The Fractal Menger Sponge and Pi

MegaMenger project:
http://megamenger.com/

Ed Pegg's article "Squeezing Pi from a Menger Sponge"
http://community.wolfram.com/groups/-/m/t/822984

Mega Menger: Building a Menger Sponge at MIT
https://www.youtube.com/watch?v=YpmP8OJJ7W4

Watch Matt calculate pi with...
pies: https://www.youtube.com/watch?v=ZNiRzZ66YN0
a pi-endulum: https://www.youtube.com/watch?v=qYAdXm69l8g
a lot of chalk: https://www.youtube.com/watch?v=HrRMnzANHHs

CORRECTIONS:
- A comment by Starkiller Base pointed out that at the end, I need eight of the Wallis Sponges stacked in a cube. As each one is a unit side, that gives the 'radius' of 1. A single sponge is one eighth of the volume of the unit sphere.
- Jon Mound (@ChthonicJon on Twitter) first spotted that 63/64 should not have been there. I accidentally animated a slip of the tongue. Product should be: 8/9 × 24/25 × 48/49 × 80/81 × 120/121 … (Also spotted in the comments by pjrkearsley87 & hweigel528.)
- Meta-correction: SithBowman noticed I had "132" instead of "121" in the above correction. The correction has since been correctly corrected.

Sorry everyone! Two mistakes and counting. I was really pushed for time this week, which is why some animations are a bit lazy and it's so late in the week (also, so many errors).

Music by Howard Carter
Design by Simon Wright

MATT PARKER: Stand-up Mathematician
Website: http://standupmaths.com/
New book: http://makeanddo4D.com/
Nerdy maths toys: http://mathsgear.co.uk/

Видео The Fractal Menger Sponge and Pi канала Stand-up Maths