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Journal for Geometry and Graphics 26 (2022), No. 2, 217--236
Copyright Heldermann Verlag 2022

New Properties of Harmonic Polygons

Ronaldo Alves Garcia
Universidade Federal de Goiás, Goiânia, Brazil

Dan Reznik
Data Science Consulting Ltd., Rio de Janeiro, Brazil

Pedro Roitman
Universidade de Brasília, Brazil

Via simulation, we revisit the Poncelet family of “harmonic polygons”, much studied in the 2nd half of the XIX century by famous geometers such as Simmons, Tarry, Neuberg, Casey, and others. We review its (inversive and projective) construction, identify some new conservations, and contrast it, via its invariants, to several other recently studied Poncelet families.

Keywords: Harmonic polygon, Poncelet, Brocard, invariants, projection, homothetic, inversion, symmetric polynomials.

MSC: 51M04; 51N20, 51N35, 68T20.

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