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
ragarcia@ufg.br
Dan Reznik
Data Science Consulting Ltd., Rio de Janeiro, Brazil
dreznik@gmail.com
Pedro Roitman
Universidade de Brasília, Brazil
roitman@mat.unb.br
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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