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[3] viXra:2610.0116 [pdf] replaced on 2026-11-09 22:40:25
Authors: James A. Smith
Comments: 4 Pages.
Introductory-level Geometric Algebra provides a simple, structured solution to an intriguing problem that has become popular online: A rectangle of unknown dimensions and area is divided into four triangles. Given the areas of three of the triangles, find the area of the fourth.
Category: Geometry
[2] viXra:2610.0097 [pdf] replaced on 2026-11-10 04:31:39
Authors: Michael Marquard
Comments: 22 Pages.
The following paper shows that some 3SAT (3-Satisfiability) problems containing only one unique solution cannot be solved in polynomial time. To do so a new technique I call "boolean isolation" is used to create an equation defining eachvariable in the 3SAT problem thus creating a system of equations. From there circuit analysis and other methods are used to show that any possible equation to find the values in the 3SAT problem would have to be equivalent to the equationcreated by boolean isolation allowing minimum bounds to be established. This paper will also discuss the possible impacts of these findings on other fields including cryptography.Keywords: P Versus NP, Computational Complexity, SAT, Polynomial Time, Exponential Time, Cryptography
Category: Geometry
[1] viXra:2610.0085 [pdf] submitted on 2026-10-22 01:16:26
Authors: Edgar Valdebenito
Comments: 14 Pages.
In this note, we recall exact formulas for calculating the perimeter of an ellipse and give an example of an ellipse whose perimeter is pi.
Category: Geometry
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