**Rectangles conformally inscribed in lines**, J. Geom. 113, 9 (2022)

**Authors: Bruce Olberding, Elaine A. Walker**

Abstract: 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 describe the geometry of the three-dimensional Euclidean space whose points are the parallelograms conformally inscribed in sequence in these four lines. In doing so, we describe the flow of inscribed rectangles by introducing a compact model of the rectangle inscription problem. Submitted 2 August, 2021; originally announced August 2021.