A famous theorem in Euclidean geometry often attributed to the Greek thinker Pythagoras of Samos (6th century, B.C.) states that if one of the angles of a planar triangle is a right angle, then the square of the length of the side opposite the right angle equals the sum of the squares of the lengths of the sides which form the right angle.
There are less commonly known higherdimensional versions of this theorem which relate the areas of the faces of a simplex having one “orthogonal vertex” by analogous sums-of-squares identities. In this note I state and prove one such result, hoping that students of mathematics will become better acquainted with it.
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