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A footnote on the mystic hexagram

Published online by Cambridge University Press:  24 October 2008

W. L. Edge
Affiliation:
University of Edinburgh

Extract

1. Cremona's projection of 15 lines on a nodal cubic surface onto a plane π is a striking example of the resolution of a highly complicated figure into its constituent simplicities, for it explains, almost at a glance, so many properties of Pascal's mystic hexagram. These may appropriately be called ((12); (10), p. 162) the Veronese properties and have been described on several occasions ((12); (6); (10); (1), pp. 219–236; (2), pp. 349–355).

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1975

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References

REFERENCES

(1)Baker, H. F.Principles of geometry, vol. II (Cambridge, 1922).Google Scholar
(2)Baker, H. F.An introduction to plane geometry (Cambridge, 1943).Google Scholar
(3)Cayley, A.Note on the theory of cubic surfaces. Philosophical Magazine 27 (1864), 493496; Collected papers, V, 138–140.Google Scholar
(4)Clebsch, A.Ueber die Anwendung der quadratischen Substitution auf die Gleichungen 5ten Grades und die geometrische Theorie des ebenen Fūnfseits. Math. Annalen 4 (1871), 284345.CrossRefGoogle Scholar
(5)Coxeter, H. S. M.Twelve points in PG (5, 3) with 95040 self-transformations. Proceedings of the Royal Society (A), 247 (1958), 279293.Google Scholar
(6)Cremona, L.Teoremi stereometrici, daiquali si deducono le proprietà dell'esagrammo di Pascal. Atti della Reale Accademia dei Lincei (3) 1 (1877), 854874.Google Scholar
(7)Eckardt, F. E.Ueber diejenigen Flächen dritten Grades, auf denen sich drei gerade Linien in einem Punkte schneiden. Math. Annalen 10 (1876), 227272.CrossRefGoogle Scholar
(8)Edge, W. L.31-point geometry. Math. Gazette 39 (1955), 113121.CrossRefGoogle Scholar
(9)Edge, W. L.Conics and orthogonal projectivities in a finite plane. Canadian J. of Maths. 8 (1956), 362382.CrossRefGoogle Scholar
(10)Richmond, H. W.The figure formed from six points in space of four dimensions. Math. Annalen 53 (1900), 161176.CrossRefGoogle Scholar
(11)Sylvester, J. J.Note on the historical origin of the unsymmetrical six-valued function of six letters. Philosophical Magazine 21 (1861), 369377. Collected Papers, II, 264–271.Google Scholar
(12)Veronese, G.Nuovi teoremi sull' hexagrammum mysticum. Atti della Reale Accademia dei Lincei (3), 1 (1877), 649703.Google Scholar