A Geometrical treatment of the Correspondence between Lines in Threefold Space and Points of a Quadric in Fivefold space
Published online by Cambridge University Press: 24 October 2008
Extract
§ 1. The six Plücker coordinates of a straight line in three dimensional space satisfy an identical quadratic relation
which immediately shows that a one-one correspondence may be set up between lines in three dimensional space, λ, and points on a quadric manifold of four dimensions in five dimensional space, S5. For these six numbers pij may be considered to be six homogeneous coordinates of such a point.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 22 , Issue 5 , July 1925 , pp. 694 - 699
- Copyright
- Copyright © Cambridge Philosophical Society 1925
References
* It seems unnecessary here to develop the pure geometrical theory of negative circles in full. It corresponds to the analytical fact that a locus
exists where g, f, c are real and g2 + f2 < c.
† Cf. Baker, , Principles of Geometry, I (Cambridge, 1922), 165–172, 182.Google Scholar
* One system of generators of an ordinary ruled quadrio surface.
- 1
- Cited by