Here’s one nice such surprise to amaze any kid (or a date, if they’re of the right mold): get a ruler or a uniform stick, balance it on your index fingers by placing them randomly along the length. Then start moving your fingers together. They’ll always meet at the center (center of mass)! Your fingers take turns moving as if by magic. Your audience will first think that you’re purposefully moving them, so next let them do it.
I was curious what the margin of error for this was (I'm conjecturing the sum of widths of the fingers touching the stick), so I tried this out, but with a pencil instead of a stick.
I was consistently getting just off-center, so I was thinking maybe the 'surprise' wasn't consistent, until I realized the end of the pencil (metal + eraser) is probably denser than the wood and shifts the center of mass to exactly where my fingers ended up. :)
I got this from Mr Wizard as a kid and use it infrequently but regularly when making things and needing to split a piece of material in two. I know it's the CG and not the geometric center, but is often close enough with reasonably uniform material.
He ranks at the very top of Brady Haran's guests. It's been at least a year since his last appearance and I hope he comes back soon.
I especially like the one with the acoustic modes of the coffee cup. My only wish is that he had spun the cup and discussed how the tone changes. The nodes move in a way that's not intuitive and that fact can be used to make gyroscopes!
I remember one year at the Gathering for Gardner, the evening before the official start is a "Bar Bets and Cons" night.
I was at a table and had gathered quite a crowd, demonstrating various physics toys and math puzzles. I noticed someone standing a little way away, watching closely, nodding occasionally.
He came up to me later in the evening and said "You've been doing a wonderful job! But now I have to re-write my talk ... you've shown half the toys I was going to talk about!".
It was Tadashi. He is a lovely, lovely man.
Some years later I was in the audience that was gathering for a talk he was about to give. He spotted me and came bounding up. "You may remember me ... we met at G4G."
Humble, charming.
And fiercely intelligent.
EDIT: I wrote about the "Tinking Coffee Cup" way back in July 2015:
