# Difference between revisions of "Pythagorean Tree"

Pythagorean Tree, in 2 Dimensions
Fields: Algebra and Fractals
Image Created By: Enri Kina and John Wallison

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

$\frac{1}{x}$

In this image, the original square ha [...]

$\frac{1}{x}$

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, $a^2 + b^2 = c^2$, to get $a^2 + b^2 = 6^2$. 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 a can be found use the $\theta$