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Dividing an angle into equal parts

Published online by Cambridge University Press:  01 August 2016

Stephen Buckley  and
Desmond MacHale
Stephen Buckley
Affiliation:
Department of Mathematics, University College, Cork
Desmond MacHale
Affiliation:
Department of Mathematics, University College, Cork
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Extract

The problem of finding a geometric construction in a finite number of steps to trisect an arbitrary angle using straightedge and compasses alone is a very old one, originally proposed by the mathematicians of ancient Greece. It was only with modern algebraic techniques in the nineteenth century that it was shown conclusively that no such construction can exist. This fact has in no way deterred a legion of crank angle-trisectors from presenting their alleged solutions to the problem! However some angles (even non-constructible ones) can be trisected: we’ll see later, for example, that given an angle π/7 it can be trisected. We can also consider the more general problem:

For which natural numbers n > 2 does there exist a geometric construction in a finite number of steps to divide an arbitrary angle into n equal parts, using straightedge and compasses alone?

Type
Research Article
Information
The Mathematical Gazette , Volume 69 , Issue 447 , March 1985 , pp. 9 - 12
Copyright
Copyright © Mathematical Association 1985

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References

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