Difference between revisions of "Pythagorean Tree"
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[[Image:pythagoreantree.png]] | [[Image:pythagoreantree.png]] | ||
| − | 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, <math>a^2 + b^2 = c^2</math>, to get <math>a^2 + b^2 = 6^2</math>. 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<math>\theta</math> | + | 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, <math>a^2 + b^2 = c^2</math>, to get <math>a^2 + b^2 = 6^2</math>. 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 <math>\theta</math> |
|other=Basic Algebra | |other=Basic Algebra | ||
Revision as of 14:27, 29 May 2013
| 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 a can be found use the 
Teaching Materials
- There are currently no teaching materials for this page. Add teaching materials.
Leave a message on the discussion page by clicking the 'discussion' tab at the top of this image page.
