Calculating π with Avogadro's Number
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- Опубликовано: 9 мар 2021
- Check out Steve Mould's Pythagorean Siphon video: • The Pythagorean Siphon...
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 ...
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. 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.
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: standupmaths.com/
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Развлечения
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.
If you do want to see some (but not all) videos actually early: join my Patreon! www.patreon.com/standupmaths I occasionally put up rough cuts or early versions.
you should probably pin this comment just so people can see it easier
smart! (some) teachers are most likely thanking you around the world for an amazing pi day :D
I'm sure if we consult stonehenge after rebuilding it according to the new, more accurate pi specification, we'll find that your timing is quite accurate.
Nice cover for making a bit of a Parker Square of this video release.
:D
I mean, 3.1 *is* _an_ approximation of pi 🤔 haha
Matt: this is a scientifical experiment
Steve: *measures atoms with a ruler*
LMAO XD Exactly! My chemistry teacher would be so proud! XD
Also, Matt: I'm going to add as many digits as possible for accuracy.
Me: ROFL Yeah, that will increase the accuracy by a lot! XD
In the end it's still impressive they ended up in the correct order of magnitude XD
Also Matt: Making it worse by trying to make it better by doing it twice.
Annoying wasn't it? Like the point of going to molecules was to get more acurate than a primary school child on square paper... I don't feel we achieved that. But kudos to Matt for presumably rolling with the punches as he saw the experiment unfold. And it's realistic to my experience of Chemistry at GCSE and A-Level and I hated it. All the calculations you do and the experiments never match up like what's even the point...
I think rulers always measure atoms.
Coming up next. Measuring speed of light with a stop watch 😆
I love how instead of reaching for the Rubiks cube, he goes for the hypercube
It does look more like a molecule model, tho.
Im so glad this was the top comment I just came to comment this. 11:30 for the people that are lost
Lol
"Things to do in the 4th dimension"!
This proves Matt is a 4-dimensional being
Finally, a nice, handy method for those who forgot pi during the exam.
I mean, even if you remember that it's roughly 3 is already better than the result of this experiment
the joke --------------->
you -> @@nickpro8116
Ikr you know when you forget the digits of pi and have to whip out your petri dish of oleic acid and measure the molecules with a ruler 🙄
Your teachers would catch you.
22/7
"I've got a cube here" _reaches past Rubik's cube_ "It's a hypercube, but"
He was embarrassed to show the unsolved Rubik’s cube.
@@stephenbenner4353 🤣🤣
@@stephenbenner4353 On closer inspection, he has TWO unsolved Rubik’s Cubes.
@@miggle2784 Plus The Pentagonal
They're both just made up of a bunch of small cubes.
Right before Archimedes shouted "Eureka!" in his bath he shouted "Oops...Aghgh...Balls!"
His bath overflowed, spilling a bunch of water on the floor, so ye, probably.
That must have hurt.
@@niekpauwels9569 No, it was just a very cold bath, thus the "Aghgh... Balls!" comment that Archimedes made...
"Oops...Argh...Balls!"
- The Roman soldier who killed Archimedes
You sir, have won the Internet today. Congrats
Matt: Do people just drop oil on lakes?
BP: 👀👀😅
Nah, they drop it on oceans.
LOL!
Actually, I think Exxon (the Valdez spill) is more accurate. BP spilled oil under the water.
"We're sorry"
This reminded me of when Philip Morrison dropped oil on a pond for the PBS documentary Ring of Truth.
You can tell that Steve is a physicist. We would happily assume that a horse is a sphere because it makes the maths easier.
😂😂😂😂😂😂
*A sphere with a central lens of evaporating pentane.
I love this comment so much
"I think everything we've done wrong canceled nicely" this is peak science
Would have been interesting to calculate the error of that result. ... probably ±10⁵ 😅
fermi estimation be like
@@rarebeeph1783 literally what I thought of
I've never seen anyone this happy about 23% relative error
Honestly, I was surprised they ended up between 1 and 10. Why would that essentially one dimensional molecule end up anywhere close to a cube? If I'd have tried this, I'd have floated a small molecule (e.g. methane, ammonia, water) where a cube wouldn't be too bad an approximation. Even better would be a noble gas, but I get that making them liquid is tricky.
