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Rectangles conformally inscribed in lines

Journal of Geometry volume 113, Article number: 9 (2022) Cite this article

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 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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Notes

  1. 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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Acknowledgements

We thank the referee for helpful comments on the paper.

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Authors and Affiliations

  1. Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM,  88003-8001, USA

    Bruce Olberding

  2. Las Cruces, USA

    Elaine A. Walker

Authors
  1. Bruce Olberding
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  2. Elaine A. Walker
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Correspondence to Bruce Olberding.

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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

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  • DOI: https://doi.org/10.1007/s00022-021-00622-2

Keywords

  • Inscribed rectangle
  • Inscribed parallelogram
  • Configuration theorems

Mathematics Subject Classification

  • Primary 52C30
  • 51N10
  • 51N15