Resumen de Rolling Squares

Derek Holton, Carol Knights

• 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.