# Calculating π with Avogadro’s Number

Check out Steve Mould’s Pythagorean Siphon video: https://www.youtube.com/watch?v=Cg8KQfaT9xY&ab_channel=SteveMould

Every Pi Day I calculate the digits of π somehow. This year I counted the number of molecules in a disc as a ‘real accurate’ way to measure its surface area. You can see all the previous videos here: https://www.youtube.com/watch?v=CKl1B8y4qXw&list=PLhtC92GarkjyYbxI3-4qzIWIRbZaw4wuP

Yes, you can buy the sheets of paper I wrote on in this video. I’ve signed them and all money goes to WaterAid UK. https://www.ebay.co.uk/usr/standupmaths

Here is the calculation (keeping mL and cm units throughout).

Our 7 drops were 0.1 mL of solution which is 0.00005 concentration.
Oleic acid is 282.47 g/mol and 0.895 g/mL.
Using Avogadro’s number of 6.02214 × 10^23 that is 9.54 × 10^15 molecules of oleic acid.
That is a volume of 5.24081 × 10^-22 mL per molecule.
Which is a length of 8.06243 × 10^-8 cm and area of 6.50028 × 10^-15 cm^2.
Total area of 62.016 cm^2.
The disc of molecules had a radius of 4.000 cm and so that gives us π = 3.876 (I lost 0.001 because I was rounding as I went).

CORRECTIONS:
– No, I didn’t publish early by accident! I try to put π-Day videos out a bit early so teachers have time to use in lessons before/on π Day.
– I’m hearing reports that oleic acid is not an oil, the carboxylate end makes it a surfactant (first mentioned Ian Roberts). I blame any and all chemistry mistakes on Steve.
– Let me know if you spot any other mistakes!

Thanks to my Patreons who are vital in keeping the videos coming. Steve has a very expensive rider.
https://www.patreon.com/standupmaths

As always: thanks to Jane Street who support my channel. They’re amazing.
https://www.janestreet.com/

Filming by Matt Parker and Steve Mould
Editing by Alex Genn-Bash
Music by Howard Carter
Design by Simon Wright and Adam Robinson

MATT PARKER: Stand-up Mathematician
Website: http://standupmaths.com/
US book: https://www.penguinrandomhouse.com/books/610964/humble-pi-by-matt-parker/
UK book: https://mathsgear.co.uk/collections/books/products/humble-pi-signed-paperback