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Calculating π with Avogadro's Number

Check out Steve Mould's Pythagorean Siphon video:    • The Pythagorean Siphon Inside Your Wa...   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:    • Calculating π by hand the Isaac Newto...   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.   / 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/bo... UK book: https://mathsgear.co.uk/collections/b...