Realizations of the Conformal Group
Perhaps one of the first to consider the problems of projective geometry was Leonardo da Vinci (1452-1519). However, projective geometry as a self-contained discipline was not developed until the work “Traite des propriés projectives des figure” of the French mathematician Poncelet (1788-1867), published in 1822. The extrordinary generality and simplicity of projective geometry led the English mathematician Cayley to exclaim: “Projective Geometry is all of geometry” [ 16]. D. Hestenes in [ 8] showed how the methods of projective geometry, formulated in geometric algebra, can be effectively used to study basic properties of the conformal group. The purpose of this article is to further explore the deep relationships that exist beween projective geometry and the conformal group.
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