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moof's prattling

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July 16th, 2003

quiz time for all you math smartypantses @ 12:51 am

Current Mood: thoughtful thoughtful
Current Music: Soul Coughing, Soundtrack to Mary

 
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From:absintheminded
Date:July 16th, 2003 10:23 am (UTC)
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Unless I'm misunderstanding what you mean by 'internal tension', this depends on factors such as the stiffness and thickness of the rubber, since the edges will have to be beveled in order to get the same curvature inside the pieces as at the boundaries. Otherwise you'll have a polyhedron which is topologically the same as a hemisphere; but a hemisphere is topologically the same as a flat disk with no curvature.

Intuition inclines me to agree with zeocin -- well, almost. Just three triangles meeting in a point will do, no rounding-off is required; moreover, I'd venture that the triangles ought to be equilateral. Proving that this arrangement has the minimal internal tension would require more information, however.

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