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A family of geometric operators on triangles with two complex variables

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 Added by Hiroaki Nakamura
 Publication date 2018
  fields
and research's language is English




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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 $DeltamapstoDelta$ 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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