Added: Or maybe Buckminsterfullerene.
Must be an engineer.
@@SlidellRobotics
My choice would have been a circular sheet of Graphene. It is known to be a molecule thick and has a regular structure. No liquid needed.
*ASSUME IT'S A CUBE*
@@OriginalPiMan also know to be expensive and hard to get, plus it's geometry does not resemble that of a square, it is more like tiled hexagons
however I did think of graphene when they started talking about the experiment
Behold, the counterpart of the Parker Square: The Mould Cube!
The Mould Circle should also be there.
I knew it would be here somewhere! You have not disappointed the fans.
If it's 3d it's either approximately a cube or a sphere.
A moldy cube
There's already Mould effect
Maths Teacher: "Assume a perfectly spherical cube"
That made me snort-laugh :)
That would be circling the square.
No that's a physics teacher
POV: you just spent hours working on a single math problem for your homework
Math teacher: you forgot that it was negative
It's a Parker cube, so the assumption is valid.
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.”
Shouldn’t the molecules, assumed to be monolayer and oriented in a manner, be more assumed to be a rectangular prism or such?
@@iantaakalla8180 Only if the "tails" are all up straight; which you could make happen by putting boundaries on the circle to squeeze them together. But since the layer was left allone (so to speak) they DO "flail around" and take up a lot of space. Of course the cube is by no means a precise representation, but the accuracy is still pretty impressive ;-)
I can only assume the numbers they have for the size of the “cube” molecule was originally calculated by another scientist using pi.
Also Steve: the diameter is 8 cm
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...
same lol
For those left unsatisfied by the end, here's some more information about tau:
τ=7,75
*accurate to a molecular level
Nice... that made me laugh (in actual fact) out loud. I got many confused looks.
@Oliolli3, you win the comments. Thank you for that. 😆
No, everyone knows that τ=6 because τ=2π and π=3
It’s close, but the results clearly show that there is something wrong with Avogadro’s number.
I mean, they estimated that the molecules are cubes. And their measurement might not have been extremely precise since he measured the diameter only once. Furthermore, the folic acid isn't going to spread in a perfect circle. But, if the answer was very accurate then that would mean that the molecules are actually cubes. So this experiment doesn't imply that there's anything wrong with avagadro's number. There could be, but this experiment doesn't imply that.
@@thebeerwaisnetwork8024 Woooooooooooooosh.
@@liesdamnlies3372 The OP made a bad joke. There is no woosh to see here.
@@angelmendez-rivera351 I don't see how the WOOSH depends on the arbitrary quality of a joke
Are you also going to say my comment is irrelevant because it is 5 months late :)?
@@annyeong5810 I never said anything was irrelevant, so I have no idea why you thought that asking that question was reasonable. Nice strawman, though.
This experiment reminds me of the joke, "How does each profession define Pi?"
Mathematician: "Pi is 3.1415926535...."
Physicist: "Pi is about 3.1415."
Civil Engineer: "Pi is about 3. But we'll double it and call it 6 for safety."
Astronomer: "Pi is usually 1, but sometimes 10."
Accountant: "Pi is 100%."
Chef: "Pi is delicious."
You need to define more digits
I remember "3.1415926535 *8979323846264338* ..."
Cosmologist: "Pi is not helium or nitrogen so it's metal"
@@wesleymays1931 impressive, I know 102 dp
Despite being an engineer I have pi memorized to 20 digits...
The definition of pi should just be whatever the most recent Parker calculation of it was.
“Oh no he’s done something completely stupid this year, all math involving circles are canceled until next March”
Does that also change the definition of Pi Day? I'm afraid we won't get a new one next year if it's on the 87th
@@calebharper9567 Calendars obviously need to be updated. I mean, we have changed calendars and timekeeping measurements before.
A Parker Pi
that'll make it a parker pi
"I think everything that's gone wrong has cancelled out nicely!" Sounds like a Fermi estimate ;)
You watched that Numberphile video too eh
Parker square eh
Sounds like me doing my math homework
@@honorarymancunian7433 i know that from game theory Mario maker possibility vid
"everything that's gone wrong has canceled out nicely" and thus: the theory behind Fermi estimation!
