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 (like the corner of 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.

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.

References

* Eric W. Weisstein, de Gua's theorem at MathWorld.

* Note on an n-dimensional Pythagorean theorem (PDF)

Geometry