The Higher-Dimensional Pythagorean Theorem
1. Introduction We have all heard of the familiar Pythagorean theorem, relating the side lengths of a right triangle. But, have you heard of De Gua’s Theorem? An interesting generalization of the Pythagorean theorem into 3 dimensions, this theorem is very similar result for “right tetrahedrons” where three of the edges are mutually perpendicular. Suppose, in such a tetrahedron we have Denote the area of as . Then, In today’s post, we will investigate whether a…