De Gua's theorem
Appearance
De Gua's theorem is a three-dimensional analog of the Pythagorean theorem and named for Jean Paul de Gua de Malves. If a tetrahedron has a right-angle corner (like the corner of 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 |
---|---|---|
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.