Characterisation of a right triangle

Community Mathematics Centre, CoMaC (2018) Characterisation of a right triangle. At Right Angles, 7 (2). pp. 91-94. ISSN 2582-1873

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Abstract

Let us start by making a few remarks on the notion of characterisation in mathematics, a theme that is central to the subject. The notion has relevance in other settings as well, but we will restrict ourselves to its meaning in mathematics. Given any set S which has been specified in some well-defined manner, we may want a test by which we can decide membership of this set. That is, we want to fill in the blanks in the following sentence in some meaningful way. Right triangles: A non-trivial characterisation of the set of right triangles is Pythagoras’s theorem: A triangle is right-angled if and only if the square of one of the sides is equal to the sum of the squares of the other two sides. The of this result is its compactness and its surprise Angle beauty bisector value: there is no obvious reason whatever why the result should be true. (But the surprise is spoiled to some extent by the great fame of this result!)

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Articles in APF Magazines

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Community Mathematics Centre, CoMaC

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