Archive for May, 2013

Meeting maths

May 21, 2013

At NRICH meetings, we like to devote a little bit of time to working on some maths together. Today I’d like to share the problem that m’colleague Mike presented.
Mike provided dotty paper and circular objects to draw round, and invited us to investigate the convex hull of the points contained within circles of our choice. (The convex hull is what you get when you join together the points nearest the edge of the circle without being allowed any concave bits – imagine the circle is a rubber band on a pegboard and when you let go of it it springs round the outermost points.)

Mike threw a few possible questions at us, and then let us get on with it. This is my favourite type of maths investigation; very open ended, and no compulsion to work on something that someone else finds interesting, at the expense of exploring my own avenues. I started by centring my circles on a grid point, and exploring possible shapes. After a very short while, I got distracted and wanted to know whether I could create something in GeoGebra to help me. Others were busily discussing symmetry, whether shapes with different numbers of sides were possible, what happened as circles got larger, and much more. We even talked about practical applications of the mathematical ideas, approximating circles on a square grid such as pixels on a computer screen.

Alas, the meeting was over all too soon (not something you’ll hear me say very often!) and I had to get back to other things, but I saved my GeoGebra file to explore a bit more when I have the time. And if this starting point provokes any interesting questions for you, do let me know in the comments!