Geometry

N-Complex Number, N-Dimensional Polar Coordinate and 4D Klein Bottle with 4-Complex Number

Authors: Kuan Peng
Comments: 21 Pages.

While a 3D complex number would be useful, it does not exist. Recently, I have constructed the N-complex number, which has demonstrated high efficiency in computations involving high-dimensional geometry. The N-complex number provides arithmetic operations and polar coordinates for N-dimensional spaces, akin to the classic complex number. In this paper, we will explain how these systems work and present studies on 4D Klein bottles and hyperspheres to illustrate the advantages of these systems.
Category: Geometry