Quadrangles which cannot be separated with two hands

Michael E. Houle, Godfried Toussaint

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Abstract

    A set of objects O is said to be separable with two hands if some proper subset of O can be simultaneously displaced by some rigid motion to infinity without disturbing its complement. It is shown that for all n ≥ 7 there exist configurations of n quadrangles in the plane, which cannot be separated by translation with two hands. Furthermore, no single quadrangle can be separated from the others by means of translation and rotation.

    Original languageEnglish (US)
    Title of host publicationInternational Conference of Numerical Analysis and Applied Mathematics 2015, ICNAAM 2015
    PublisherAmerican Institute of Physics Inc.
    Volume1738
    ISBN (Electronic)9780735413924
    DOIs
    StatePublished - Jun 8 2016
    EventInternational Conference of Numerical Analysis and Applied Mathematics 2015, ICNAAM 2015 - Rhodes, Greece
    Duration: Sep 23 2015Sep 29 2015

    Other

    OtherInternational Conference of Numerical Analysis and Applied Mathematics 2015, ICNAAM 2015
    CountryGreece
    CityRhodes
    Period9/23/159/29/15

    Fingerprint

    complement
    infinity
    set theory
    configurations

    Keywords

    • Algorithms
    • Artificial Intelligence
    • Collision Avoidance
    • Computational Geometry
    • Discrete Geometry
    • Interlocking Polygons
    • Object Mobility
    • Robotics
    • Spatial Planning

    ASJC Scopus subject areas

    • Physics and Astronomy(all)

    Cite this

    Houle, M. E., & Toussaint, G. (2016). Quadrangles which cannot be separated with two hands. In International Conference of Numerical Analysis and Applied Mathematics 2015, ICNAAM 2015 (Vol. 1738). [480021] American Institute of Physics Inc.. https://doi.org/10.1063/1.4952257

    Quadrangles which cannot be separated with two hands. / Houle, Michael E.; Toussaint, Godfried.

    International Conference of Numerical Analysis and Applied Mathematics 2015, ICNAAM 2015. Vol. 1738 American Institute of Physics Inc., 2016. 480021.

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Houle, ME & Toussaint, G 2016, Quadrangles which cannot be separated with two hands. in International Conference of Numerical Analysis and Applied Mathematics 2015, ICNAAM 2015. vol. 1738, 480021, American Institute of Physics Inc., International Conference of Numerical Analysis and Applied Mathematics 2015, ICNAAM 2015, Rhodes, Greece, 9/23/15. https://doi.org/10.1063/1.4952257
    Houle ME, Toussaint G. Quadrangles which cannot be separated with two hands. In International Conference of Numerical Analysis and Applied Mathematics 2015, ICNAAM 2015. Vol. 1738. American Institute of Physics Inc. 2016. 480021 https://doi.org/10.1063/1.4952257
    Houle, Michael E. ; Toussaint, Godfried. / Quadrangles which cannot be separated with two hands. International Conference of Numerical Analysis and Applied Mathematics 2015, ICNAAM 2015. Vol. 1738 American Institute of Physics Inc., 2016.
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