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The Cross and the Foundations of Euclidean Geometry

Published online by Cambridge University Press:  03 November 2016

H. G. Forder
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Extract

The main aim of this note is to give a new foundation of Euclidean geometry based on the notions of “cross” and “signed angle”. The reckoning with crosses, or directed angles, advocated by D. K. Picken has many merits: the rules are few, general, and simple, and one proof covers a number, often large, of special cases. I will first sketch the method, assuming Euclidean geometry already known.

Type
Research Article
Information
The Mathematical Gazette , Volume 31 , Issue 296 , October 1947 , pp. 227 - 233
Copyright
Copyright © Mathematical Association 1947

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References

page 227 note * Math. Gazette, Dec. 1992, p.188; Proc. London Math. Soc., 23 (1924), p.45, and later papers in the Gazette.

page 228 note * Many examples will be found in Forder, Higher Course Geometry (1931).

page 228 note † It is not really necessary to assume this. Only a very few properties of real numbers are used, and these could be stated in terms of our symbols.

page 229 note * Q might by accident coincide with A.

page 230 note * Forder, Foundations of Euclidean Geometry, (1927), p. 154.

page 230 note † Forder, preceding reference, p. 214, or the last edition (1930) of Hilbert’s Grundlagen, p.111.