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Good tables on bad floors
Published online by Cambridge University Press: 22 September 2016
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The following problems concern a rigid four-legged table whose feet may be considered as coplanar points, on a floor to be treated as rigid, conveniently smooth and large, but not flat.
(a) If the feet form a square, show that there is a position where all feet are on the floor.
(b) As (a), but with isosceles trapezium in place of square.
Of course (b) includes (a), but the diminished symmetry calls for a subtler argument.
(c) If the feet do not form a cyclic quadrilateral, show that there may be no position with all feet on the floor.
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- Copyright © Mathematical Association 1978
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