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.
A very interesting question, actually
"This is why we work so well together: our failings cancel out!" Utterly relatable.
To all those saying this was posted early- it's posted according to the Parker Calendar so it's quite on time.
Sure?
I literally just got here from his calendar drifting video
He should post it in the day corresponding to whatever value he gets for pi.
@@gabrielhamoui6504 sure?
@@cadekachelmeier7251 that’s a brilliant idea
"oh woops, balls" definitely sounds like a unit in the English system.
MURICA!
Yes, the "oh woops balls" is a measurement of how poorly an experiment is going at any given time. For example, when I was testing how flammable a pile of powdered sugar was, that measures at .1 oh woops balls because absolutely nothing was happening when I put a match to the pile.
@@epauletshark3793 isn't sugar flammable though?
@@shmuels1383 yes, but only when there is enough air around it. I had a pile of powdered sugar, and nothing happened, if the sugar was loosely floating like a dust in the air, it probably would have caused a fireball.
8.ohwhoopsballs cm is accurate to 13 hexavigesimal places.
We had a special day in high school: the 7/8/90. We all gathered round my digital watch at 12:34 to watch the time click over to 12:34:56 7/8/90 and got in trouble for disrupting class
previous year would have been great as well with the 01:23:45 6/7/89
@@Fasmistic but who wants to be at school in the middle of the night?
Parker's uncertainty principle: one cannot know both the exact radius and the exact area of a circle.
Food for thought
Well, you can't really know the either exactly. You can say "imagine a circle with radius 5". Yeah but 5 what? There's nothing that you know the length of exactly so you have no exact units, so you can't know anything exactly.
If you do count using a unit you don't know as an "exact amount", then you can just say you have a radius of 2 cm and an area of 4 cm^2.pi where cm is whatever you want it to be and cm^2-pi is the EXACT area of a circle with radius 1 cm.
/s
It collapses into a little swirly tear drop shape.
@@aienbalosaienbalos4186 The metre is currently defined as the length of the path travelled by light in a vacuum in 1/299 792 458 of a second.
So yes you can define it
@@miguel5030 But pi is irrational, so given that the exact value of pi cannot be known it is impossible to convert exactly between radius and area since you have to use pi to do it. I would argue that this principle is accurate.
Impressive how some people finish their work before the deadline. This hybrid type of human never fails to amaze me.
@QED Impossible!
@QED im in a proofs class rn and your name gives me ptsd
Impressive how some people finish their work.
This was Matt and Steve’s idea for last years video.... 😉
Is it possible to learn this power?
I somehow feel that the children's textbook squares would have estimated better.
Next year
Just did it -
~ 3.12245
:D
I counted the squares on his notebook, plugged them into the equation and got 3.1604...
I don't think that's the point
@@gustavoaroeira7329 The aim of this experiment was to calculate pi more accurately than using squares on a notebook
18:00 Engineer: 4 take it or leave it.
The woeful disregard for sig figs in this video was very entertaining
As a chemist it simultaneously ate me up and entertained me.
@@chrissabal7937 Do scientific professionals actually use sig figs? As a university student we always learn about them but never actually make sure we're doing them correctly.
@@joehead4081 I'd be willing to bet it depends on the field of science and applications but honestly I have no clue.
What are you talking about? They carefully put down 8.00 cm diameter. Clearly their top concern was to account very precisely for all possible measurement error.
@@joehead4081 It depends on context. When doing analytical chemistry, absolutely sig figs are crucial -- when doing biochemistry there's typically so much error every step of the way with every component, it's not worth worrying about.
"I bet we've gone wrong in two mutually complimentary ways" lmao Steve is great
Well, at least two.
"I feel dirty doing it"
Me every day working as a data scientist in industry.
Why?
@@superneenjaa718 Sooooo many estimations, inferences, and "just do that, and that, and that and BAM! Alpha Centauri is actually an apple." Or something like that.
@@liesdamnlies3372 I'm actually studying data science as my 2nd bachelor course. Hope I don't end up hating it.
@@superneenjaa718 creating solutions to solve complex real life problems is often a messy task.
