is an extension of geometric algebra (GA)

is an extension of projective geometric algebra (PGA) that includes another dimension based on the stereographic projection

a CGA based on 𝑛-D space is a GA with signature (𝑛+1, 1, 0)

a CGA is a PGA that contains only flat geometries (points, lines, planes, hyperplanes) and can only perform rigid transformations (i.e. preserving distances and angles)

a CGA also contains round things (circles, spheres, etc) and can perform conformal transformations (i.e. preserving only angles)

adds two dimensions to ordinary space and includes everything in the rigid geometric algebra (RGA)

it also adds representations for round objects like circles and spheres as well as dilations, inversions, and other conformal transformations