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Topology and Transformations in High School Geometry

In: The Teaching of Geometry at the Pre-College Level

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  • Paul J. Kelly

    (University of California)

Abstract

There is a simple and natural way of regarding Euclidean geometry that has been largely ignored in the teaching of geometry. This is the view that Euclidean geometry is the mathematical study of the size and shape attributes of physical objects. The motivation of the study is that such attributes are intrinsically interesting and also that the information obtained is useful. It is my belief that this functional approach to the subject not only provides a natural dynamics to the development but leads to surprisingly sophisticated and vital mathematical concepts. Though I shall sketch the basis for only the innovative topics, topology and transformations, the view I am advocating leads with equal naturalness to other aspects of the subject, such as vectors or analytic geometry.

Suggested Citation

  • Paul J. Kelly, 1971. "Topology and Transformations in High School Geometry," Springer Books, in: Hans-Georg Steiner (ed.), The Teaching of Geometry at the Pre-College Level, pages 201-205, Springer.
    • Handle: RePEc:spr:sprchp:978-94-017-5896-3_13
    DOI: 10.1007/978-94-017-5896-3_13
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