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Problem of the Week 1151

Construct a Regular 7-Gon

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You have seven one-foot long pieces of pipe and a supply of right-angle connectors. Show how to arrange the seven pieces into a closed path in 3-space, with a right angle between each piece.

It is easy to do this with four pieces, but impossible with three or five pieces.

A full solution is a list of seven points in space making the required right angles.

Source: Problem of the month #97 (Sept. 2010) at http://mathcentral.uregina.ca/mp/previous2010/

© Copyright 2012 Stan Wagon. Reproduced with permission.

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7 September 2012