Calculating pi with a pendulum

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Inspired by Paul Taylor, I have made a pendulum to calculate pi. A pi-endulum. Its length is a quarter of the value for the acceleration due to gravity, so its period is exactly one pi.

Music by Howard Carter
Design by Simon Wright

MATT PARKER: Stand-up Mathematician

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Love how you waved your hand to divide by 10 at 3:21

EddyProca

The formula for the time a pendulum takes is in a way related to a circle, though

Friek

2:31 you'll notice the time is exactly 3.14 when the pie is above the arrow on the first swing. The 0.4% error was mainly due to effect of air resistance slowing it down slightly as it reached 10 swings.

Mellonix

the pendulum formula shouldn't be surprising to have pi in it, since it's based on (semi)circular motion

BigDBrian

Your first video-3.1512
Your second video-3.128
The average-3.1396
% error-.0634%
The average is a remarkably close approximation to pi.

Narbris

I approve of any science experiment that involves the eating of food.

mizzraika

Actually the first swing was already 3.14 seconds.

vizualeditr

i just spent 31 seconds of my life intently watching a pie swinging on a string, haha. please upload more often - your channel is brill!

jennylf

If you pause the video after the first swing. It's exactly pi!

stephenkamenar

I just want to clear something up (because I'm a bored physics student procrastinating from his finals revision, but ironically now talking about physics). A lot of comments are saying: "Matt, you should have swung it from smaller angles to be more accurate!"... "But Matt, what about the small-angle approximation?" Etc.

When I watched it initially, this is exactly what I was thinking - Matt should have swung it from smaller angles to get better accuracy; he was seemingly ignorant about this and swung it from what looked like about 20 degrees which means that the small-angle formula for period has about ~1 % error. [I know this because you can calculate the *exact* period of a pendulum using elliptic integrals and expanding in powers of initial angle theta, and wind-up with a (1 + (theta^2)/16 + O(theta^4)) correction factor].

Anyway, we note that because the real period is greater than the period predicted by the small-angle formula, Matt's value for pi *should* be *greater* than pi (assuming all other aspects of the experiment were perfect, e.g. exact length of string and pie, local 'g' exactly precise, experiment performed in-vacuo to stop air resistance etc.). However, Matt's value of pi is *smaller*! Therefore, quite clearly the error in the small-angle period formula is negligible compared to the other errors in the experiment (namely string-pie length, local 'g', and camera timings). In-fact, had he used the corrected period formula, he would have been *further* from pi (as he would have got an even smaller value)..

Given all of this it's actually a wonder that he managed to get it correct to 0.4 % error...
But I would say congrats Matt!... Clearly you figured that you had to compensate for the ~1 % error (assuming your initial angle was 20 degrees, though it's hard to tell from your video) in the period formula, and so made your string a few cm shorter than 2.45 m!...
Or, your angle of swing just looked big on camera and was indeed small, and the rest of the experiment was well-controlled.
Either way, well done.

edmundwoolliams

But can you calculate it with a Little Professor?

JustOneAsbesto

Very well edited and fun video to watch!

htechhd

I'm really digging the dubstep in the intro. Good job!

wmconorbrown

0:44 "The formula is based on pi."
0:45 *displays a formula based on tau*

jesusthroughmary

I can't watch this video without imagining Matt's wife coming home and seeing a pie suspended from what looks like a broomstick in the stairs. You're awesome, man. Greetings from Portugal

angelosousa