of Fibonacci numbers) of n includes a 1, and 0 if it does not include a 1.
A repfigit, or Keith number, is an integer such that, when its digits start a Fibonacci sequence with that number of digits, the original number is eventually reached. An example is 47, because the Fibonacci sequence starting with 4 and 7 (4, 7, 11, 18, 29, 47) reaches 47.