Calculating π with Avogadro's Number

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.

As always: thanks to Jane Street who support my channel. They're amazing.

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

[standupmaths]

No, I didn’t publish early by accident! I try to put π-Day videos out a bit early so teachers have time to watch and then use in lessons before/on π Day.

[rua]

I love how instead of reaching for the Rubiks cube, he goes for the hypercube

[azarathe]

Matt: this is a scientifical experiment
Steve: *measures atoms with a ruler*

[mateuszniewczas]

Finally, a nice, handy method for those who forgot pi during the exam.

[pseudo_goose]

"I've got a cube here" _reaches past Rubik's cube_ "It's a hypercube, but"

[danilooliveira]

"I think everything we've done wrong canceled nicely" this is peak science

[twojuiceman]

Right before Archimedes shouted "Eureka!" in his bath he shouted "Oops...Aghgh...Balls!"

[minewarz]

Behold, the counterpart of the Parker Square: The Mould Cube!

[thomasroddis]

Matt: Do people just drop oil on lakes?
BP: 👀👀😅

[lynk_]

You can tell that Steve is a physicist. We would happily assume that a horse is a sphere because it makes the maths easier.

[smokey]

1:08
Matt: “The trouble is … squares - it’s not very accurate.”
**Matt and Steve work out the most complicated way to calculate π by using molecules and Avogadro’s number**
11:06
Steve: “Assume the molecule is a cube.”

[Oliolli]

For those left unsatisfied by the end, here's some more information about tau:

τ=7, 75

[NoisqueVoaProduction]

11:25
"I think I have a cube"

Me: Looking at the Rubik's Cube... He is going to reach it!!

Matt Parker: ... So, there is this Hypercube...

[Sam-eynn]

To all those saying this was posted early- it's posted according to the Parker Calendar so it's quite on time.

[tzisorey]

Maths Teacher: "Assume a perfectly spherical cube"

[jacefairis]

"everything that's gone wrong has canceled out nicely" and thus: the theory behind Fermi estimation!

[PC_YouTube_Channel]

I've never seen anyone this happy about 23% relative error

[MrAidanFrancis]

"I think everything that's gone wrong has cancelled out nicely!" Sounds like a Fermi estimate ;)

[EPgeek]

"This is why we work so well together: our failings cancel out!" Utterly relatable.

[jurjenbos]

Exercise for the reader: analyse the accuracy of every step in the process, and find out the margin of error, and compute the likelihood of this result to be so close.