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Notes on the Place of Similarity in School Geometry
Published online by Cambridge University Press: 03 November 2016
Extract
The principles underlying my proposals with regard to this matter were published in an article in the Mathematical Gazette (May 1922). They may be briefly restated as follows.
The first principle is that school geometry should be organised not as a purely logical system but rather on the lines of the natural sciences. This means that it should be based explicitly upon the pupils’ spatial experiences, which it should seek to extend, to make precise, to analyse and to co-ordinate. Under this description one includes the important field in which geometrical observations and conclusions have practical utility.
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- Copyright © Mathematical Association 1938
References
page no 234 note * A short selection from the theorems given in the second part was included in the Second Report on the Teaching of Geometry sent out with the May Gazette.
page no 247 note * The assumption is made here partly because it is usual in school work and partly for the sake of brevity. If commensurability is not assumed, the proof becomes more complicated but follows the same lines. We need, however, a more sophisticated definition of equality in ratios.
page no 249 note * I.e. has uniform Gaussian curvature, positive, negative or zero.