Using an Out-of-Control Car to Calculate π.
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- čas přidán 9. 03. 2023
- Happy Pi Day: 14 March 2023. (Yes, the video goes out a few days early. So teachers have time to plan their Pi Day activities.)
Huge thanks to Eric and the whole team for letting us in to skid some cars and calculate pi.
It was an active and working site and they did a great job making time, staff and cars available for us.
If you want to learn more about traffic reconstruction calculations, check out this (slightly odd) 1983 book "Handbook For The Accident Reconstructionist". www.ojp.gov/pdffiles1/Photoco...
If you want to sign-up and hear about Pi Day 2024 plans, here is the form: bit.ly/piday24help
Huge thanks to my Patreon people who support all my silly Pi Day videos with their irrational funding. Join in and we'll make Pi Day 2024 bigger and sillier. / standupmaths
And sorry I could only put the names of Statistically Significant and higher Patreon tiers on the scrolling credits. A bunch of that was done by hand and that was the limit of what could be lined up.
CORRECTIONS
- If we had used 26/38 exactly were would have π = 3.136421 which is basically 3.14 (First spotted by CK.)
- Let me know if you spot anything else!
Filming and editing by Alex Genn-Bash
Pi Reconstruction by Eric
Stunt Driving by A Colleague Of Eric's
Location provided by Like We're Going To Tell You
Extra help by Why Are You Asking So Many Questions
Written and performed by Matt Parker
Credits Animation by William Marler
Produced by Nicole Jacobus
Music by Howard Carter
Design by Simon Wright and Adam Robinson
MATT PARKER: Stand-up Mathematician
Website: standupmaths.com/
US book: www.penguinrandomhouse.com/bo... - Zábava
UPDATE: If we had used 26/38 exactly were would have π = 3.136421 which is basically 3.14. (I stand by my 3.12 but I am kicking myself.)
Yes, yes, it's not Pi Day for a few more days. As always: I try to get the Pi Day video goes out a few days early so teachers have time to plan their Pi Day activities. And leaving it until Monday next week felt too late.
So, ah, what are we all doing for Pi Day this year?
I'll be wondering what's so special about 14.3!
Given pi = 3.112, the viedo release isn't that badly timed
Calculate pi by pi day release dates.
On π day i am going celebrate my birthday
I'll probably be giving pepper to a friend xd
Every time someone says "we can ignore" or "lets not worry about", an angel takes away a digit of precision.
Fortunately ♾️-1 = ♾️
Nice
Let's not worry about that though.
@@murk1e where'd you get that fancy infinity? Is that like a deep cut emoji near the bottom? All I have is the ∞ from the = long press.
≈
Fun fact: It's important that the undisclosed location was in North America. Due to the Coriolis Effect, skidding cars spin in the other direction in Australia/South Africa/etc.
Somewhere out there, someone believes you.
Fun fact you need to use the chiral version of Pi in the southern hemisphere
What happens with skidding cars at the equator, then!? :P
@@bsharpmajorscaleCars do not spin at the equator.
@@jacksonpowers4459 That's what I thought, but I wanted to confirm it. Very linear.
Fun fact: The value of pi for 2023 matches the one for 2019 to three decimal places.
2019: pi = 3.11791
2023: pi = 3.11712
The the real value of pi must be 3.117505 +- 0.49, amazing
How does this, not have more likes!?!
Good to know that pi isn't changing too rapidly over time. I hope next year most of the digits I memorised will still be correct.
@@oskarthompson3789 Come on. You know the real value of pi was in our hearts all along...
@@robbiemer8178is that a suggestion for next year’s calculation?
Matt: Happy Pi Day
But it's not Pi day yet?
Matt: calculates Pi to 3.117, posts video at 3am on 0311 AU eastern time
I stand corrected
The other pi approximation day.
Nice coincidence
As I say every year, π is closer to 22/7 than 3.14, so he's really just humouring his US viewers by posting the videos four months early. The fact that professionals are bumbling with feet and pounds and miles mean they may as well be using 3.12 for π in the US… or 7/22… 😏
@@nomadMikyes, the imprecision of 0.3048 metres and 0.45359237 kg is the real problem..
I'm imagining an xkcd based on this. "The pi button on my calculator is broken, so whenever I want to calculate the area of a circle I have to put my car into a skid."
