The Poncelet grid

By Richard Evan Schwartz. 2007

61 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Computer Graphics and Computer-Aided Design, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/a7d66ff0e7262e7e3e158b75f63b7c072a514d69

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Biomedical Engineering

1. Serge Tabachnikov
2. Misha Bialy

In Computer Graphics and Computer-Aided Design

1. Serge Tabachnikov
2. Misha Bialy
3. Richard Evan Schwartz

In Geometry and Topology

1. Misha Bialy
2. Serge Tabachnikov
3. Richard Evan Schwartz
4. Anna Pratoussevitch
5. Elisha Falbel
6. Sophie Morier-Genoud
7. Max Glick
8. Valentin Ovsienko

Citations in the corpus

• Dan Reznik’s identities and more (2020, methodology): “According to the Poncelet Grid Theorem, [9, 8], the quadrilateral (in fact, a parallelogram) made by these sides is a 4-periodic billiard trajectory in a confocal ellipse.”
• Billiards in ellipses revisited (2020, background): “ points lies on a confocal ellipse and comprises several polygons, each a periodic billiard trajectory (the number of polygons equals gcd (n,k)). This statement is a part of the Poncelet Grid theorem [14, 8]. Figure 7 illustrates the case of n = 13. The angles of these new polygons are expressed via”