Delta-K,  Student Corner,  Volume 34, Issue 1

Examining the Impossible

Journal of the Mathematics Council of the Alberta Teachers’ Association

Volume 34 Issue 1, May 1997

15

Examining the Impossible

Michael G. Stone

One of the most well-known impossibilities in mathematics is the trisection of an angle with compass and straightedge. In particular, it is impossible to trisect a 60° angle using only these tools. Roughly speaking, this is because the available operations will only allow us to construct from a unit length only all of those lengths which can be obtained by arithmetic operations and square roots. For a fascinating, yet simple, account of this and other mathematical impossibilities, see John Paulos’ (1991) Beyond Numeracy: Ruminations of a Numbers Man. For a more detailed account, see Howard Eves’ ( 1976) wonderful An Introduction to the History of Mathematics.