3.1023 is quite the Parker approximation of pi
I was just wondering what he was saying that for
It's definitely closer than some of his previous approximations
2.0230310 is quite close as well
Huh? He estimated 3.117, not 3.1023.
@@jessehammer123 r/woosh
After so many Calculator Unboxing videos, Matt still uses the phone calculator
The ability to screengrab is just too convenient! It's not for a lack of other calculators in my office.
@@standupmaths you gotta go hardcore and use a circular slide rule for pi day
Go abacus or go home! LoL
Honestly, all youtuber's need merch and he already have Maths Gear so he should just bite the bullet and make he's own graph calculator and include screengrab. Maybe add spreadsheet capabilities and color screen for the graphs, use USB to charge the replaceable battery and have a nice keyboard and make sure that it can write the equations probably. There have been no new innovation on the calculator market since the mobile phone. I am still using my two old trusty voyage 200 and I think it is time for something new.
@@standupmaths maybe you could unbox a capture card for your calculators?
You would've got 3.136 if you didn't round 26/38 as 0.68 13:15
OH DANG YOU'RE RIGHT
What would happen if the 15 approximation hadn't been used in preference over the real value?
I'm waiting for the day when Matt discovers significant digits and stops prematurely rounding everything off
@@cragonaut Punching it in with 14.962 instead of 15, and going with the better 0.684 coefficient of friction gets you pi as 3.128 rounding to 3 decimal places.
@@ratboy2713 that comment made me laugh so hard! The irony 😅
How my brain viewed Matt's drawing:
2:26 Car from above
2:28 Car from side (I expected a round view of the tire)
2:40 I think Matt has gone insane before finally realizing it's a head-on view (or a rearview tbf, is a rearview a head-off? 🤔)
Keep up the vids, interesting as always :)
Same!!
Ditto!
Same
No, a rearview is a mooning 🙃
I was doing the same thing.
Looking forwards to "calculating pi by taking the average of all the times I've calculated pi"
It'll be glorious in 20 years time
The series of values of Matt's calculations diverges to pi.
Average is easy. I want the most likely value of pi assuming the guesses follow a normal distribution.
i was curious to see what his current average is: 3.186.
Folks, find yourself someone who looks at you how Matt looks at 3.117
"I think that might drag my average track record closer to pi"
I can't wait for next year's video to be 'finding pi by averaging pi attempts'
Pi Day is like Groundhog Day, except instead of setting the start of spring, we're setting the value of pi for the year.
Also its like the movie Groundhog Day where we keep doing the same thing over and over (calculating pi), and things going wrong.
"Okay everyone, this year pi is equal to four!"
*A roar of complaints and cursing from mathematicians, engineers, and other pi users everywhere*
All those imperial units... *shudder*.
Your sacrifice is appreciated, Matt
In North America it was more likely "conventional units," which predate so-called "Imperial Units."
No, they're North American units, which don't even match Imperial! 🤦
@@paulcrumley9756 Well, "predate" isn't the correct way to describe it - the introduction of imperial units occurred 1826, and that of the US customary system in 1832 - but yes, they are technically not directly related, both were separately derived from the prior "English units" system, albeit in very similar manners.
My comment is technically wrong, so fair enough for the correction, but in my defense, I'm from the UK, so the bad units were always called imperial when I was growing up, and it was a joke lol.
I was thinking maybe these wouldn't be the really bad ones (like hole gages). Then I checked... there's a factor 11 in the number of yards per mile, and it's 15% off from a nautical mile. WTF.
What?! No scores of furlongs per fortnight speed measurements?!?!
... using Roman numerals?!?!
... in base 60?!?!
... in Braille?!?!
Tsk, tsk, tsk.
Next year, you should try using the buckling equation. It gives the maximum load that a column can support before buckling. F = pi^2 * E*I / L^2, where E is the Young's modulus (material property), I depends on the size and shape of the cross section, and L is the length. The equation is slightly different depending on how the two ends are supported. There are also the beam bending equations which relate the displacement of a cantilever beam to the amount of force applied (displacement of the end = F*L^3 / (3*E*I) ), so if you don't have E and I, you can calculate (E*I) from displacement of a cantilever beam and plug it into the buckling equation.
