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Shortest Enclosures on Surface of Cube (Math Chat)

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Visit this site: http://www.maa.org/features/mathchat/mathchat_4_1_99.html

Author:Frank Morgan, MAA Online
Description: The circle provides the least-perimeter way to enclose given area in the plane. What is the least-perimeter way to enclose given area in the surface of the unit cube? Answer: Al Zimmerman correctly finds that the best way to enclose small area is not a small circle on one of the sides of the cube, but better a "circle" around one of the corners... For intermediate areas, he proposes a rectangle about one of the edges, but it turns out that you can do better than that, using circular arcs enclosing two or three of the corners...

Levels: Middle School (6-8), High School (9-12)
Languages: English
Resource Types: Problems/Puzzles, Articles
Math Topics: Higher-Dimensional Geometry, Euclidean Plane Geometry

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