Clifford Algebras for Projective and Conformal Geometry

Question

According to Clifford Algebra: A Visual Introduction,

• A Clifford Algebra over $\mathbb{R}^3$ may describe the rigid motions in space (namely, conjugation acts as a reflection by a plane).
• A Clifford Algebra over $\mathbb{R}^4$ may describe the projective geometry in space.
• A Clifford Algebra over $\mathbb{R}^5$ may describe the conformal geometry in space.

Where could be found an intuitive explanation for the last two items?

Answer 1

Scroll to the bottom of Clifford Algebra: A Visual Introduction, right under Clifford the Big Red Algebra and you will find two links:

The story continues with Geometric Algebra: Projective Geometry.

The final chapter is Geometric Algebra: Conformal Geometry.

If you like this intuitive graphical presentation of Clifford Algebra you might also be interested in another item by the same author

Double Conformal Mapping: A Finite Mathematics to Model an Infinite World

in monochrome pdf format, and there is a full color version of that paper here:

Double Conformal Mapping: A Finite Mathematics to Model an Infinite World

Answer 2

Doran and Lasenby's book Geometric algebra for physicists does an OK job of presenting those three topics.

Normally the way physicists write does not make me very happy, but their exposition for these particular topics was very helpful to me.