Community Mathematics Centre, CoMaC
(2018)
Characterisation of a
right triangle.
At Right Angles, 7 (2).
pp. 9194.
ISSN 25821873
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 welldefined 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 nontrivial characterisation of the set of
right triangles is Pythagoras’s theorem: A triangle is
rightangled 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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