Euler's Distribution Theorem
Euler's Distribution Theorem
For signed distances on a line segment (so that XY = -YX), AB×CD + AC×DB + AD×BC = 0. If , , , and are the coordinates of the four points on the line, this follows from the algebraic identity .
a
b
c
d
(b-a)(d-c)+(c-a)(b-d)+(d-a)(c-b)=0