# The conic geometry of rectangles inscribed in lines

```@article{Olberding2019TheCG,
title={The conic geometry of rectangles inscribed in lines},
author={Bruce Olberding and Elaine A. Walker},
journal={Proceedings of the American Mathematical Society},
year={2019}
}```
• Published 15 August 2019
• Mathematics
• Proceedings of the American Mathematical Society
We develop a circle of ideas involving pairs of lines in the plane, intersections of hyperbolically rotated elliptical cones and the locus of the centers of rectangles inscribed in lines in the plane.
3 Citations

## Figures from this paper

Rectangles conformally inscribed in lines
• Mathematics
Journal of Geometry
• 2022
A parallelogram is conformally inscribed in four lines in the plane if it is inscribed in a scaled copy of the configuration of four lines. We examine the geometry of the three-dimensional Euclidean
Aspect ratio and slope of algebraic rectangles inscribed in lines over fields
• Mathematics
• 2020
Let \${\mathbb{k}}\$ be a field. By an algebraic rectangle in \${\mathbb{k}}^2\$ we mean four points in \${\mathbb{k}}^2\$ subject to certain conditions that in the case where \${\mathbb{k}}\$ is the field
Paths of rectangles inscribed in lines over fields
• Mathematics
Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry
• 2022
We study rectangles inscribed in lines in the plane by parametrizing these rectangles in two ways, one involving slope and the other aspect ratio. This produces two paths, one that finds rectangles

## References

SHOWING 1-6 OF 6 REFERENCES
A trichotomy for rectangles inscribed in Jordan loops
We prove a general structural theorem about rectangles inscribed in Jordan loops. One corollary is that all but at most 4 points of any Jordan loop are vertices of inscribed rectangles. Another
Four Lines and a Rectangle
This paper presents some configuration theorems concerning rectangles inscribed in four lines.
Aspect ratio and slope of algebraic rectangles inscribed in lines over fields
• Mathematics
• 2020
Let \${\mathbb{k}}\$ be a field. By an algebraic rectangle in \${\mathbb{k}}^2\$ we mean four points in \${\mathbb{k}}^2\$ subject to certain conditions that in the case where \${\mathbb{k}}\$ is the field
A survey on the Square Peg Problem
This is a short survey article on the 102 years old Square Peg Problem of Toeplitz, which is also called the Inscribed Square Problem. It asks whether every continuous simple closed curve in the
Balancing acts.