License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SoCG.2018.6
URN: urn:nbn:de:0030-drops-87199
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Bae, Sang Won ; Cabello, Sergio ; Cheong, Otfried ; Choi, Yoonsung ; Stehn, Fabian ; Yoon, Sang Duk

The Reverse Kakeya Problem

LIPIcs-SoCG-2018-6.pdf (0.6 MB)


We prove a generalization of Pál's 1921 conjecture that if a convex shape P can be placed in any orientation inside a convex shape Q in the plane, then P can also be turned continuously through 360° inside Q. We also prove a lower bound of Omega(m n^{2}) on the number of combinatorially distinct maximal placements of a convex m-gon P in a convex n-gon Q. This matches the upper bound proven by Agarwal et al.

BibTeX - Entry

  author =	{Sang Won Bae and Sergio Cabello and Otfried Cheong and Yoonsung Choi and Fabian Stehn and Sang Duk Yoon},
  title =	{{The Reverse Kakeya Problem}},
  booktitle =	{34th International Symposium on Computational Geometry (SoCG 2018)},
  pages =	{6:1--6:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-066-8},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{99},
  editor =	{Bettina Speckmann and Csaba D. T{\'o}th},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-87199},
  doi =		{10.4230/LIPIcs.SoCG.2018.6},
  annote =	{Keywords: Kakeya problem, convex, isodynamic point, turning}

Keywords: Kakeya problem, convex, isodynamic point, turning
Collection: 34th International Symposium on Computational Geometry (SoCG 2018)
Issue Date: 2018
Date of publication: 08.06.2018

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