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[5] viXra:2105.0174 [pdf] submitted on 2021-05-30 19:31:26
Authors: Russell P. Patera
Comments: 3 Pages.
The Pythagorean Theorem is derived by performing an infinitesimal rotation of a right triangle and using the equation for arc length and the equation for the area of a triangle.
Category: Geometry
[4] viXra:2105.0065 [pdf] submitted on 2021-05-10 21:48:13
Authors: James A. Smith
Comments: 8 Pages.
We present two Geometric-Algebra (GA) solutions to a vector-rotation problem posed by Professor Miroslav Josipovic. We follow the sort of solution process that might be useful to students. First, we review concepts from GA and classical geometry that may prove useful. Then, we formulate and carry-out two solution strategies. After testing the resulting solutions, we propose an extension to the original problem.
Category: Geometry
[3] viXra:2105.0054 [pdf] replaced on 2021-05-31 16:42:04
Authors: Antoine Balan
Comments: 2 pages, written in french
We propose the LCK+ Seiberg-Witten equations which are the Seiberg-Witten equations for a LCK+ metric.
Category: Geometry
[2] viXra:2105.0038 [pdf] submitted on 2021-05-09 12:23:20
Authors: Theophilus Agama
Comments: 9 Pages.
In this paper we introduce and develop a method for studying problems concerning packing and covering dilemmas and explore some potential applications.
Category: Geometry
[1] viXra:2105.0028 [pdf] submitted on 2021-05-06 20:51:08
Authors: Xavier Gisz
Comments: 8 Pages. [Corrections made by viXra Admin to conform with the requirements on the Submission Form]
These are currently four well known isohedral space-filling convex polyhedra: parellelepiped (the most symmetric form being the cube), rhombic dodecahedron, oblate octahedron (also known as the square bipyramid) and the disphenoid tetrahedron. In this paper it is shown that a Bilinski dodecahedron is an isohedral space-filling tessellating polyhedron, thus bringing the number of these to five.
Category: Geometry
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