Hopeless love and other lattice walks

T. Verhoeff, Koos Verhoeff

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    The Hopeless Love theme arose from observations about chess bishops and their walks on the chessboard. In chess, there are two types of bishops: one confined to the white squares and the other to the black squares. If two bishops of opposite type fall in love, then they can walk around each other, coming very close together, but they can never meet. Their love is hopeless. In this article, we explore the generalization of bishop walks to the 3D chessboard and define when their paths are considered a hopeless love. This has led to several mathematical sculptures. A fictitious 3D chess piece that walks in directions of the main diagonals of the cube we call a rhomber. Again, hopeless love is in the picture, and has resulted in a mathematical sculpture.
    Original languageEnglish
    Title of host publicationProceedings of Bridges 2017
    Subtitle of host publicationMathematics, Art, Music, Architecture, Education, Culture
    EditorsDavid Swart, Carlo H. Séquin, Kristóf Fenyvesi
    Place of PublicationPhoenix, Arizona, USA
    PublisherTessellations Publishing
    Number of pages8
    ISBN (Print)978-1-938664-22-9
    Publication statusPublished - Jul 2017
    EventBridges 2017 : Mathematics, Arts, Music, Architecture, Education, Culture - University of Waterloo, Waterloo, Canada
    Duration: 27 Jul 201731 Jul 2017
    Conference number: 20

    Publication series

    NameBridges Conference Proceedings
    PublisherTessellations Publishing
    ISSN (Print)1099-6702


    ConferenceBridges 2017 : Mathematics, Arts, Music, Architecture, Education, Culture
    Abbreviated titleBridges Waterloo 2017
    Internet address


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