Abstract
We discuss a classical result in planar projective geometry known as Steiner’s theorem involving 12 interlocking applications of Pappus’ theorem. We prove this result using three dimensional projective geometry then uncover the dynamics of this construction and relate them to the geometry of the twisted cubic.
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References
Coxeter, H. S. M.:Projective Geometry, Blaisdell Publishing Company, 1964.
L Kadison M.T. Kromann (1996) Projective Geometry and Modern Algebra Birkhäuser Basel Occurrence Handle0848.51001
Pedoe, D.: A Course of Geometry for Colleges and Universities, Cambridge University Press, 1970.
J. F. Rigby (1983) ArticleTitlePappus lines and Leisenring lines J. Geometry 21 IssueID2 108–117 Occurrence Handle745203 Occurrence Handle10.1007/BF01918135
R. Schwartz (1993) ArticleTitlePappus’s theorem and the modular group Publ. Math. 78 187–206 Occurrence Handle1259431 Occurrence Handle10.1007/BF02712918
Todd, J. A.: Projective and analytical geometry, Sir Isaac Pitman Sons, 1958.
D. Witczyńska (1979) ArticleTitlePappus’ configuration in the projective space Pn Demonstratio Math. 12 IssueID3 593–598 Occurrence Handle560352 Occurrence Handle0435.51003
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Mathematics Subject Classification (2000). Primary 51N15.
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Hooper, W.P. From Pappus’ Theorem to the Twisted Cubic. Geom Dedicata 110, 103–134 (2005). https://doi.org/10.1007/s10711-004-0543-y
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DOI: https://doi.org/10.1007/s10711-004-0543-y