Elements, topology, and T-shirts

Details Elements, topology, and T-shirts Elements, topology, and T-shirts

2006-03-05

arxiv.org/abs/physics/0603026v1

Physics

Physics Education

2 pages, 3 figures, 4 refs, cf. http://www.umsl.edu/~fraundor/edisc.html

Scientific paper

Consider the network of elements connected by adjacency in atomic number and periodic table column. If all elements except H-He are connected by identical springs and constrained to a z-spiral in 2D, a map sans spring-crossing results for various values of rest length in units of the H-He distance. If the z-spiral is removed, and the network allowed to relax in 3D, the resulting surface with three holes has the topology of a T-shirt or open-handle teapot. Mapping this to a shirt's front-back pattern yields a 2D table of elemental inter-connects in tabular (nearly rectilinear) form. Sample applications: The flat spiral (like other spiral patterns) might serve as basis for an educational board game, while the T-shirt table might serve as a starting point for ``topologically informed'' classroom periodic-table design projects with wearable awards.

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