De Gua's theorem
From Wikipedia, the free encyclopedia
De Gua's theorem is a generalization of the Pythagorean theorem to three dimensions and named for Jean Paul de Gua de Malves. If a tetrahedron has a right angle corner (a corner like a cube), then the square of the area of the face opposite the right angle corner is the sum of the squares of the areas of the other three faces.
| front - face opposite of the right angle corner | back - faces at right angle corner | view from the side |
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The Pythagorean theorem and de Gua's theorem are special cases (n=2,3) of a general theorem about n-simplexes with a right angle corner.
[edit] References
- Eric W. Weisstein, de Gua's theorem at MathWorld.
- Note on an n-dimensional Pythagorean theorem (PDF)
