Gyrovector spaces are a brilliant mathematical construction which generalizes on the idea of vector spaces. The gyrovectors in gyrovector spaces can be considered vector spaces in hyperbolic geometry. The is repository contains a simple web app for playing with two gyrovector spaces, the Mobius gyrovector space, and the Einstein gyrovector space. It shows what addition of two vectors in the spaces looks like, as well as scalar multiplication.
For more information on gyrovector spaces, see Ungar's book "A Gyrovector Space Approach to Hyperbolic Geometry".