Another Jam Handy video from the 1930s. This is very well done. It explains how powerful a lever (one of the six simple machines).
Towards the end, to demonstrate the utility of synchromesh transmission, they get a car going 60 MPH down hill. “[The driver] will shift into second speed and bring her car easily and safely under control before it reaches the bottom of the hill.” Cars where much harder to drive 80 years ago.
As a wannabe math geek, I loved this video explaining the Banach-Tarski Paradox, which illustrates the strange world of infinities. Infinity is a fascinating field that defies “common sense”. Infinity plus one is infinity. There are an infinite number of rational number and between every two rational numbers there are an infinity of real numbers. Strange, mind altering stuff.
The Monty Hall Problem illustrates how probability is often unintuitive. This article tells an interesting story about how Marilyn vos Savant (of “Ask Marilyn”) schooled many educated and math-savvy people. Her answer is correct but because it is not intuitive many people think the answer is wrong. It is humous to see people using their PhD as an appeal to authority to dismiss her solution. Math should be argued with logic.