Rolling Squares

• Derek Holton ^[1] ; Carol Knights ^[2]
  1. [1] University of Otago

     University of Otago

     Nueva Zelanda

     
  2. [2] University of Chichester

     University of Chichester

     Chichester District, Reino Unido

     
• Localización: Teaching mathematics and its applications, ISSN 0268-3679, Vol. 27, Nº. 4, 2008, págs. 174-186
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • Here, we investigate what loci are produced when a square of side-length one is allowed to rotate around a square of side-length n, where n is a whole number. We find that if i = 1, 2, 3 or 4 (mod 4), the loci obtained for n ≡ i (mod 4) all have the same symmetry and we show how the perimeter of each class can be determined. We also analyse the case of rotation of a square of side-length one about a rectangle of dimensions m × n when m and n are whole numbers. A similar result is obtained for classes of rectangles modulo 4 to that obtained in the square case. Finally, we suggest that this is a useful investigation to undertake with secondary school pupils. We discuss how we have used this investigation with such a group.