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Geometry and Relativity

Published online by Cambridge University Press:  03 November 2016

Extract

Thus Euclidean geometry does not hold in the gravitational field even in the first approximation, if we conceive that one and the same rod independent of its position and orientation can serve as the measure of the same extension.

This quotation from Einstein is merely one of the many disturbing statements that a teacher of geometry may find in recent books on physics or even in the newspapers. It will not be long before some of our pupils will ask if it is worth while to continue the study of a subject of which the principal results are apparently contradicted by the latest discoveries. The object of the present article is to examine these apparent contradictions. To do this we shall trace the evolution of ideas concerning the nature of geometry and consider their relation to school work. The conclusion will be reached that certain changes in our teaching are desirable. Fortunately these changes will actually make school geometry easier as well as more scientific.

Type
Research Article
Copyright
Copyright © Mathematical Association 1922

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References

Page 100 of note * For the objections to this see Prof. Nunn’s article in the May number of the Gazette.

Page 100 of note † Plane Geometry, by V. Le Neve Foster (Bell).

Page 100 of note ‡ Such as J. W. Young’s Fundamental Concepts of Algebra and Geometry (Macmillan).

A. Einstein’s Sidelights on Relativity (Methuen).

D. Hilbert’s Foundations of Geometry (Open Court).

H. S. Carslaw’s Non-Euclidean Geometry and Trigonometry (Longmans).

D. M. Y. Sommerville’s Non-Euclidean Geometry (Bell).