Related quadrics and systems of a rational quartic curve
Published online by Cambridge University Press: 24 October 2008
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
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.
- 2
- Cited by