Definiton: A square is an equiangular, equilateral construct consisting of four line segments and their terminating points, such that they construct an Euler circuit, and all meet at right angles.
S = Set of all polygons.
X = Polygons with 3 sides
Y = Polygons with 4 sides.
X is disjoint Y, both of which are subsets of S.
There does not exist a three sided square.
Suppose not (proof by contradiction):
Suppse there exists a square with three sides.
S = Set of all polygons.
X = Polygons with 3 sides
Y = Polygons with 4 sides.
X is disjoint Y, both of which are subsets of S.
Such a square is in in set X, as a three sided polygon.
Since a square by definition has four sides, it is in set Y.
Thus, a three sided square is in both set X and set Y.
This is a contradiction. Since X and Y are disjoint, no element can be held in common.
Therefore, the supposition is false. There are no three sided squares.
2007-06-15
08:53:53
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22 answers
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asked by
Anonymous