Bubbles and Tilings: Art and Mathematics

Year: 2014 Authors: Frank Morgan

Core claim

Visual imagination and artwork are essential for narrowing possibilities and proving optimality in both double bubbles and pentagonal tilings.

Topics

double bubble conjecture, pentagonal tilings, mathematical visualization, symmetry, optimal area and perimeter

Domains

geometric measure theory, isoperimetric problem, tiling theory, surface of revolution, wallpaper groups, scientific illustration, mathematical art, architecture

Methods

proof by instability, symmetry reduction, trial-and-error exploration, geometric sketching, combinatorial construction

Media

soap bubbles, illustrations, Geometer’s Sketchpad, photographs, computer-rendered images

Source status

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