Journal of the Mathematics Council of the Alberta Teachers’ Association
Volume 34 Issue 1, May 1997
15
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.