How do you get the right data? What do you even collect? How do you combine and transform the raw data? How should you clean it? What do you do with it? What kind of model? What assumptions are we assuming by using said model, and is our data fit for the model? What biased may we have introduced and how would these affect the results? Does any insight come from the result? How much can we trust it? How do we sell it to management? Etc
You're lucky to have a straightforward solution to any of these questions/steps, and dealing with the uncertainties and approximations can feel rather dirty.
@@dexterrity doesn't matter if it's good enough 🙃
This is kind of an example of Fermi estimation: just make a lot of estimations and they'll likely cancel out and you'll get something in the correct order of magnitude. :D
Truth!! And to the one significant figure of the original density value used...
"So we can assume that this complex jagged structure waggling around in all directions is basically a cube, yeah?"
- D&D wizard explaining Hypnotic Pattern to his students
lol i've always wondered why they chose to make it a cube. I think it's because the aoe rules allow you to cast a cube around yourself without affecting yourself, which spheres or cylinders don't allow for some reason
@@majorfallacy5926 Probably because cubes fit nicely into the grids that DMs use for dungeon maps. Don't lots of things in D&D have a cubical volume of effect?
@@MattMcIrvin dnd has a lot of different spell shapes like cones, spheres and cylinders that have rules on what squares they affect depending on where they originate (even though everybody i've ever played with makes up their own). Cubes are relatively uncommon with hypnotic pattern being one of the most prevalent in 5e.
@@majorfallacy5926 Actually since the diagonal movement rules were "simplified" in 5e, the very fabric of D&D geometry has been altered so that several of the other spell shapes are now equivalent to cubes (or at least cuboids), too.
I always treated the cones as square-base pyramids because that meant I didn't need to care about the arc of the circle, I could just think about a triangle against my 2D map grid.
Should have posted on March 87th, apparently. *Way* early.
At noon of course.
The 31st of august is better, because pi is (from now on) exactly 31/8.
fun at parties comment: i get the joke but it's not great. by the same logic pi day could as well be on the 141st of march, or the 1415th and so on. so if pi were 3.875(...), we'd stop at the 8th of march, making the posting late. that's the better joke because it's more to the point, it makes less false assumptions. (and it's also already been made in the comments).
This is a lesson in the difference between accuracy and precision.
As a longtime sub from both, the most surprising thing in this video for me was discovering none of the two channels got 1M subs yet
Steve got so many viral videos with many millions views that it was outside my expectations for him to have only 800k
It's roughly 23% error... I've seen entire buildings going up with less accuracy than that!
From now on, π=3,875 in my daily engineering practice.
Tell me which buildings... so I can avoid them!
@@3Ppaatt as a tradie I can tell you that the way builders cut corners its probably better not to know
Lol
Better take π² = g = 10 for overall massive simplifications (g = gravity constant)
@@samueldevulder 10^0.5 is actually a pretty good approximation for pi, I'm surprised.
3.875 is 31/8, so we should start celebrating it on 31st of August instead
I say we should celebrate pi month throughout March.
Yeah and tau is 31/4 so we should celebrate... wait
@@debblez This is why pi is superior to tau
awfully european of you
@@oliviapg Heretic.
To add to the "when is Pi day" debate, perhaps calculations should be done on 22nd July, as then they will be more accurate...
Every time Parker touched his phone with his sharpie in hand, my anxiety went up, just like the scientific accuracy of Steve’s measurements of his circle
Back in the 1980s in 3rd year Chemistry, I remember calculating the HEIGHT of an Oleic acid molecule using exactly the same technique (with lycopodium powder) where pi was assumed, rather than the other way around. The molecule is not a cube, but you are also ignoring the space between molecules, so you do have two effects cancelling out as you suggest!! Another fun way of calculating pi is to use a dartboard on a square pad and evaluate probabilities! On a separate note, I am a rebel and use 22 July as pi day since every schoolchild is taught to approximate pi by 22/7 and the date is in the English format.... Still, a fun video regardless - you guys do wonders for making maths fun :-)
Yes, I also remember doing that experiment, my recollection was it was in Introductory Physical Sciences class, but perhaps it was chemistry.
We do it in our school all the time to get to Avogadro's number!
@@AelwynMr As a matter of interest, what number did you get for Avogadro's constant using this method?
