Incidence

H. S. M. Coxeter and George Beck
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H. S. M. Coxeter: University of Toronto, Department of Mathematics

Chapter Chapter 2 in The Real Projective Plane, 1993, pp 12-24 from Springer

Abstract: Abstract The geometry considered in this book is called real, because if we chose to work it out analytically, the coordinates would be real numbers, whereas otherwise they might have been complex numbers, or the ‘numbers’ of a finite arithmetic (Galois field),* or something still more bizarre. However, the present chapter deals with those properties of the projective plane which depend only on the simple processes of joining and intersection and which are consequently valid in the other geometries mentioned above, as well as in real geometry. These properties include the principle of duality, perspectivity, and harmonic conjugacy. Many of the ideas can be traced back to Desargues (who defined harmonic conjugates by dividing a segment internally and externally in the same ratio), but their essentially projective nature was first understood by an extraordinarily talented German, von Staudt (1798–1867).

Keywords: Collinear Point; Galois Field; Primitive Concept; Linear Point; Harmonic Conjugate (search for similar items in EconPapers)
Date: 1993
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DOI: 10.1007/978-1-4612-2734-2_2

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