Geometric Algebra and the Prehistory of Multidimensional Geometry

Our terms square and cube go back to the Pythagoreans, for whom quadratic numbers and cubic numbers were special cases of figurate numbers. These included plane numbers mƷn, solid numbers lƷmƷn, as well as the more complex triangular numbers n(n + 1)/2, pentagonal numbers n(3n – 1)/2, pyramidal numbers n(n + 1) (n + 2)/2Ʒ3, and so on.1 This terminology derives from the notion that points―which the Pythagoreans identified with units―are distributed in a discrete manner in figures in accordance with definite rules.