@@Mike-H_UK If you do it really well, you get the correct order of magnitude, no more. Still, I find it amazing to think that you can actually tell anything about the size, mass, and amount of molecules just by measuring a macroscopic volume, a diametre and knowing a chemical formula!
PS: Steve's model is wrong, having no -COOH group at one end. It is just because of that that once the drop stops growing you can assume that a single layer was formed: that part is attracted to water much more than it is to the tails of the other molecules, so they *have to* spread in a single layer. Pity they do not make it clear!
@@AelwynMr Thanks. That's about what I'd expect. Still even getting to within the correct order of magnitude is pretty amazing, as you say.
"Rounding error": using small squares to calculate the area of a circle ... i see what you did there.🙃
It's a Parker circle.
All these squares make a circle!
I came to the comments to boo this very pun.
circling the square!
It's not a pun, it's literally where the word "rounding" comes from.
I remember doing this in high school, but in reverse. Using Pi to calculate Avogadro's Number. We did it like 5 times and none of the circles were even close to the same diameter. So we used the look at the appendix in the back of the book method as our fudge answer.
"two best teachers from high school" energy
“It is pi day this week.” THIS WEEK. Calm down everyone.
DON'T TELL ME TO CALM DOWN
@@MonsieurBiga I WONT CALM DOWN AAAAAAAA
haha
It's the most wonderful time of the year!
Today is Wednesday and pi day is Sunday which is the 1st day of NEXT WEEK!
"These are quite big squares, so there's a lot of _rounding_ going on"
Heh
Lol.
He calculates pi by counting the number of Parker's squares inside a circle.
9:37 "okay, I've got here 8 cm o whoops balls. So that means 8.00, right?"
"Yeah yeah, we should go with the average if we don't know the exact number."
You guys are so fun! Loved this video, looking forward to the journey to a million!
3.8 is what we like to call a "Parker Pi"
When you mess up so many times they cancel each other out and the result is almost correct.
More pi for everyone. I see nothing wrong with that
Call it 4 🤷
Dang! I just said that.......grumble....grumble....early viewers.
I was almost crying with laughter several times. This was like every almost perfect lab I've ever done in school. Well done boys
right? when the ruler fell onto the oil and prevented a second measurement, I laughed out loud -- at work.
I love these two guys! I followed both of them separately and I really like seeing these collabs
I really really reallly love the idea of you two collaborating all the time. No other two people on youtube have the commedic and educational chemistry that you two have.
And a water computer sounds awesome
Smaller than molecules are atoms. Hahaha. This pi calculation tradition will be very fun when you are 80 years old. It gets more interesting every year.
2070: Calculating π by consulting a wormhole
In 2061.
@TheLazy0ne and it will result in pi=73
Atoms next year ....
you always make me smile, laugh, and learn; all at the same time. thank you for this wonderful journey Mr.Parker!
I subbed to Steve a few weeks ago. Been subbed to Matt for ages. Great to see this collaboration.
You and Steve each have only one ear bud, are you sharing a pair? Does that make you two ear buds?
Ear Buddies, coming direct-to-DVD this summer!
Ear Bud? Isn't that the one about the dog who becomes an ear doctor?
@@vigilantcosmicpenguin8721 it was about the pup that lost his hearing when he saved the kittens from an exploding orphanage.
They have it in the same ear though 🤣
"I have a cube right here" *reaches past the rubix for a hypercube*
It's a Parker Cube xD
11:10 "Corporate needs you to find the difference between these two images" (Hold pictures of a cube, and his molecule thingy)
"They're the same picture"
I fully support more stuff with both of you! Some of my favorite videos of either of you are the ones with both of you :)
If Steve is like the Jamaican bobsled team, then technically he needs to crash his channel right before the end and then manually carry it over the million subscriber threshold.
Get himself “canceled,” then make it to 1 million by making bot accounts
Yes, Cool Runnings isn't the movie I would use for an "crushes the competition eventually" comparison.
The friendship crashes and goes up in flames at tied 0.99M subs and he limps over the finish line with utter disregard of the competition
4:05
This is actually a really cool Math Thing™: the decimal expansion is 0.142857 repeating, which is actually the multiples of 7 appended (14, 28, 56/7, 14, 28, etc...)
