Geometry of moving planes

TL;DR

This paper explores the geometry of moving planes to introduce new mathematical frameworks, emphasizing the potential of advanced algebraic methods like Clifford's geometric algebra for future mathematical development.

Contribution

It demonstrates how studying moving planes can lead to new mathematical insights and encourages learning powerful algebraic techniques for extending current mathematical theories.

Findings

New perspectives on the geometry of moving planes

Potential for developing advanced algebraic methods

Encouragement for further mathematical exploration

Abstract

The concept of number and its generalization has played a central role in the development of mathematics over many centuries and many civilizations. Noteworthy milestones in this long and arduous process were the developments of the real and complex numbers which have achieved universal acceptance. Serious attempts have been made at further extensions, such as Hamiltons quaternions, Grassmann's exterior algebra and Clifford's geometric algebra. By examining the geometry of moving planes, we show how new mathematics is within reach, if the will to learn these powerful methods can be found.