WT68: Euler's Four Point Relation
Euler found the volume of a tetrahedron in terms of the six quadrances of its sides. When the four points lie instead in a plane, the volume is zero, so Euler's formula gives a relation between the six quadrances. We work towards discovering this relation by studying a particular quadrilateral in the plane, and using rational trigonometry to determine the sixth quadrance from the other five. This video is part of the WildTrig series, which introduces Rational Trigonometry and applies it to many different aspects of geometry.