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A characterization of motions as bijections preserving inradius or circumradius one

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Abstract

It is proven that a bijection from the Euclidean plane to itself which preserves triangles of inradius 1 or which preserves triangles of circumradius 1 must be a Euclidean motion.

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References

  1. Beckman, F. S., Quarles, D. A., Jr.: On isometries of Euclidean spaces. Proc. Amer. Math. Soc.4, 810–815 (1953).

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  2. Coxeter, H. S. M.: Introduction to Geometry. New York: Wiley. 1961.

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  3. Lester, J. A.: Euclidean plane point-transformations preserving unit area or unit perimeter. Archiv Math.45, 561–564 (1985).

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  1. Department of Mathematics and Computer Science, California State University at Los Angeles, 5151 State University Drive, 90032, Los Angeles, CA, USA

    J. A. Lester

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  1. J. A. Lester
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Lester, J.A. A characterization of motions as bijections preserving inradius or circumradius one. Monatshefte für Mathematik 101, 151–158 (1986). https://doi.org/10.1007/BF01298927

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  • DOI: https://doi.org/10.1007/BF01298927

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