Interesting question from 11yo Young Bill: what's the 'average' of a circle and a square? After a couple of questions, he clarified that he meant in terms of distance from their common centre, and he (quite impressively, imo) built the thing in Geogebra. I've reproduced it in Desmos.
The next question: what *are* those curves? Circular arcs?
When I woke, my son greeted me with a proposed counterexample to the Four Colour Theorem. He said he’d woken with the idea.
He’d made this map of seven regions where the two that are brown here are discontiguous parts of the same country, as are the blues. This isn’t covered by the FCT, but still - what a thing for a 10 year old to come up with! #tmwyk
Maths Week Scotland
Peter Rowlett
Colin Beveridge