Magnetic Sphere Constructions
Inhaltsverzeichnis
Referenz
Henry Segerman and Rosa Zwier: Magnetic Sphere Constructions. In: Bridges 2017, Pages 79–86.
DOI
Abstract
We investigate constructions made from magnetic spheres. We give heuristic rules for making stable constructions of polyhedra and planar tilings from loops and saddles of magnetic spheres, and give a theoretical restriction on possible configurations, derived from the Poincaré-Hopf theorem. Based on our heuristic rules, we build relatively stable new planar tilings, and, with the aid of a 3D printed scaffold, a construction of the buckyball. From our restriction, we argue that the dodecahedron is probably impossible to construct. We finish with a simplified physical model, within which we show that a hexagonal loop is in static equilibrium.
Extended Abstract
Bibtex
@inproceedings{bridges2017:79,
author = {Henry Segerman and Rosa Zwier},
title = {Magnetic Sphere Constructions},
pages = {79--86},
booktitle = {Proceedings of Bridges 2017: Mathematics, Art, Music, Architecture, Education, Culture},
year = {2017},
editor = {David Swart, Carlo H. S\'equin, and Krist\'of Fenyvesi},
isbn = {978-1-938664-22-9},
issn = {1099-6702},
publisher = {Tessellations Publishing},
address = {Phoenix, Arizona},
note = {Available online at \url{http://archive.bridgesmathart.org/2017/bridges2017-79.pdf}}
}
Used References
[1] Tai L. Chow. Introduction to electromagnetic theory: a modern perspective. Jones & Bartlett, 2006.
[2] Samuel Earnshaw. On the nature of the molecular forces which regulate the constitution of the luminiferous ether. Trans. Camb. Phil. Soc., 7:97–112, 1842.
[3] Victor Guillemin and Alan Pollack. Differential Topology. AMS Chelsea Publishing. AMS, 2010.
[4] Heinz E. Knoepfel. Magnetic Fields: A Comprehensive Theoretical Treatise for Practical Use. Wiley, 2008.
Links
Full Text
http://archive.bridgesmathart.org/2017/bridges2017-79.pdf