I just ran an experiment with angel hair pasta, where I measured force vs. displacement of a bundle of 20 angel hair pastas using a kitchen scale to calculate E*I (divide by 20 to get a single pasta). Then measured the buckling load for individual pieces of angel hair of various length by pressing it onto the scale until it broke. My estimate for pi was 2.675, less than 15% error with only 6 trials.
I can imagine a fun video where you have a bunch of students run the same experiment with different pasta (spaghetti, fettucini, etc.), and then bring in some heavy machinery to run it with metal rods/tubes.
My intuition says something a little less brittle would work better, but I could be way off. Regardless, that's an interesting idea.
That equation is an upper bound and very sensitive to imperfections so it's always going to give you a large(ish) underestimate no matter how many times you run the experiment.
So, when is Matt going to use his previous approximations of pi to calculate pi again?
By the way, not using the simple average way. Rather, treat his values as normally distributed and calculate pi by reconstructing the Gaussian curve and solving for the area under is as sqrt(pi)
I'm here for it
How exactly does your method work? You can't reconstruct a gaussian curve because you only have the observation, not the probability of getting each observation
@@freshrockpapa-e7799 I think they may be talking about Maximum Likelihood Estimation (MLE). There are some good videos explaining on it on YT.
@@cinemaker321 that would result in the same pi estimation as just making the average...
Probably a log normal distribution. Maybe even something weirder since some calculations get lots of digits and some very few.
Unicar might be the most terrifying concept for a vehicle I've ever seen.
If you use another decimal point of precision for the coefficient of friction you get 0.684, which yields an even better approximation of 3.135!
r/unexpectedfactorial
Snap
That's not how precision works...
684
@@freshrockpapa-e7799 What do you mean? That's exactly how precision works.
As a chemistry professor, not showing units during dimensional analysis is killing me! Love the videos
I refuse to follow SI advice to put a thin space between a number and a unit because I feel so strongly that the two are not separable.
@@nicholasvinen I feel the same about numbers and currencies for sums of money. I'm always wanting to keep them together in an object when I'm working on computer programs - but a lot of programmers are willing to pass them around the program separately and just hope they'll always remember not to put a number together with a currency that doesn't belong to it.
@@barneylaurance1865 yeah, that's a recipe for mistakes. I agree that currencies are basically like units. The number without it has no real meaning any more.
@@nicholasvinen I grew up with mechanical typewriters and then fixed-width fonts on character-mapped displays, i.e. not having any way to create a thin space, so it's natural to type the unit butted-up hard against the number even if that is not the way I would hand-write it.
But I also think of the prefix as belonging more to the number than the unit. For instance, 170cm. can be thought of as (170 centi) metres, with "170 centi" being just a funny way of saying 1.7. (OK, this gets awkward with mass ..... we would have to rename the kilogram, and then the renamed gram would have milli in it, and maybe the cooks would be annoyed, which probably why it wasn't done before.)
Casio calculators actually used to have an "ENG" button, short for "Engineers' notation" which would adjust the mantissa of a number upwards or downwards (depending if or not you pressed "INV" beforehand) to make the exponent a multiple of three and therefore align with a named prefix, e.g. 06 = mega, 03 = kilo, -03 = milli, -06 = micro &c. So if you get an answer of 5.89e-7 you can render this as 589e-9 or 0.589e-6. (And many other, less-sensible ways of writing it!)
Technically, you shouldn't show units during dimensional analysis. Units are, though related, not quite the same thing as dimensions. Dimensions (in the context of dimensional analysis) are things like length, time, mass, while units are meters, miles, seconds, hours, kilograms, pounds, etc... So you can't attach actual numerical values to dimensions (because of the lack of unit), but the whole purpose of dimensional analysis is a sanity check that an equation isn't nonsense equating apples and oranges, so that doesn't matter.
I'm actually a Volvo enthusiast so that car drawing works very well for me
It's a Parker Car
They're Boxy, But They're Good
@@KSignalEingang Yes! Someone else who's seen that movie!
@@KSignalEingang didn't that movie bomb? Assuming it's the one I think it is, of course. Dudley Moore as the lead, IIRC. It's been so freaking long since I even thought about it, I might be wrong.
@@MaryAnnNytowl I don't know how well Crazy People did at the box office, but I suspect more people know that quote than have seen it..which is a shame, it's a really funny film.
