Abstract
An oval C In a projective plane is a set of triply noncollinear points such that each point of C is on exactly one line which contains no other point of C. An oval has the Pascalian property if each of its hexagons has collinear diagonal points. The author considers those hexagons in which at least two vertices coincide and shows that if every hexagon in this class of 5-point hexagons is Pascalian then the oval has the Pascalian property. Therefore, the 5-point Pascalian property is equivalent to the full Pascalian property. The proof makes use of the coordinatization found in Artzy [1, 2].
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References
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This research is contained in the author's doctoral dissertation submitted to Temple University and was supported in part by a grant from La Salle College. The author wishes to thank his advisor Professor R. Artzy for his assistance throughout the work.
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Hofmann, C.E. Specializations of Pascal's theorem on an oval. J Geom 1, 143–153 (1971). https://doi.org/10.1007/BF02150268
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DOI: https://doi.org/10.1007/BF02150268