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1 results

  • How to see a cube moving into its mirror image

  • Ester Dalvit, Domenico Luminati
  • Journal:
    The Mathematical Gazette / Volume 96 / Issue 537 / November 2012
    Published online by Cambridge University Press:
    23 January 2015, pp. 471-479
    Print publication:
    November 2012

  • In n-dimensional Euclidean space no reflection with respect to a hyperplane can be realised by a rigid motion. But this is possible if we allow rigid motions in (n + 1)-dimensional space. These notes show a way to visualise a rigid motion of a cube in 4-dimensional space that flips the cube ‘as the page of a book’.

    The two terms rigid motion and isometry are sometimes used as synonyms. Yet they do refer to different concepts. The first one has a purely kinematic connotation: the swing of a door or the movement of a piece of furniture pushed over the floor are described by rigid motions. On the other hand to ensure that two figures are isometric it is enough that there exists a correspondence between their points that maintains the relative distances.