(Ok if I'm honest most of the good jokes are in the first half. Still! Def'ly underrated.)
Eric: "Surly somewhere there's Pi,"
Me: "There's always Pie, and never call me Shirley."
Surely you can't be serious...
@@samarvora7185 They're not serious, they're Shirley.
@@mattb5816 Samar got the joke... and probably watched the movie, too. Gotta love ol' Leslie Nielsen
@@jackielinde7568 I just wanna tell you both good luck. We're all counting on you.
@@samarvora7185 Looks like I picked the wrong week to quit amphetamines.
I had wondered where the 'spherical cow' part would come in, then you explained that it is a single tire car. :D
physicists after assuming planet Earth as a cube (it's close enough)
@@PeachCrusher69 i mean the triangle wave on the NES is supposed to be "close enough" to a sine wave (it isn't)
@@TorutheRedFox it works better than a sine wave because of the overtones caused by the uneven jagged edge of the triangle. The NES triangle is meant for lower tones and goes out of tune quickly at higher tones, and low notes of a pure sine wave are very difficult to hear without good speakers. It wasn't really meant to work like a sine wave.
@@trulyinfamous that's... a bit difficult to believe, as drastically different as the two are.
Happy Parker-Pi day everyone!
Parker-Pi = 3.1
I was wondering why this video was released early. 🤦♂️
Happy Mario Day
I somehow expected you to continue "testing track at an undisclosed location," with "...just off the A281 between Bramley and Bucks"
Should we update Pi Day to March 12th this year? We need to hurry and make the official announcement!
It's the 22nd of July, duh.
π = 3.10 based on this video's release date
@@nicholasvinen LOL, another day to celebrate maths? Let's do both! Both is good!
@@MaryAnnNytowl 22/7 would be a good day to celebrate approximations.
Obviously, pi day is 31-4 (since there is no 3-14 because we have only 12 months)...
Oh man, I love the [undisclosed individuals] at [undisclosed location]. They're so friendly!
They're very undisclosed.
Kudos to your guest for saying 'formulae'.
The calculation was nice and all, but I was most fascinated by learning about Eric's job! I'd never realized that was something people did for a living. I love hearing about unusual careers.
12:59 you know things get serious when Matt uses the Scientific Mode
When you pressed the equal sign I went “Oooh!” loud enough to make my son ask what’s up. I had to tell him that Matt got pretty close to pi and he was impressed.
Thanks for the early reminder that pi day is coming up!
Now that we've seen the preview for Fast and Furious 3.14, I can't wait for the theatrical release!
The critics don't love it. They have qualms with the pacing; it just goes on forever.
You really went "sphere in a vacuum" on this one and I love it.
LOL at measuring the circumference when you had to set a rope to the length of the radius.
Can't spell yearly without early, great video Matt!
I like the real-world application, thanks Eric for bringing this to us this Pi Day!
Hey Matt, as an idea for pi day next year; the max slope of the lift coefficient for an ideal 2D wing is 2*pi.
So, Tau?
@@nicholasvinen Depending which part of Greece they (or whoever taught them to speak Greek .....) are from, some people pronounce it Tav.
I was wondering why the PI day video was up on 3/11, then I burst up laughing when the 3,117 result came up.
Of course I then realized this was not in fact related but I would totally back the idea that PI day is just whatever day you end up calculating each year!
Dude. Your videos are literally my favourite bedtime stories and I have been /waiting/ for this one. Had a burnout week and for some reason thought pi day was 3/3 so I've been holding out on the edge of my seat since before then
This was just too awesome 😅 I'm a mechanic and tyre specialist by trade and super nerd by heart so I was on the edge of my seat the whole way and the ending did not disappoint. Love that rounding killed your average too 🤣👌 as before I started watching with kids I quite literally gave them a talk and said more than a couple decimals is useless for all but going to mars and gave an example of being off a little at short distance but still hitting an edge, then another one far away where you would miss by a star shot at same error margin 👏 I want Pi day every day now 😊
I really thought when Matt said he was at an undisclosed test track he was gonna pull the old top gear bit where he says exactly where it is.
10:15 "I don't want to alarm you but for the historical level of precision from my calculations we're good!" 🤣🤣
This is an engineering discussion, if it were a physics discussion, the car would be spherical.
