Abstract
Abstract To say that a triangle has one side of integer length or that a circle has integer radius is not mathematically signiFB01cant, as the unit of length can always be adjusted so that this is the case. To say that a triangle has all its sides of integer length is mathematically signiFB01cant. It means that, whatever the unit of length, the ratio of any pair of side lengths is a rational number. However, even if signiFB01cant, it is scarcely interesting. This is because, if you are given three positive integers such that the greatest is smaller than the sum of the other two, then you can always construct a triangle having sides with these integer lengths. Integer-sided triangles become mathematically interesting only when some further condition is imposed.
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