You can multiply 142857 by 2 to get 285714, by 3 to get 428571, and by 7 to get 999999. Just all around a really interesting number and a great pattern to know -- as this expansion appears for all divisions by 7 (that aren't evenly divisible, of course.) Impress your friends by giving incredibly accurate calculations for 1/7! (not factorial)
Can't wait for the water computer! Love you guys' content. Big fan of APOUD and A Problem Squared as well. Great stuff!
"...so there is a lot of rounding going on" i can't believe i chuckled
9:06 “I’m gonna get a new piece of paper for this.”
Numberphile meets Periodic Videos type stuff
Yeah, lol
"Let me know if you spot any other mistakes!"
Well... in the description, you have "I blame and and all chemistry mistakes on Steve." instead of "... any and all... " :P
Super excited about more collabs!
Just wondering if you assume each molecule occupied a shape closer to a circle, which is 78.5% (0.5x0.5xPI for a unit circle) then this would mean there are more molecules and therefore decrease the answer by a factor of 0.785? Meaning PI would be 3.042 which is closer? I might be wrong but the packing and alignment might be the contributing factor to the overestimate. :)
Yes, the packing is the problem. Each sphere or cylinder would take less area, but then you would leave empty space between them when you put them into a monolayer. I think it's actually a pretty difficult calculation to figure out how much area on average each molecule would take.
Cube is just so much simpler as it packs perfectly. Volume or area taken by 1 molecule is exactly 10^15 times smaller than what 10^15 molecules take
i think you are wrong in multiple ways. many people mention the cube approximation as suspicious, so here are my thoughts.
first, alternative packing is not applicable. they calculated the number of molecules (directly from the volume of oleic acid, without making any assumptions), then divided the volume of oleic acid by the number of molecules, obtaining the average space a molecule takes up - this is to say, they assumed perfect packing, 100% filled space. the shape of this molecular space could indeed be many things, for example thin vertical square prisms; if the ratio of side to height of such a shape is 1:10 you'd get pi=4.297. in absence of detailed knowledge about the molecules, the cube is the shape that makes the least assumptions.
what they did next is calculate the total area of the circle by finding the top-viewed area of the (cubic) molecules (of now known volume) and multiplying that by the number of molecules.
so second, if molecules were (smaller area) circles, you could only get that 21% unused space back by smushing them down to squares again, which is unfair as you've simply made them smaller on no grounds. what you're probably thinking about is square vs hexagonal close packing of circles, which have a filled space parameter of 78.5% vs 90.7%. if better packing were an option (which again it isn't), going from square to hexagonal would decrease the unused space, hence the area calculated, hence pi, though by only around 12%. but what you are saying is that better packing equates to more molecules - it does if you are keeping the area constant, in which case nothing changes in the calculation.
at the end of the experiment they solved the circle area equation for pi, having calculated the area and measured the radius.
my third point is then that any calculation involving circles or spheres for molecules (including your 78.5%) needs some value of pi, which is assumed unknown. is such an equation solvable if the unknown is on both sides? i don't know because there is no such equation because it doesn't make sense.
in conclusion, there's nothing wrong with the math, the main source of error is probably the experiment itself, i.e. steve's handling of the solution (measuring, mixing, dripping), which is to be expected, as they only did the experiment once on a small scale. measuring the radius sure was janky as well but the error couldn't have been more than say 2-3%, which corresponds to about 5% for the final result. all things considered it ended up being a pretty good estimation.
@@calinguga -- Could they not assume the thickness of the sheet was the length of the acid molecule, and then assume square packing in the area instead of the volume?
@@calinguga Addressing only your worry in the 3rd point (re: pi on both sides of the equation), perhaps I'm misunderstanding something. Equations where an unknown appears on both sides do exist. For example, here's such an equation , sqrt(x) = ln(1+1/x) + 1. Thus, certainly such an equation exists and it seems to make sense to me.
You can easily move everything to one side by subtraction, so sqrt(x) - ln(1+1/x) - 1 = 0. That resolves the 'unknown on both sides' worry. As a matter of solving this, no easy analytical solution exists -- you'll have to tackle this numerically (e.g., guess & check, iterative solving, Newton's method), or graphically (plot y = sqrt(x) - ln(1+1/x) -1 then find the x-intercept). In the example, you'll find that x = 1.98324...
