MegaMenger project:
http://megamenger.com/

Ed Pegg's article "Squeezing Pi from a Menger Sponge"
http://community.wolfram.com/groups/...

Mega Menger: Building a Menger Sponge at MIT
   • Mega Menger: Building a Menger Sponge...  

Watch Matt calculate pi with...
pies:    • Calculating Pi with Real Pies  Numbe...  
a piendulum:    • Calculating pi with a pendulum  
a lot of chalk:    • Calculating π by hand  

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.)
Metacorrection: 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: Standup Mathematician
Website: http://standupmaths.com/
New book: http://makeanddo4D.com/
Nerdy maths toys: http://mathsgear.co.uk/