Thursday 21 July 2016

Going Loopy

One the things I've been fooling around with this year is Polygon Loops. Anyone remember the old Octagon Loops task from the early days of the National Curriculum, with its translucent green stencils?

Loop of eight regular octagons
Loop of ten regular pentagons
This task generalises nicely to other types of regular polygons (and combinations of regular polygons) and there is some heavyweight literature on it, too (see the references below). 

References
Griffiths, M (2001): Two proofs concerning `Octagon loops', Mathematical Gazette 85, 80-84.
McLean, K R (2000): Loops of regular polygons, American Mathematics Monthly 107, 500-510.