There's interesting stuff like Conformal Geometric Algebra and Projective Geometric Algebra. The idea behind them being that geometric objects like lines, circl

There's interesting stuff like Conformal Geometric Algebra and Projective Geometric Algebra. The idea behind them being that geometric objects like lines, circles and points can be represented as elements of a Clifford algebra, with the various different products in GA having some natural geometric meaning. I don't know if it's useful, but it's certainly interesting.