It’s hard to find ideas for math projects which are elementary and fun and with lots of things to say.
Tried:
- My favourite example is the inscribed square probleme, aka the Toeplitz conjecture: every simple closed curve in the plane contains an inscribed square. On the one hand it’s an open problem which is very elementary to state. On the other hand, there are lots of particular cases (the graph of a continuous function, the Koch snowflake) or variants (the case of an equilateral triangle) which can be done with very little background. There is a beautiful topological proof of the inscribed rectangle problem, which I learned about from this fantastic video by 3blue1brown,
Want to try:
- Something around the Kakeya set conjecture
- Something about this: Conjecture: if $2^x,3^x$ are integers, then $x$ is as well.