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}
}

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.

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… Expand

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… Expand

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… Expand

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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… Expand

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… Expand