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On the Vector Algebra of Eight Associated Points of Three Quadric Surfaces

Published online by Cambridge University Press:  24 October 2008

H. W. Turnbull
H. W. Turnbull
Affiliation:
Trinity College.
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Extract

Let the eight points in space common to three arbitrary quadric surfaces be called eight associated points. These points possess the property that any one of them is uniquely determined if the other seven are given. It is interesting to give the analytical expressions for eight associated points in terms of symbols entirely free from coordinate systems. Thus we take the first eight digits 1, 2,…8 to denote the points; a group of two digits to denote the line joining these two; a group of three to denote a plane, and so on. Also a conjunction of two groups denotes the point, line or plane common to the two groups, thus (34, 678) is the point common to the line 34 and the plane 678.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 22 , Issue 4 , March 1925 , pp. 481 - 487
Copyright
Copyright © Cambridge Philosophical Society 1925

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References

* Baker, Cf., Principles of Geometry (Cambridge, 1923), vol. 3, p. 155.Google Scholar

* Math. Annalen, 1870, vol. 2, p. 397.Google Scholar

† Study, Cf., Vectorenrechnung (Braunschweig, 1923), vol. 1, p. 68.Google Scholar

‡ Crdle, 1880, vol. 89, p. 47.Google Scholar