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The broadest three-segment unit arc

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Abstract

We describe the broadest three-segment unit arc in the plane, and we conclude with some conjectures about the broadest n-segment unit arc for n > 3.

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References

  1. Ani Adhikari and Jim Pitman, The Shortest Planar Arc of Width 1, Amer. Math. Monthly, 96 (1989), 309–327.

    Article  MATH  MathSciNet  Google Scholar 

  2. Steven R. Finch and John E. Wetzel, Lost in a Forest, Amer. Math. Monthly, 111 (2004), 645–654.

    Article  MathSciNet  Google Scholar 

  3. John Gerriets and George Poole, Convex Regions Which Cover Arcs of Constant Length, Amer. Math. Monthly, 81 (1974), 36–41.

    Article  MATH  MathSciNet  Google Scholar 

  4. Rolf Klötzler, Universale Rettungskurven I, Z. Anal. Anwendungen, 5 (1986), 27–38.

    MATH  MathSciNet  Google Scholar 

  5. Rolf Klötzler and Sabine Pickenhain, Universale Rettungskurven II, Z. Anal. Anwendungen, 6 (1987), 363–369.

    MathSciNet  Google Scholar 

  6. John M. Maki, John E. Wetzel and Wacharin Wichiramala, Drapeability, Discrete Comput. Geom., 34 (2005), 637–657.

    Article  MATH  MathSciNet  Google Scholar 

  7. Chatchawan Panraksa, John E. Wetzel and Wacharin Wichiramala, Covering n-Segment Unit Arcs Is Not Sufficient, Discrete Comput. Geom., 37 (2007), 297–299.

    Article  MATH  MathSciNet  Google Scholar 

  8. Jonathan Schaer, The Broadest Curve of Length 1, Department of Mathematics, Statistics, and Computer Science Research Paper No. 52, University of Calgary, May, 1968.

  9. John E. Wetzel, Fits and Covers, Math. Mag., 76 (2003), 349–363, 398.

    MATH  MathSciNet  Google Scholar 

  10. Viktor A. Zalgaller, How to Get Out of the Woods? On a Problem of Bellman, Matematicheskoe Prosveshchenie, 6 (1961), 191–195 (in Russian).

    Google Scholar 

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Correspondence to Chatchawan Panraksa.

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Communicated by Imre Bárány

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Panraksa, C., Wetzel, J.E. & Wichiramala, W. The broadest three-segment unit arc. Period Math Hung 55, 157–168 (2007). https://doi.org/10.1007/s10998-007-4157-9

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  • DOI: https://doi.org/10.1007/s10998-007-4157-9

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