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A Theorem by Wakeford* and its Extensions to Hyperspace†

Published online by Cambridge University Press:  03 November 2016

H. Lob
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Extract

By a space of n dimensions we mean a region in which the position of a given point is determined by n independent coordinates. If the region is such that the shortest distance between any two given points is the straight line joining them, the space is termed flat, the geometry of a flat space is akin to that of the plane as contrasted with, say, spherical geometry For brevity, a flat space of n dimensions will be denoted by the symbol [n].

Type
Research Article
Information
The Mathematical Gazette , Volume 20 , Issue 240 , October 1936 , pp. 264 - 271
Copyright
Copyright © Mathematical Association 1936

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Footnotes

*

Edward Kingsley Wakeford, a young Cambridge geometer, was killed in action in 1916. For an account of his work see a memoir by J. H. Grace in the Proceedings of the London Mathematical Society, vol. 16. Even whilst at the Front, Wakeford contrived to continue his geometrical researches, and attempts have been made to put together the scattered notes found in his trench kit.

The theorem on which this paper is based was published in the Messenger of Mathematics, vol. 42.

†

The subject-matter of the present paper has also been dealt with by F P White (Proceedings of the Cambridge Philosophical Society, vol 23). White derives comprehensive result, which include those given here, from the properties of related pencils.

page no 264 note ‡

For a full discussion of curves in space see Baker’s Principles of Geometry, vol. v.

References

* Edward Kingsley Wakeford, a young Cambridge geometer, was killed in action in 1916. For an account of his work see a memoir by J. H. Grace in the Proceedings of the London Mathematical Society, vol. 16. Even whilst at the Front, Wakeford contrived to continue his geometrical researches, and attempts have been made to put together the scattered notes found in his trench kit.

The theorem on which this paper is based was published in the Messenger of Mathematics, vol. 42.

† The subject-matter of the present paper has also been dealt with by F P White (Proceedings of the Cambridge Philosophical Society, vol 23). White derives comprehensive result, which include those given here, from the properties of related pencils.

page no 264 note ‡ For a full discussion of curves in space see Baker’s Principles of Geometry, vol. v.