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A conic theorem generalised: directed angles and applications

Published online by Cambridge University Press:  01 August 2016

R. W. D. Nickalls
R. W. D. Nickalls*
Affiliation:
Department of Anaesthesia, City Hospital, Nottingham NG7 2UH, UK, e-mail: [email protected]
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Extract

A new and general proof of theorem [1] is presented, which accommodates directed angles and covers all possible configurations of line and conic. A sign convention for the use of directed angles in this setting is developed, and examples are given showing how this fundamental theorem can be used to establish, much more directly and succinctly, the many tangent/focus properties of conies.

Type
Research Article
Information
The Mathematical Gazette , Volume 84 , Issue 500 , July 2000 , pp. 232 - 241
Copyright
Copyright © The Mathematical Association 2000

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References

1. Nickalls, R. W. D., A line-and-conic theorem having a visual correlate. Math. Gaz., 70, (1986) pp. 27–29.Google Scholar
2. Loney, S. L., The elements of coordinate geometry. Part I. (Macmillan and Co Ltd., London) (1933).Google Scholar
3. Klein, F., Elementary mathematics from an advanced standpoint: Geometry. (The Macmillan Company, New York) (1939). [Translated from the third German edition by Hedrick, E. R. and Noble, C. A.].Google Scholar
4. Nickalls, R. W. D., The rotating Pulfrich effect, and a new method of determining visual latency differences. Vision Research 26, (1986) pp. 367–372.Google Scholar
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