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Spirograph is a geometric drawing device that produces mathematical roulette curves of the variety technically known as hypotrochoids and epitrochoids.The well-known toy version was developed by British engineer Denys Fisher and first sold in 1965.
Thus, a golden rectangle can be constructed with only a straightedge and compass in four steps: Draw a square; Draw a line from the midpoint of one side of the square to an opposite corner; Use that line as the radius to draw an arc that defines the height of the rectangle; Complete the golden rectangle
In each step, a square the length of the rectangle's longest side is added to the rectangle. Since the ratio between consecutive Fibonacci numbers approaches the golden ratio as the Fibonacci numbers approach infinity, so too does this spiral get more similar to the previous approximation the more squares are added, as illustrated by the image.
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The Fibonacci numbers are a sequence of integers, typically starting with 0, 1 and continuing 1, 2, 3, 5, 8, 13, ..., each new number being the sum of the previous two. The Fibonacci numbers, often presented in conjunction with the golden ratio, are a popular theme in culture. They have been mentioned in novels, films, television shows, and songs.
The Secret City was a television series designed to teach children how to draw. [1] The series was produced by Maryland Public Television and aired on PBS [2] and TVOntario in the late 1980s. The series starred Mark Kistler as Commander Mark who led viewers through various drawing exercises and examples. It also featured other characters ...
The figure shows that 8 can be decomposed into 5 (the number of ways to climb 4 steps, followed by a single-step) plus 3 (the number of ways to climb 3 steps, followed by a double-step). The same reasoning is applied recursively until a single step, of which there is only one way to climb.
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.