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The Poncelet grid
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Richard Evan Schwartz
Published/Copyright:
June 18, 2007
Abstract
Given a convex polygon P in the projective plane we can form a finite “grid” of points by taking the pairwise intersections of the lines extending the edges of P. When P is a Poncelet polygon we show that this grid is contained in a finite union of ellipses and hyperbolas and derive other related geometric information about the grid.
Received: 2005-03-17
Revised: 2005-12-03
Published Online: 2007-06-18
Published in Print: 2007-04-19
© Walter de Gruyter
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- On hyperbolic Coxeter n-polytopes with n + 2 facets
- Dense near octagons with four points on each line, II
- On the Hermitian curvature of symplectic manifolds
- Surjectivity of Gaussian maps for curves on Enriques surfaces
- Compact Tits quadrangles as Lie geometries of topological Laguerre spaces
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- Circular surfaces
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Articles in the same Issue
- The Poncelet grid
- On hyperbolic Coxeter n-polytopes with n + 2 facets
- Dense near octagons with four points on each line, II
- On the Hermitian curvature of symplectic manifolds
- Surjectivity of Gaussian maps for curves on Enriques surfaces
- Compact Tits quadrangles as Lie geometries of topological Laguerre spaces
- On the roots of the Steiner polynomial of a 3-dimensional convex body
- Circular surfaces
- Addendum to “Classification of generalized polarized manifolds by their nef values”
