That might partially be true, but GA can mostly be given an API that hides the gory and confusing algebra. This is actually quite a natural thing to do. The ide

That might partially be true, but GA can mostly be given an API that hides the gory and confusing algebra. This is actually quite a natural thing to do. The idea is pretty much that in 3D you can begin with reflections through planes, which most people do understand, and then represent other Euclidean transformations as straightforward compositions of those. Once you have an API for transformations, then a geometric figure like a point or a line can be represented by the reflection (which is a transformation again) through it.