Surprise pi: Videos for high school students

3Blue1Brown
3Blue1Brown

Grant Sanderson poses an interesting problem related to blocks colliding, and (surprisingly) finds pi in the modeled solutions via conservation of energy and momentum. Sanderson's videos combine mathematics and physics, specifically showing how to translate physical situations into geometrical models, and then use geometry to solve the problem.

The videos show a surprising emergence of pi, in a situation that does not seem to be about circles. The first two videos are accessible to students in a high school geometry course: https://www.youtube.com/watch?v=HEfHFsfGXjs

After the first video poses the problem and points out a connection to pi, the second video shows the solution using ideas from geometry. https://www.youtube.com/watch?v=jsYwFizhncE

The third video then shows a different model that draws on calculus and other collegiate mathematics ideas. However, the explanations are very clear, so high school students could appreciate the model in the third video (even if they haven't heard of vectors and dot products).

These videos come from the Youtube channel 3Blue1Brown. According to Wikipedia, "3Blue1Brown is a math YouTube channel created by Sanderson. The channel focuses on higher education mathematics with a distinct visual perspective. Some of the topics covered include linear algebra, calculus, neural networks, the Riemann hypothesis, Fourier transform, and quaternions." Other videos on this channel include additional descriptions and illustrations of high school (and college) mathematical concepts.