Poncelet Porisms and Loci of Centers in the Isotropic Plane

Ema Jurkin ()
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Ema Jurkin: Faculty of Mining, Geology and Petroleum Engeenering, University of Zagreb, Pierottijeva 6, HR-10000 Zagreb, Croatia

Mathematics, 2024, vol. 12, issue 4, 1-10

Abstract: Any triangle in an isotropic plane has a circumcircle u and incircle i . It turns out that there are infinitely many triangles with the same circumcircle u and incircle i . This one-parameter family of triangles is called a poristic system of triangles. We study the trace of the centroid, the Feuerbach point, the symmedian point, the Gergonne point, the Steiner point and the Brocard points for such a system of triangles. We also study the traces of some further points associated with the triangles of the poristic family, and we prove that the vertices of the contact triangle, tangential triangle and anticomplementary triangle move on circles while the initial triangle traverses the poristic family.

Keywords: isotropic plane; Poncelet porism; centroid; Feuerbach point; symmedian point; Gergonne point; Steiner point; Brocard points (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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