Zobrazeno 1 - 10
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pro vyhledávání: '"Poncelet P"'
We study the geometric structure of Poncelet $n$-gons from a projective point of view. In particular we present explicit constructions of Poncelet $n$-gons for certain $n$ and derive algebraic characterisations in terms of bracket polynomials. Via th
Externí odkaz:
http://arxiv.org/abs/2408.09225
We study relations between $(n_4)$ incidence configurations and the classical Poncelet Porism. Poncelet's result studies two conics and a sequence of points and lines that inscribes one conic and circumscribes the other. Poncelet's Porism states that
Externí odkaz:
http://arxiv.org/abs/2408.09203
We tour several harmonious Euclidean properties of Poncelet triangles inscribed in an ellipse and circumscribing the incircle. We also show that a number of degenerate behaviors are triggered by the presence of an equilateral triangle in the family.<
Externí odkaz:
http://arxiv.org/abs/2409.19464
Autor:
Lomeli, H. E., Meiss, J. D.
Poncelet maps are circle maps constructed geometrically for a pair of nested ellipses; they are related to the classic billiard map on an elliptical domain when the orbit has an elliptical caustic. Here we show how the rotation number of the elliptic
Externí odkaz:
http://arxiv.org/abs/2309.08013
Autor:
Kaplan, Nathan, Wang, Tianhao
We say that a pair of smooth plane conics satisfies the Poncelet Triangle Condition if they intersect transversally and there is a triangle (possibly defined over the algebraic closure instead of the original base field) inscribed in one conic and ci
Externí odkaz:
http://arxiv.org/abs/2309.16978
Akademický článek
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Akademický článek
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Autor:
Reznik, Dan
We've built a web-based tool for the real-time interaction with loci of Poncelet triangle families. Our initial goals were to facilitate exploratory detection of geometric properties of such families. During frequent walks in my neighborhood, it appe
Externí odkaz:
http://arxiv.org/abs/2201.06960
Autor:
Ema Jurkin
Publikováno v:
Mathematics, Vol 12, Iss 4, p 618 (2024)
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
Externí odkaz:
https://doaj.org/article/9a5468488a5e4e4a8e6810656a4f1c38
We explore geometric and topological properties of 3d surfaces swept by Poncelet triangles, as well as tangles formed by associated points.
Comment: 8 pages, 9 figures, 4 live apps
Comment: 8 pages, 9 figures, 4 live apps
Externí odkaz:
http://arxiv.org/abs/2201.09300