A Threefold Möbius Band with Constant Twist and Minimal Bending as the Limit of Tetrahedral Rings

Year: 2018 Authors: Johannes Schönhke; Michael Grunwald; Eliot Fried

Core claim

A sequence of linked twisted tetrahedra converges to a unique threefold Möbius band whose midline appears to minimize total curvature among closed curves with fixed nonzero torsion.

Topics

tetrahedral rings, Möbius band, minimal bending, space curves

Domains

differential geometry, topology, curvature and torsion, ruled surfaces, geometric form, kinetic sculpture, paper model, visual aesthetics

Methods

limit process, numerical investigation, quadratic equations, geometric construction

Media

tetrahedra, linked polyhedra, rulings, midaxes

Source status

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