An Algebraist's Look at Classical Geometry

Mary H. Wright

Abstract


It is well-known among math teachers that many construction problems (using straight-edge and compass) have no solution. It seems to be a little less well-known that "no solution" here means not "we have so far failed to find a solution," but rather, "we now know that these constructions are impossible." Unfortunately for many, the reasons lie buried in some obscure abstract algebra course usually offered at the senior or beginning graduate level. It is my contention that the abstractalgebra necessaryto understandthese problems is essentially no more mysterious than finding the roots of a cubic polynomial with integer coefficients.

Keywords


Geometry; Algebra; Construction

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