# The Pythagorean Theorem: Interactive Puzzle

The Pythagorean Theorem
$\color{NavyBlue}c\color{Black}^2 = \color{ForestGreen}a\color{Black}^2 + \color{BrickRed}b\color{Black}^2$
$\color{ForestGreen}a$
$\color{BrickRed}b$
$\color{NavyBlue}c$
You've proved
the Pythagorean theorem!
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Theorem (Boyaj, 1832; Gervin, 1833). If two polygons have the same area, then they are decomposable in the same set of polygons.

That is, if two polygons have equal areas, then any of them can be decomposed into a finite set of pieces with which it is possible to reconstruct exactly the other polygon.

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