I do agree that GA is overhyped, but it's definitely not useless. GA brings many separate concepts into a common framework. He's a couple of things that are jus

I do agree that GA is overhyped, but it's definitely not useless. GA brings many separate concepts into a common framework. He's a couple of things that are just ugly: - Cross product only works in 3d - Why is it that the cross product seems mysteriously related to determinants? - Multivariate calculus as typically taught is very ugly - Complex numbers for 2d, quaternions for 3d, then what? - Rotations/reflections using linear algebra - Cauchy's integral formula, Stokes' theorem, Helmholz decomposition, etc. - Etcetera GA just makes all of that much nicer and brings it together into a coherent framework. Here's a simple problem that illustrates why GA is nice: given 3 points A,B,C in 2-d space with integer coordinates, determine whether B is on the line segment AC. Now do it in 3-d, and then in n-d.