/Internship-WS22-Rolling-Knots

Code produced during the "Rolling Knots" student project at the Heidelberg Experimental Geometry Lab. A part of the Heidelberg University mathematics faculty.

Primary LanguagePython

HEGL-Rolling_Knots

This code is rewritten from a Matlab code of the same name by Stephen Lucas (http://educ.jmu.edu/~lucassk/). Link to the original paper: https://archive.bridgesmathart.org/2020/bridges2020-367.html

It was produced during the "Rolling Knots" student project at the Heidelberg Experimental Geometry Lab. A part of the Heidelberg University mathematics faculty. The bulk of the code concerns testing the rolling ability of a given Morton Knot. The rolling ability is taken from the vertical and transversal displacement of the center of mass of the knots which are plotted by the code. Finding knots with the optimal rolling ability is done by minimizing an objective function (2 included) numerically.

The premise stemming from Morton's paper on the existence of trefoil knots without tritangent planes: https://www.researchgate.net/publication/243028042_Trefoil_Knots_without_Tritangent_Planes