Your videos made me love math!!! I catch myself teaching my daughter and little cousin math tricks and watching their brains figure it out looking off into space is the coolest thing ever. Matt you’ve inspired so many I feel it’s my job to pass the torch along. Keep making us say wow! Love your channel
Love it when my interests of maths, cars and Matt calculating pi in weird ways come together! I am always surprised by how often pi turns up in equations that at first glance seem to have nothing to do with circles.
As a physicist, a few nits: 1) The force of friction is pointed inward, not outward. It *is* the centripital force; it doesn't *balance* it. 2) The coefficient of friction is usually represented as mu.
I hate all the imperial units in these formulas, but apart from that, very nice approximation!
agree. Wonder if there's a metric equivalent
@@stevewandel9317 dude it's the exact same thing in metric
@@freshrockpapa-e7799 I kind of glossed over the bit where g for gravity was being screwed around with. Probably don't need to do anything for metric as everything is base 10
It's not out of control! It's doing exactly what he wants it to do! 😉
Also, pretty impressed you managed to get two digits of accuracy out of that.
The true PI-day celebration would be inventing time travel and going back to March 14 1592
At 6:53:58 am
I love how you removed your cap at the beginning as a cue to the driver
As a physicist, I really think you should measure each of the uncertainties and find the total uncertainty using the error propagation law. This way you get a feel of how luck-based you accuracy is.
3/10 is my favorite PI day
its 10.03 tho
@@defense200x then there is no pi day because there's no 14th month of the year
This is the second Pi Day video I’ve seen put out a few days early for teachers. LOVE that! :)
I'm absolutely amazed that the result was so 'precise' given the amount of rounding and the uncertainty of the measurements.
I love the creative ways you find Pi.
Next year, Matt calculates Pi by herding border collies with squeaky toys.
I was slightly nervous too, Matt! I'm always excited for these annual videos.
... After hitting "send", I realized that maybe there's a way to calculate pi using the fact that Pi Day comes around once a year??
@@DragCadRacing Does it involve furlongs per fortnight in the circumference of the year?!?!
I was wondering why this was early, then I read the description. Thanks for being great not just to students, but to teachers as well :)
Also, as a physicist, it causes me physical pain that you drew the friction force in the opposite direction to the mv^2/r. The friction force *is* the centripetal force (it is the force acting on the car that points towards the centre of the circle). It doesn't oppose the centripetal force. There is no actual force called "the centripetal force". We need some force to "be centripetal" for the car to turn, and in this case it happens to be friction that is playing that role.
Thanks.
"It's not just drifting, I'm actually doing math"
"Remember kids, the only difference between screwing around and science is writing it down." Adam Savage, Mythbusters
3.30 So Matt's drawing an MGf skidding round a corner. Something that particular car is very good at: been there, done that!
Thank you for coming across the pond to -5 UTC enduring our freedom units, to our First in Flight state as I watch from my chilled Birthplace of Aviation state.
I really like this tradition of stupid/silly/ridiculous/interesting ways to compute the floating point representation of pi each yeah.
I'd love to participate in calculating pi by hand, but the odds are against it happening in the US, and I can't afford to travel internationally. Have fun everyone that can afford to participate.
The speedometers in my cars are about 5-10% fast. Dropping that 25 mph by 5% seems to get you so much closer!
(I'm doing the math in my head, I could be wrong, haha)
The discrepancy in your cars' speedometers could be because your speedometers were calibrated for larger wheels. To go the same speed a smaller wheel has to turn faster than a larger one would, and the speedometers are based on wheel rotation speed (sort of).
@@hoebare No, the wheels and tires are the stock size. And the odometers have read accurately! Seems to be a German car thing (VW and BMW), my folks' cars have always been accurate (Honda, Subarua, Kia...).
When considering the errors inherent with your measurements, you can calculate the expected error of the answer, and it seems you actually nailed it. You can say the same thing about most of your π-day calculations.
This was a good Pi Day video. Good job and thanks to Eric both for suggesting this and helping you make this video.
2:25 to a topologist, a car with 2 open windows is a teacup.
Laughed so hard at this!
Never seen anyone use imperial units for physics calculations. It was... horrifying.
