How to entertain a crowd with mathematics? [closed]

I am a high school student who follows a university level curriculum, and recently my teacher asked me to hold a short lecture to a crowd of about 100 people (mostly parents of my classmates and such, I’m not the only one to do something, other kids will sing and play the piano and such). I actually self-studied linear algebra and basic differential equations, but I felt that would be too boring (and the non-boring parts would be too difficult) to explain. I then decided to try and explain Euler’s identity, since it looks so counter-intuitive and almost everyone knows $e$, $\pi$ and $i$. But I decided that it’s undoable in like 10 minutes; only a handful of people would be able to follow it if I rush through it.

So I guess my question is; Is there any mathematical ‘thing’ which is easy to follow and will blow the minds of the parents, literally? I literally want to see some heads pop. It doesn’t need to be related to Linear Algebra/Calculus, but I need some interesting problems/theorems/formulas etc. which is understandable to the layman. I think this question might be useful to some other people on this site who are in a similair situation, and want to show math can be mindblowing.

At the moment the best idea I’ve come up with is the birthday problem, I think my introduction would be pretty epic:

Me: Hello audience! Let me ask you a question: How big does a group of people have to be minimally if you want the chance of a pair sharing a birthday to be 100%?

Crowd: 367!

Me: Very good crowd! And approximately how many people for it to be 99%?

Crowd: Around 360?!

Me: Nope, 57.

Crowd: POP!

And I would continue to explain why, which is not hard at all.

Are the similair mathematical results which will blow the mind of a layman?

Answer

Bottema’s Theorem

You’ve found a treasure map. Two large rocks and a tree made a triangle, and the lines between the trees and rocks were used to make two big square plots. The treasure was buried between the two opposite corners of the square plots.

(show the picture)

You get to the site, and you find the two big rocks. But the tree and the plots are long gone. How can you find the treasure?

(pause) Now move the position of the tree around. The treasure is always in the same place.

There are many other interesting interactive math demonstrations there, such as
1. Pick’s Theorem
2. Minimally Squared Rectangles
3. Densest Tetrahedral Packing
4. Pentagon Tilings
5. The Circles of Descartes
6. The Bomb Problem
7. Random Chord Paradox
8. The Penrose Unilluminable Room
9. Drilling a Square Hole

With 3, talk up that mathematicians have answered this wrong for 4000 years. With 4, mention that a housewife solved this problem when all the mathematicians got it wrong. With 8, mention that it was a teenager that solved the problem.

I’ve given various math entertainment lectures — and of the hundreds of quick pieces of fun math, it’s Bottema’s theorem that always seems to work the best, as the tree gets moved.

Another good one — the Homicidal chauffeur problem.

To finish you can appeal to the people that still don’t like math if they’ll give up all the items they have that have mathematically generated curves. Then explain Guilloché Patterns, which are on all money. “You can just lay the money on the table if you still don’t like math — otherwise, my work is done.”

Attribution
Source : Link , Question Author : MathisFun , Answer Author : Ed Pegg

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