Pythagorean Theorem Visual Proof Art

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Pythagorean Theorem Visual Proof Art

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0.16mm layer, 2 walls, 15% infill
0.16mm layer, 2 walls, 15% infill
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5.7 h
1 plate

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Description

This is a 3D artistic representation of the Pythagorean Theorem visual proof, based on this diagram:

 

 

The model consists of four identical right triangles with legs a, b, and hypotenuse c that correspond to three different squares.

 

 

The larger central square shares edges with the hypotenuse of the right triangles (c). In other words, this square has an area of c^2.

 

The 4 medium squares around the outside share edges with leg b of the right triangles. Thus, they have an area of b^2.

 

And finally, the 4 small squares around the outside share edges with leg a of the right triangles. So, they have an area of a^2.

 

As it turns out, the combined areas of square A and B is equal to the area of square c. In other words, a^2 + b^2 = c^2! To emphasize this relationship, squares a and b have their own unique visual pattern, while square c features an overlay of a and b's patterns.

 

This is meant to be a simple but elegant visualization of these relationships that might help explain this theorem.

 

Cheers!

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