Geometry as a gateway to mathematics

Abstract

Introduction The role of geometry in the study of mathematics has been a special interest of mine for several years. During the past year I have enjoyed a sabbatical from my university teaching and made a special effort to discover what is happening to the role of geometry. I have found two papers particularly enlightening and would like to quote from them as background for our considerations of geometry as a gateway to mathematics. I believe that geometry serves this role at all levels – in elementary schools, in secondary schools, and in colleges and universities. Professor E. Spanier wrote in 1970, in an article entitled ‘The Undergraduate Program in Mathematics’, that: Broadly speaking, the goal of undergraduate mathematics education should be to help the student to understand something about mathematics both in its internal structure and in its relations with other disciplines. He should get a feeling of the vitality of the subject and enough history to appreciate current trends and progress. He should have studied some areas of mathematics, possibly only small parts, in depth, but he should also obtain some sort of global view of mathematics by the time he graduates. These objectives are important for all mathematics majors.