1606 Submissions

[2] viXra:1606.0253 [pdf] submitted on 2016-06-24 06:43:12

A Very Brief Introduction to Reflections in 2D Geometric Algebra, and their Use in Solving ``Construction" Problems

Authors: James A. Smith
Comments: 8 Pages.

This document is intended to be a convenient collection of explanations and techniques given elsewhere in the course of solving tangency problems via Geometric Algebra.
Category: Geometry

[1] viXra:1606.0050 [pdf] submitted on 2016-06-05 13:16:17

Bellman’s Escape Problem for Convex Polygons

Authors: Philip Gibbs
Comments: Pages. DOI: 10.13140/RG.2.2.28270.61767

Bellman’s challenge to find the shortest path to escape from a forest of known shape is notoriously difficult. Apart from a few of the simplest cases, there are not even many conjectures for likely solutions let alone proofs. In this work it is shown that when the forest is a convex polygon then at least one shortest escape path is a piecewise curve made from segments taking the form of either straight lines or circular arcs. The circular arcs are formed from the envelope of three sides of the polygon touching the escape path at three points. It is hoped that in future work these results could lead to a practical computational algorithm for finding the shortest escape path for any convex polygon.
Category: Geometry