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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
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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

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