Hostname: page-component-848d4c4894-xm8r8 Total loading time: 0 Render date: 2024-06-29T12:17:30.006Z Has data issue: false hasContentIssue false
  • English
  • Français

Geometry of a simplex inscribed in a normal rational curve

Published online by Cambridge University Press:  09 April 2009

Sahib Ram Mandan
Sahib Ram Mandan
Affiliation:
Indian Institute of Technology, Kharagpur and College of Science, University of Baghdad
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In 1959, Professor N. A. Court [2] generated synthetically a twisted cubic C circumscribing a tetrahedron T as the poles for T of the planes of a coaxal family whose axis is called the Lemoine axis of C for T. Here is an analytic attempt to relate a normal rational curve rn of order n, whose natural home is an n-space [n], with its Lemoine [n—2] L such that the first polars of points in L for a simplex S inscribed to rn pass through rn anf the last polars of points on rn for S pass through L. Incidently we come across a pair of mutually inscribed or Moebius simplexes but as a privilege of odd spaces only. In contrast, what happens in even spaces also presents a case, not less interesting, as considered here.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 7 , Issue 1 , February 1967 , pp. 17 - 22
Copyright
Copyright © Australian Mathematical Society 1967

References

[1]Baker, H. F., Principles of Geometry 4 (Cambridge, 1940).Google Scholar
[2]Court, N. A., Sur la Cubique Gauche, Application de la Transformation Harmonique, Mathesis 68 (1959), 110–127.Google Scholar
[3]Coxeter, H. S. M., ‘Twelve points in PGL (5, 3) with 95040 self-transformations’, Proc. Roy. Soc. A 247 (1958), 279–293.Google Scholar
[4]Mandan, Sahib Ram, ‘Properties of Mutually Self-polar Tetrahedra’, Bul. Cal. Math. Soc. 33 (1941), 147–155.Google Scholar
[5]Mandan, Sahib Ram, ‘A Set of 8 Associated Points (Q. 1809)’, Math. St. 10 (1942), 104.Google Scholar
[6]Mandan, Sahib Ram, ‘Moebius Tetrads’, Amer. Math. Mon. 64 (1957), 471–478.Google Scholar
[7]Mandan, Sahib Ram, ‘An S-configuration in Euclidean and Elliptic n-space’, Can. J. Math. 10 (1958).CrossRefGoogle Scholar
[8]Mandan, Sahib Ram, ‘Harmonic Inversion’, Math. Mag. 33 (1959–1960), 71–78.CrossRefGoogle Scholar
[9]Mandan, Sahib Ram, ‘Medial Simplex’, Math. St. 28 (1960), 49–52.Google Scholar
[10]Mandan, Sahib Ram, ‘Cevian Simplexes’, Proc. Amer. Math. Soc. 11 (1960), 837–845.CrossRefGoogle Scholar
[11]Mandan, Sahib Ram, ‘Isodynamic and Isogonic Simplexes (To Enrico Bompiani on his Scientific Jubilee)’, Ann. Mat. Pura ed app. (4) 53 (1961), 45–56.CrossRefGoogle Scholar
[12]Mandan, Sahib Ram, ‘Tetrads of Moebius Tetrahedra’, J. Australian Math. Soc. 3 (1963), 68–78.CrossRefGoogle Scholar
[13]Mandan, Sahib Ram, ‘On Configuration of Arguesian Spaces’, Cas. Pes. Mat. 90 (1965), 54–57.Google Scholar
[14]Room, T. G., The Geometry of Determinantal Loci (Cambridge, 1938).Google Scholar