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The focal form of the quadric in n dimensions

Published online by Cambridge University Press:  24 October 2008

H. Gwynedd Green
H. Gwynedd Green
Affiliation:
University CollegeNottingham
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Extract

The object of this note is to show that the equation of the quadric in n dimensions can be transformed to a ‘focus-directrix’ form which is exactly similar to those for two and three dimensions: this form is extended throughout by the introduction of a constant k. A short discussion of confocal quadrics is appended.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 39 , Issue 3 , October 1943 , pp. 159 - 167
Copyright
Copyright © Cambridge Philosophical Society 1943

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References

REFERENCES

(1)Whittaker, E. T.A treatise on the analytical dynamics of particles and rigid bodies. [The full bibliography of the orthogonal reduction of a quadratic form to the sums and squares of differences, including the case of equal final coefficients, is somewhat complex. Whittaker's treatment of the reduction of two quadratic forms is readily accessible, and with the additional discussion as given meets the needs of the problem.]Google Scholar
(2)Bell, R. J. T.Coordinate geometry of three dimensions.Google Scholar
(3)Sommerville, D. M. Y.An introduction to the geometry of N dimensions.Google Scholar
(4)Salmon, G. (revised by R. A. P. Rogers). Analytical geometry of three dimensions, vol. 1.Google Scholar