Pythagorean Tree
Pythagorean Tree, in 2 Dimensions |
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Pythagorean Tree, in 2 Dimensions
- A Pythagorean Tree is a fractal that is created out of squares. The space between the squares in each iteration creates a right triangle. The top line of the square becomes the hypotenuse of the triangle above it.
Basic Description
This animation shows how the angles of the triangle affect the shape of the tree.
A More Mathematical Explanation
- Note: understanding of this explanation requires: *Basic Algebra
In this image, the original square has an area of 36, meaning its side length s = 6. This can be put into the Pythagorean theorem, , to get . This means the sum of the areas of the two branched-off squares will always be equal to the original square. The length of a
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