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Illumination of Pascal’s Hexagrammum and Octagrammum Mysticum

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Abstract

We prove general results which include classical facts about the 60 lines of Pascal as special cases. Along similar lines we establish analogous results about the configurations of 2,520 conics arising from the mystic octagon. We offer a more combinatorial outlook on these results. Bézout’s theorem is the main tool; however, its application is guided by the empirical evidence and computer experiments with the program Cinderella.

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Acknowledgments

This research was supported by Grant 174020 from the Ministry for Education and Science of the Republic of Serbia. The authors are greatly indebted to the anonymous reviewers for their valuable comments and remarks, which significantly improved the presentation of the paper. The authors are grateful for useful suggestions and discussions to the participants of the seminars Mathematical Methods of Mechanics, Seminar for Geometry, and CGTA Seminar in Belgrade and for their permanent support.

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Authors and Affiliations

  1. Mathematical Institute SASA, Kneza Mihaila 36, p.p. 367, 11001, Belgrade, Serbia

    Djordje Baralić

  2. University of Cambridge, Cambridge, UK

    Igor Spasojević

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  1. Djordje Baralić
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  2. Igor Spasojević
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Correspondence to Djordje Baralić.

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Baralić, D., Spasojević, I. Illumination of Pascal’s Hexagrammum and Octagrammum Mysticum. Discrete Comput Geom 53, 414–427 (2015). https://doi.org/10.1007/s00454-014-9658-6

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  • DOI: https://doi.org/10.1007/s00454-014-9658-6

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