Applications of the theorem of Pythagoras in R3.

Three distinct points [image omitted] and [image omitted] with [image omitted] are taken, respectively on the x, y and the z-axes of a rectangular coordinate system in [image omitted] Using the converse of the theorem of Pythagoras, it is shown that the triangle [image omitted] can never be a right-angled triangle. The result seems to be intuitive, but nevertheless requires a proof. As an application, some intuitive results about a tetrahedron are confirmed. [ABSTRACT FROM AUTHOR]