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Can the Range of Geometry Taught in Schools Be Widened?

Published online by Cambridge University Press:  03 November 2016

H. R. Baker
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Extract

The following, written at the reguest of the Editor of the Gazette, gives an account of the mathematical part of the remarks made by the lecturer at the Annual Meeting of the Association last January. There are added some words dealing with geometry on a sphere, in regard to which some questions were raised at the meeting.

Type
Research Article
Information
The Mathematical Gazette , Volume 13 , Issue 188 , May 1927 , pp. 349 - 353
Copyright
Copyright © Mathematical Association 1927

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References

* If we were not illustrating the generalization of the ordinary metrical proof, we could say simply : (1) As AFBR and AECQ are harmonic ranges, the points P, E, F are in line; (2) Thence, by definition, AO contains the harmonic conjugate, D, of P, in regard to B and C. And this remark shews up nicely the cumbrousness of the metrical theory of mid points. For the two results; (1) that the join of the mid points of two sides of a triangle is parallel to the third side; (2) that if in a quadrilateral (trapezium) BCEF, the opposite sides BC, FE be parallel, while BF, CE meet in A, and BE, CF meet in 0, then AO bisects BC undFE, do not lie at the beginning of the subject. To a boy who has appreciated the point of view here propounded these results would be obvious.