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trisection of an angle


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One of the problems that the Greek geometers attempted (like the duplication of the cube and the squaring of the circle) was to find a construction, with ruler and compasses, to trisect any angle; that is, to divide it into three equal parts. (The construction for bisecting an angle is probably familiar.) Now constructions of the kind envisaged can give only lengths belonging to a class of numbers obtained, essentially, by addition, subtraction, multiplication, division and the taking of square roots. It can be shown that the trisection of certain angles is equivalent to the construction of numbers that do not belong to this class. So, in general, the trisection of an angle is impossible.

Subjects: Mathematics.


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