منابع مشابه
Poncelet Theorems
The aim of this note is to collect some more or less classical theorems of Poncelet type and to provide them with short modern proofs. Where classical geometers used elliptic functions (or angular functions), we use elliptic curves (or degenerate elliptic curves decomposing into two rational curves). In this way we unify the geometry underlying these Poncelet type statements. Our starting point...
متن کاملA Poncelet Theorem for Lines
Our aim is to prove a Poncelet type theorem for a line configuration on the complex projective plane P. More precisely, we say that a polygon with 2n sides joining 2n vertices A1, A2, · · · , A2n is well inscribed in a configuration Ln of n lines if each line of the configuration contains exactly two points among A1, A2, · · · , A2n. Then we prove : Theorem Let Ln be a configuration of n lines ...
متن کاملThe Poncelet Grid
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.
متن کاملThe Pentagram Integrals for Poncelet Families
The pentagram map is now known to be a discrete integrable system. We show that the integrals for the pentagram map are constant along Poncelet families. That is, if P1 and P2 are two polygons in the same same Poncelet family, and f is a monodromy invariant for the pentagram map, then f(P1) = f(P2). Our proof combines complex analysis with an analysis of the geometry of a degenerating sequence ...
متن کاملGeometry of Syzygies via Poncelet Varieties
We consider the Grassmannian Gr(k, n) of (k+1)-dimensional linear subspaces of Vn = H 0(P1,OP1(n)). We define Xk,r,d as the classifying space of the k-dimensional linear systems of degree n on P whose basis realize a fixed number of polynomial relations of fixed degree, say a fixed number of syzygies of a certain degree. The first result of this paper is the computation of the dimension of Xk,r...
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ژورنال
عنوان ژورنال: International Journal of Number Theory
سال: 2018
ISSN: 1793-0421,1793-7310
DOI: 10.1142/s1793042118501580