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The cyclides of dupin

The cyclides of dupin
The cyclides of dupin

This thesis has three main sections. The first describes the notion of linked conics, a pair of plane conics in Euclidean three space '3 being linked if and only if they lie in perpendicular planes and each passes through the foci of the other. The Cyclides of Dupin are an algebraic surfaces which can be constricted as the envelope of a family of spheres having their centres on one conic and all passing through a fixed point of its linked conic. The Cyclides are then classified according to their focal sets, and a parametrisation is devised to represent isometry classes of cyclides by points in a three-dimensional subset of R3 An action of the additive group of real numbers on the parameter space is discussed.

University of Southampton
Hirst, A. E
Hirst, A. E

Hirst, A. E (1976) The cyclides of dupin. University of Southampton, Doctoral Thesis.

Record type: Thesis (Doctoral)

Abstract

This thesis has three main sections. The first describes the notion of linked conics, a pair of plane conics in Euclidean three space '3 being linked if and only if they lie in perpendicular planes and each passes through the foci of the other. The Cyclides of Dupin are an algebraic surfaces which can be constricted as the envelope of a family of spheres having their centres on one conic and all passing through a fixed point of its linked conic. The Cyclides are then classified according to their focal sets, and a parametrisation is devised to represent isometry classes of cyclides by points in a three-dimensional subset of R3 An action of the additive group of real numbers on the parameter space is discussed.

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Published date: 1976

Identifiers

Local EPrints ID: 458410
URI: http://eprints.soton.ac.uk/id/eprint/458410
PURE UUID: 8e893013-2aee-42f9-bd45-5561955b55fb

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Date deposited: 04 Jul 2022 16:48
Last modified: 04 Jul 2022 16:48

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Contributors

Author: A. E Hirst

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