It's very common actually and not an issue at all as long as you're consistent, knock it off
@@freshrockpapa-e7799 Why? imperial is a horrid system when trying to do calculations like this. And it's not 'common'. Most scientists use metric, even those in 'Murica!
@@freshrockpapa-e7799 With this kind of units, you'll end up with any result you want. Add 2 cups of flour and 1 cup of water, 1 teaspoon of yeast and a pinch of sugar. Mix everything and wait a day or so. Ball it and stretch it to 12" and call it a pie.
@@Chris-hx3om uh, no it isn't, if you can't figure out how to use another system of units you clearly shouldn't be working in stem
@@freshrockpapa-e7799 Oh, I can work in either unit set (and I'm frequently forced to), and because of that I know just how difficult US imperial is! When will Murica join the rest of the world and ditch those archaic units?
Very cool computational experiment! And no serious injuries as a bonus! Thanks to all!
I’m glad you returned home for your derivations. It’s not safe to drive and derive.
❤ that you posted this on the date you calculated pi to be.
The former physics teacher in me is screaming at you for not keeping your units in your equations. Yes, it takes more room, but then you don't lose track of anything. :beaming_face_with_smiling_eyes:
Yep! And Matt should have written 3600/5280 in his explanation instead of 5280/3600; writing the units would've made that clearer
@@MathNerd1729 When he read the units out loud without writing them down, it irritated me so much that it took me a minute to realize he had it upside down. It always helps to look at the units first to see where which variable goes.
Happy Pi Day everyone. Another brilliant effort. Mathematicians of yesterday could only dream of such a sophisticated method.
So cool i absolutely love the different ways you can experimentally derive pi!
Is today Pi day? No... Was this supposed to be auto released on Tuesday? Yea, probably. Did I watch and enjoy anyway? Most absolutely!
maybe he calculated it to be 3.10 this year?
@@sergey1519 Well, to be honest, not done watching yet, but I'm half expecting 3.1 to be the result of his calculation HERE!
If I remember from past years he likes to get them out early for use in classrooms and such.
Parker Circle
Happy Engineers-Pi Day!
There hasn't been a truer comment to date
This was a really fun collab and celebration of pi. Kudos to Eric for reaching out!
@Stand-up Maths I love your annual pi series. It’s always great to see what ways you use to calculate pi each year.
I thought I had lost a week! 🤣
I don't think today is pi-day lol
If the speed is taken from the car's odometer, then it already incorporates pi to calculate the speed, as well as the "roller tool" that you used to measure the circumference.
9/10 PI calculation. -1 for using f for coefficient of friction instead of µ
1 digit is a good enough approximation!
Happy pi day for 4 days!!
Undisclosed Location is beautiful this time of year. So jealous.
The formula and measurements in this science leaves no decimal places of accuracy, yet it's good enough to determine the speed of a vehicle with stunning accuracy. Being off 2 or 3 mph at highway speeds is very impressive.
Hi Matt. US collision reconstructionists may use 'f' for the coefficient of friction, but in the UK we use mu and sensible metric units. Didn't want everybody to think that we were making up our own names for the variables and not using SI units! Happy Pi Day. Thanks for what you do in showing maths (yep, with an 'S' on the end) in real world situations.
Matt's Pi = 3.10 ? Hmmm 😀
2:22 Car person here. You actually drew a very accurate Volvo 240
Man I rewatched all the pi day videos to get myself hyped for this year's, not realizing that this one came out this year.
prediction: this approximation of pi is 3.10
"It's Pi Day 2024 and we've calculated Pi in many different ways so far. Today we're sacrificing the unworthy to the God of Math who will approximate Pi for us, a Parker Pi if you will, and they just happen to live here, in this active volcano! It's sure to be a hot episode if I do say so myself. 😏"
That was really cool! I love this series!
I'm happy! This was a fun and informative video.
Which one is better, Matt's car drawing or Ben Sparks' mouse drawing
The mouse.
Today can't be pi day pi day would be on 7th month of 22th day hahahahah💀
My wife and I bought our first house and when asked to pick a closing date, March 14th was an actually reasonable option so... We're celebrating Pi day with a house!
Now that I think about it, we have the final walkthrough on the 12th, which is 3.12 and therefore very 2023 Pi indeed.
I've been waiting for this video for a month now. It's the annual, "Matt figures out PI" video!