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**Author:**

Michaud, André

**Category:**

Research Papers

**Sub-Category:**

Mathematical Physics

**Language:**

English

**Date Published:**

August 04, 2024

**Downloads:**

119

**Keywords:**

N/A

**Abstract:**

The object of this article is a comparative analysis of the geometric characteristics of the 2D unit vector set of the complex plane as used in Quantum Mechanics and in the treatment of electric LC circuits, of the 3D unit vector set of Hamilton's hypersphere as used in quantum theory and finally of the 3x3D unit vector set of the trispatial geometry as used in electromagnetic mechanics. Analysis of the implications of extending the use of the hypersphere coordinate system to the treatment of LC circuits and to the traditional 3D Cartesian coordinate system, and of the consequences of using a unique property of the vectorial cross product of the quaternion complex unit vectors of reversing the direction of application of the resulting real unit vector in the development of electromagnetic mechanics by means of the trispatial geometry.

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