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Related quadrics and systems of a rational quartic curve

Published online by Cambridge University Press:  24 October 2008

H. G. Telling
H. G. Telling
Affiliation:
Newnham College.
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Extract

1·1. The points, tangents, osculating planes, …, osculating primes of a curve may be said to form a system which is characterised by the number of these elements which are incident with a prime, …, line, point, respectively. For the normal rational quartic curve the system is (4, 6, 6, 4); projection of this system from a general point gives the system (4, 6, 6) in [3]; section by a general prime gives the system (6, 6, 4). These two systems in [3], which are the systems with which we are concerned in this paper, are duals of one another, and will be called systems of the first and second kinds respectively.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 29 , Issue 2 , May 1933 , pp. 195 - 206
Copyright
Copyright © Cambridge Philosophical Society 1933

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References

* An account, with references, of the rational quartic curve and developables associated therewith is given by Berzolari, Rohn u., Encyklopädie der Math. Wiss., iii C 9, 1373–1382.Google Scholar

* If the points of K are represented by points (u, v, w) of a plane by means of the formula 3·71, the (2, 2) correspondence appears in a familiar form on two apolar conies given by the equation 3·72.