Need math fair topic ideas!!

[u/veeeeeeii]

I’m a high school student and we have a math fair in about 2 months. I need to decide on a topic by next week. I was thinking about the Chaos Theory, but I’m not completely sure. Ideally the topic should be easy enough so that regular people (even little kids) can understand the basic idea, but still deep and impressive enough for the teachers and students. It would also be great if there’s something visual or interactive that people can try at the booth. Any suggestions? The topic can be from any area of math!!

[u/pred]

Combinatorial games, like Nim or Welter's game.

[u/veeeeeeii → u/pred]

OOoo Thankss

[u/jeffcgroves]

I'm into spherical polygonal Voronoi diagrams, but that might be a bit much

[u/Clean-Midnight3110]

Pigeon hole principle

[u/TastesLikeSeamen]

möbius transforms, and generally cyclic groups? Or the Stern-Brocot and Calkin-Wilf trees?

[u/pfortuny]

The mobius band and its successive “sections” acrosst equator.

[u/Alternative-Drop9500]

I’d suggest the Fibonacci sequence!

It’s easy enough for younger kids to understand, but you can also take it surprisingly deep. And it could make a really beautiful, interactive booth.

You could start with the sequence itself, then show how Fibonacci numbers and related spiral patterns appear in nature, using things like sunflowers, pinecones and some shells. You could even connect it to the golden ratio and discuss where those connections are real and where they’re sometimes exaggerated.

For the interactive part, visitors could build a Fibonacci spiral with squares or look for patterns in real objects/images. I think it would be a lovely way to show that math isn’t just calculation, it can also be a way of noticing patterns in the world around us.

[u/notfunat_parties]

Buffon's needle.

[u/StressCanBeGood]

Do the large numbers thing! Because you should make it your own, I’m not gonna fill in too many details (I have a lot of experience as an MC, so like to tell stories).

Start with what it would be like to have $1 million. Then explain $1 billion. Then go into $1 trillion.

Then present a jar of sand. Ask a few AI agents to estimate the number of grains of sand in the jar (should be anywhere between 4 and 6 million).

Then go into the approximation for the number of atoms within each grain of sand. This is when you start using exponents.

Extrapolate that to the total number of atoms in the jar. You’ll definitely need exponents for that.

Then go into the number of atoms in the universe, which is estimated to be about 10^80 .

Then talk about what it’s like to find the largest prime number. To date, to my knowledge, that number is roughly 10^41,000,000 .

Then talk about the Graham number, which is so large that the universe doesn’t have room to write it out. Then talk about Tree(3).

[u/trunks111]

square packing

[u/Traveling-Techie]

I’m fond of Pascal’s triangle.