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 space whose points are the parallelograms conformally inscribed in sequence in these four lines, and we use this to describe the flow of inscribed rectangles in a compact model of the rectangle inscription problem.
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While we allow degenerate rectangles, i.e., those whose vertices lie on a line, we don’t count the zero parallelogram in \(\Pi \), the parallelogram all of whose vertices are the origin, as a rectangle.
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We thank the referee for helpful comments on the paper.
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Olberding, B., Walker, E.A. Rectangles conformally inscribed in lines. J. Geom. 113, 9 (2022). https://doi.org/10.1007/s00022-021-00622-2
- Inscribed rectangle
- Inscribed parallelogram
- Configuration theorems
Mathematics Subject Classification
- Primary 52C30