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[4] viXra:2207.0169 [pdf] submitted on 2022-07-28 22:20:37
Authors: James A. Smith
Comments: 11 Pages. (Note by viXra Admin: The name on the Submission Form and article in pdf should be the same - Please conform in the future)
To help fill the need for examples of introductory-level problems that have been solved via Geometric Algebra (GA), we show how to calculate the angle through which a given vector must be rotated in order that its endpoint be at a given distance d from a specified point P. The three solution methods that are employed here start from a trigonometric equation is derived from GA’s formula for rotating vectors. The first two solutions use methods that are "automatic", but produce formulas that are not readily interpreted. In contrast, the third method —which does produce a readily interpreted formula— is based upon an examination of the geometric significance of terms in the initial trigonometric equation.
Category: Geometry
[3] viXra:2207.0095 [pdf] submitted on 2022-07-14 00:51:48
Authors: Theophilus Agama
Comments: 9 Pages.
In this paper we study the global electrostatic energy behaviour of mutually repelling charged electrons on the surface of a unit-radius sphere. Using the method of compression, we show that the total electrostatic energy $U_k(N)$ of $N$ mutually repelling particles on a sphere of unit radius in $mathbb{R}^k$ satisfies the lower boundbegin{align} U_k(N)gg_{epsilon}frac{N^{2}}{sqrt{k}}.onumberend{align}.
Category: Geometry
[2] viXra:2207.0050 [pdf] replaced on 2023-02-02 23:11:29
Authors: Thomas Halley
Comments: 48 Pages.
A basic smooth manifold and a rational smooth set is explored with variations in proving that R is not equal to i.
Category: Geometry
[1] viXra:2207.0017 [pdf] replaced on 2022-07-05 22:53:07
Authors: Volker Thürey
Comments: 6 Pages.
We give a new formula for the barycenter of a 4-gon.
Category: Geometry
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