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Description

This article is from the Puzzles FAQ, by Chris Cole chris@questrel.questrel.com and Matthew Daly mwdaly@pobox.com with numerous contributions by others.

195 geometry/shephard.piano.p


What's the maximum area shape that will fit around a right-angle corner?

geometry/shephard.piano.s

This problem is unsolved. A simple solution called the "Shephard
piano" has area 2.2074+, but this can be improved upon with local
modifications. A solution exists with area 2.215649+. It is known
that a maximum area exists, but not whether the shape achieving it is
symmetric, smooth, or even unique.

See Problem G5 in Croft, Falconer, and Guy, _Unsolved Porblems in
Geometry_, Springer-Verlag, 1991.

 

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