Math Paper

Constructing three and higher n-dimensional complex number spherical and Cartesian coordinate systems based on rotation factors

(2023) by Qiujiang Lu

Abstract:

Based on the set of real numbers and the set of rotation factors, the constructions of three and higher n-dimensional complex number spherical coordinate systems are realized. The projections of complex numbers or position vectors from four-dimensional space to three-dimensional space as well as from a higher n-dimensional space to a lower dimensional space are conceived. The projections are consistent throughout regardless of the dimensional levels and the generalization of the n-dimensional coordinate systems are achieved with n=2 for two-dimensional plane, n=3 for three-dimensional space, n=4 for four-dimensions and so on. The generalization of transformation to n-dimensional Cartesian coordinate systems from the spherical systems are obtained. The rotation operations in the n-dimensional complex number spherical coordinate systems are succinct and efficient, and the results can be transformed back to Cartesian coordinate systems, and vice versa.

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