There will be cases where the equation isn't "solvable". If the equation is a contradiction (e.g., x = x +1), then no values of x will solve this equation. If it's a tautology (e.g., exp(ln(x)) = x), then all values of x will solve the equation. In other cases, you may need to use complex numbers to solve the equation.
In the pi calculation, since there's only one unknown, the fact that it appears in multiple places shouldn't give us worry. Since we're expecting a real number, it would be easy to solve graphically. Hopefully that answers your worry (a) that equations with unknowns on both sides do exist, (b) that they can make sense, and (c) those that do are usually solvable but not necessarily analytically.
@@ProfChristopherLam absolutely, i was just saying that in this particular case, i don't know how the equation would look, and how much of a pain would it be to solve it given the extra complication. i shouldn't have specifically said "both sides", it was more of a figure of speech.
I'm frankly amazed you managed to get the right order of magnitude, let alone as close as you did.
I actually did a similar experiment in chemistry class in high school. The difference was, we assumed Pi and wanted to calculate what a mole was.
It's a small furry animal that spoils putting greens on golf courses
We did that experiment in Chemistry and my teacher didn't appreciate the joke so I thought I would try it here.
Please vote by clicking like or dislike as you feel about the joke
@@trueriver1950 Then molar mass = 100 gr +/- 50,
molar concentration = # moles / putting green
molar fraction is when you use your spade... no, I'm not going to elaborate on that one.
New subscriber here! My birthday is on PI day, and I'm looking forward to watching your videos every year on the eve of my birthday. I love your content. Keep up the good work.
You two are fantastic with your collaborations!
17:15 Steve laughs because Matt starts his sentence with "Pi equals 6.2 ....."
It was tau all along!
"Assume the molecules are cubes." Is that like the spherical cows in a frictionless vacuum? 😂 I guess that's partly why you were off by bout 24% 😜
a unit circle area is pi*1^2 = 3.14
a unit square is 2^2 = 4
difference is pi/4 = 78,5%
explains some of the error?
@@diynevala The error you're talking about applies to using 1 square to estimate the area of the circle; they used quadrillions of squares.
Also why does your unit square have a side length of 2 rather than 1?
It just occurred to me that your comment might be satire, but I'm gonna post this anyway lol
@@schizophrenicenthusiast I should not have said UNIT square. I meant "a square with same width."
A unit circle has a radius of 1, therefore a diameter (width) of 2. Equally wide square has side length of 2, area of 4.
I am thinking about the actual molecules assumed to be circles (or possibly hexagons) - I have no idea how one, two, seven or hundred molecules are standing side by side - but I suspect that they are definitely not organized just along X and Y -axis, few things in nature are squares.
there is some truth to the original comment, and y'all are thinking about circle close packing, so here's a copy-and-paste of another more detailed comment i left:
first, alternative packing is not applicable. they calculated the number of molecules (directly from the volume of oleic acid, without making any assumptions), then divided the volume of oleic acid by the number of molecules, obtaining the average space a molecule takes up - this is to say, they assumed perfect packing, 100% filled space. the shape of this molecular space could indeed be many things, for example thin vertical square prisms; if the ratio of side to height of such a shape is 1:10 you'd get pi=4.297. in absence of detailed knowledge about the molecules, the cube is the shape that makes the least assumptions.
what they did next is calculate the total area of the circle by finding the top-viewed area of the (cubic) molecules (of now known volume) and multiplying that by the number of molecules.
so second, if molecules were (smaller area) circles, you could only get that 21% unused space back by smushing them down to squares again, which is unfair as you've simply made them smaller on no grounds. what you're probably thinking about is square vs hexagonal close packing of circles, which have a filled space parameter of 78.5% vs 90.7%. if better packing were an option (which again it isn't), going from square to hexagonal would decrease the unused space, hence the area calculated, hence pi, though by only around 12%.
at the end of the experiment they solved the circle area equation for pi, having calculated the area and measured the radius.
my third point is then that any calculation involving circles or spheres for molecules (including your 78.5%) needs some value of pi, which is assumed unknown. is such an equation solvable if the unknown is on both sides? i don't know because there is no such equation because it doesn't make sense.
in conclusion, there's nothing wrong with the math, the main source of error is probably the experiment itself, i.e. steve's handling of the solution (measuring, mixing, dripping), which is to be expected, as they only did the experiment once on a small scale. measuring the radius sure was janky as well but the error couldn't have been more than say 2-3%, which corresponds to about 5% for the final result. all things considered it ended up being a pretty good estimation.
