On geometrical configurations

Autor: James M. McQuillan, Aiden A. Bruen
Rok vydání: 2017
Předmět:
Zdroj: European Journal of Mathematics. 4:73-92
ISSN: 2199-6768
2199-675X
Popis: 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.
Databáze: OpenAIRE
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