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A family of geometric operators on triangles with two complex variables

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Abstract

Given a plane triangle \(\Delta \), one can construct a new triangle \(\Delta '\) whose vertices are intersections of two cevian triples of \(\Delta \). We extend the family of operators \(\Delta \mapsto \Delta '\) by complexifying the defining two cevian parameters and study its rich structure from arithmetic-geometric viewpoints. We also find another useful parametrization of the operator family via finite Fourier analysis and apply it to investigate area-preserving operators on triangles.

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Authors and Affiliations

  1. Department of Mathematics Graduate School of Science, Osaka University, Toyonaka, Osaka, 560-0043, Japan

    Hiroaki Nakamura & Hiroyuki Ogawa

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  1. Hiroaki Nakamura
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  2. Hiroyuki Ogawa
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Correspondence to Hiroaki Nakamura.

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Funding was provided by Japan Society of Promotion of Science (Grant No. 16K13745)

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Nakamura, H., Ogawa, H. A family of geometric operators on triangles with two complex variables. J. Geom. 111, 2 (2020). https://doi.org/10.1007/s00022-019-0514-y

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  • DOI: https://doi.org/10.1007/s00022-019-0514-y

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