On geometrical configurations View Full Text


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Article Info

DATE

2018-03

AUTHORS

Aiden A. Bruen, James M. McQuillan

ABSTRACT

Given two triangles which are in perspective from a vertex V, there are, in general, three other associated pairs of triangles which are also in perspective from V. If the Desargues axes for two of the four pairs are equal, and if the original two triangles form a 6-arc, we show that the Desargues lines for the four pairs are equal. We obtain a complete classification of such pairs of triangles. Then, we examine pairs of triangles in perspective using the inherent polarity of the associated configuration. In particular, we classify all cases when one or more of the 10 points is self-conjugate. Finally, we study a well-known classical result on double perspectivity of pairs of triangles inscribed in a conic. Using new methods, we provide a significant extension to perspectivities of pairs of inscribed n-gons. More... »

PAGES

73-92

References to SciGraph publications

  • 1965-06. Some implications of the geometry of the 21-point plane in MATHEMATISCHE ZEITSCHRIFT
  • 2012-09. The Pascal Mysticum Demystified in THE MATHEMATICAL INTELLIGENCER
  • 2013. Symmetry and Pattern in Projective Geometry in NONE
  • 2012-07. Drawing on Desargues in THE MATHEMATICAL INTELLIGENCER
  • 2013-06. Extending the Pascal Mysticum in THE MATHEMATICAL INTELLIGENCER
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s40879-017-0208-7

    DOI

    http://dx.doi.org/10.1007/s40879-017-0208-7

    DIMENSIONS

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