Year: 2026
Type: article
Abstract: The starting point is a pair of a circle $${\mathcal {D}}$$ D and ellipse $${\mathcal {E}}$$ E , which is within $${\mathcal {D}}$$ D , so that there is a triangle inscribed in $${\mathcal {D}}$$ D and circumscribed about $${\mathcal {E}}$$ E . According to the famous Poncelet porism, we know that there is an infinite family of such triangles, so we will call $$\{D,E\}$$ { D , E } a 3-Poncelet pair. Using isogonal conjugacy, we develop a geometric construction that produces new families of circles that also form a 3-Poncelet pair with $${\mathcal {E}}$$ E . In fact, any circle that is the locus of isogonal conjugates of a fixed point with respect to the family of Poncelet triangles of the original 3-Poncelet pair $$\{D,E\}$$ { D , E } serves as an outer circle in a new 3-Poncelet pair with the same inner conic $${\mathcal {E}}$$ E . In the process, two special pairs of circles emerge as guide marks.
Source: Aequationes Mathematicae
Language: English
Topic: Mathematics and Applications
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
OpenAlex ID: W7136197894