Geometry

2404 Submissions

[2] viXra:2404.0116 [pdf] replaced on 2024-05-11 15:34:03

A Geometric Algebra Solution to a Hard Contest Problem

Authors: James A. Smith
Comments: 4 Pages.

We show how to use rotations of vectors in GA to solve the following problem: "The following are known about a triangle: The ratio of the lengths of two sides; the angle formed by those sides; and the length of that angle’s bisector. Find the length of the side opposite that angle."
Category: Geometry

[1] viXra:2404.0039 [pdf] submitted on 2024-04-07 06:30:48

Constructing Legendrian Links from Chiral Reeb Chords

Authors: Ryan J. Buchanan
Comments: 8 Pages.

Some theorems on the construction of links (defined herein) from Reeb chords are established and proved. We relate these concepts to physics by constructing an arbitrary spacetime from a background knot using Reidemeister moves.
Category: Geometry