@@calinguga I can agree with all that - I am not an expert on any of these fields. Having these huge (amount of molecules) and tiny (their size) numbers calculated near pi is amazing, as errors could pile up.
They have these molecule mock-ups where you can identify every atom in the molecule, but it is very seldom we see multiple molecules simulated as an area or volume.
Two of the best minds in the field of explaining math and science. Great double act.
This was simply great. I loved it!. I just enjoyed every second of the video. Thanks to both. :D
Can't decide if I'm more impressed by Parker Squares or Mould Cubes
“Doesn’t look cuboid to me” You got him there Steve, no it does not 😆
When I did this experiment in 2006, I remember dividing the volume of the oleic acid by 2, because of the hydrophobic ends touched the water, and the hydrophilic sides of the oleic acid kept the oil in one blob. This gave the molecular length of the oleic acid, or a single stratum.
Matt: Has a Rubik's Cube on the shelf
Also Matt: Shows a hypercube as an example for a cube
Well the hypercube is the more cubie cube if you ask me. ^_^
That's just as much a cube as any other cube.
Although as I learned in mathematics: both are spheres.
Am I crazy, or was this published early?
Edit: Intentionally early for teachers! Happy early Pi Day everyone.
Just a tad.
Downloaded the video in case he takes it down.
"it's Pi day, this week"
Nope! Pi day is in fact "this week", as stated in the video
It's a parker release date
Can we now start calling Steve Mould, Steve Mole just for this special occasion.
This was hilarious, interesting, and informative. I love you guys!
*I just love both of you guys*
Has Matt averaged all of this Pi-Day calculations to see if he's approaching it more correctly with each passing year?
3,205891795 so far
although he did 2 videos in 2015 so idk if both of them count as pi day calculations
it's a very slowly converging infinite series,
🎶
Monolayer
What's it called?
Monolayer
That's right! Monolayer
Monolayer!
Monolayer!
Monolayer!
🎶
I couldn't help myself 😆
Congrats on already hitting 800.000, Matt!
I look forward to these every year
Pi fact: 39 digits after the decimal point is all you need to measure the observable universe within the width of a single atom.
These guys: measure atoms of width 8cm and get the second digit wrong.
Those are some big atoms!
They are making some HUGE assumptions about the molecular packing density in a thin film. (as lampshaded by all the just "assume it's a cube") I'm quite surprised they were in the correct order of magnitude, nevermind having the first digit right.
...and 42 digits to measure to within the radius of the smallest atomic nucleus.
Another reason 42 is The Answer
16:59 "That feels like something I can see with the naked eye that isn't as big as a country"
Could we approximate pi using the Vatican?
Assume the Vatican is a circle. Walk around it and through it
Perfect blend of physical science and arithmetic by two amazing fun-loving experts. I love seeing the colabs here. Getting so close to Pi in such a unique way is really fun to watch too.
This is great.
My two almost favorite RUclips channels at once.
Bump it up.
ThankYou.
Oh man, already a new method? I hadn't finished calculating with the old one...
Tried it for different cuboids, and gotta say, am convinced this molecule is a cube now.
Would you mind posting the results for those of us who get off on these sorts of things?
😂😂
Love these Pi Day videos!!!
π has updated in the background. Recalculate everything to finish the update.
Version number: π release 2.0
Changes made in this update: π now equals 3.875
Now to wait for someone to redo the calculations to a greater number of significant figures, to see if increased accuracy takes you closer to or further from the official value... :D
3.8760011. Surprising close what Matt calculated
If all of RUclips was like this the world would,be a better place.
*muttering under his breath* "glad I got a science person..."
I love it.
The videos with both Matt and Steve are my favorite, their chemistry(heh) is great