Barycentric coordinates
Three weights that sum to one, expressing a point as a blend of a triangle's three vertices.
Möbius described them in 1827. A point inside the triangle gets weights (α, β, γ) that are all positive and sum to one; outside, one weight goes negative — which hands you a point-in-triangle test for free.
In rasterization they are the workhorse: the same weights that decide whether a pixel hits the triangle are used to interpolate depth, colour, normals and texture coordinates across the vertices. Gouraud shading and perspective-correct texture mapping are barycentric interpolation under the hood.