Calculating π by hand: the Chudnovsky algorithm
ฝัง
- เผยแพร่เมื่อ 13 มี.ค. 2018
- For Pi Day 2018 I calculated π by hand using the Chudnovsky algorithm.
en.wikipedia.org/wiki/Chudnov...
k = 0
42698672/13591409 = 3.141592|751...
k = 0 and k = 1
42698670.666333435968/13591408.9999997446 = 3.14159265358979|619...
Watch me do the second term working out on my second channel:
• Calculating π by hand:...
See me do the entire final calculation again (without a mistake) on Patreon:
/ 17542566
Proof that I did actually do it properly:
www.dropbox.com/s/64vc5iz7yt4...
This was my attempt two years ago. Look at how much hair I had!
• Calculating π by hand
The Chudnovsky Brothers used their algorithm to be the champion pi calculators of the early 1990s: going from half a billion to four billion digits of pi.
en.wikipedia.org/wiki/Chronol...
This video was filmed at Queen Mary University of London.
CORRECTIONS
- None yet. Let me know if you spot anything!
Thanks to my Patreon supporters who enable me to spend a day doing a lot of maths by hand. Here is a random subset:
Christopher Samples
Sean Dempsey-Gregory
Emily Dingwell
Kenny Hutchings
Rick de Bruijne
Support my channel and I can make more videos:
/ standupmaths
Music by Howard Carter
Filming and editing by Trunkman Productions
Audio mastering by Peter Doggart
Design by Simon Wright
MATT PARKER: Stand-up Mathematician
Website: standupmaths.com/
Maths book: makeanddo4D.com/
Nerdy maths toys: mathsgear.co.uk/ - บันเทิง
The accuracy on the first term was brilliant, especially considering that you used the Parker Square root of 10005.
Given that the actual is 10.024996, I don't think that broke things too badly.
Oscar Smith I think you mean 100.024997.
Well, the continued fraction [3, 7, 15, 1, 292] = 103993 / 33102 also yields 3.141592653... with less effort.
BTW, the way he subtracts numbers seems quite complicated to me O_o.
ROFL
I think you mean ~100
"I am going to calculate pi by hand again..." All I could think was; "You must have a really big, and really round hand."
And he copied all the numbers in a big, round hand!
Mind blown part was the most funny thing I have ever seen
Chud bros we won
sqrt(10005)=100.025
Parker square root
More like the first-order Taylor series square root :D
It was an approximation, however he was *VERRY* close. Asking Siri (who uses Wolfram Alpha) even she approximate it to 100.025. Using Wolfram Alpha you get the approximation of 100.0249968757810...
It is a decent approximation - i think and error of 10^-7 is acceptable to be used in another approximation.
well, if you use a more accurate sqrt(10005), then you get more π.
426880*sqrt(10005)/13591409 ≈ 3.141592653589734207668453591578
ABaumstumpf he could've has 13 digits of precision on the 1st calculaion if he had used a more precise square root tho
I find it fascinating that, looking for a good decimal approximation of the number π, you have come up with an extremely accurate approximation of the constant e at 7:25. Although I don't know if it's a coincidence or not.
Euler number made a cameo!
:O this blew my mind. Didn't even notice that watching it the first time!
wow , correct upto 7 decimal places ,nice observations, even this is blowing my mind now
pi and e go hand in hand everywhere.... "Where there's a pi, there's an e"
@@omaanshkaushal3522squares are god's favorite exponents
that converges STUNNINGLY quickly. WOW.
weesh It had better: it's hideous!
Gold161803 It's amazing how many interpersonal relationships function more or less in this manner.
Every iteration gives approximately another 14 decimal places
The hair, or lack of it, is awesome! I did the same thing last year and it was liberating not to worry about the impending baldness. It's a bit cold in the winter so invest in a cap.
That was a real Parker Square of a division.
The division was correct though. The subtraction however...
What seemed wrong to me about the division was Matt's statement at 9:11 "If I need extra bits on the end, I just put zeroes". Surely you have to bring down *exactly* one zero each time. Otherwise, you'll never have a zero in the answer - you'll have invisibly skipped them.
Luckily for Matt, (as calculated by calc, see www.isthe.com/chongo/tech/comp/calc/ ):
42698672 / 13591409 ~3.14159275171544024611
and Matt didn't get anywhere near the first 0 of the answer.
Taking more piss than a racetrack of thoroughbreds....
it’s not a parker square, it’s extremely accurate, more accurate than you ever meed
David Gould mate you would get a zero when the two numbers subtracted at the end are equal 0. He just didn’t go that far. The method was perfectly valid. You’re just confused.
Pi Day is now both Einstein's birthday and Hawking's deathday. :(
It's also Karl Marx's deathday, so it evens out.
Fun odd fact, Dr Hawking was born 300 years to the day after Galileo Galilei's death. So, come March 14, 2318 we should have an awesome astrophysicist come back around, kind-of like a Halley's Comet of brains!
We can only wait in hope, now.
... if the world is still here by then. We live at a time when Hawking is no longer with us and the "most powerful man" on the planet doesn't have a clue.
Hawking died late yesterday
Hawking died on March 14th in the UK. GMT is named after Greenwich, which is in London, which is in England, ...
13:45 the face I make every time I finish a calculation and my answer isnt any of the choices
K= 0 Mind = blown 🤯
How does my calculator even do it in 0.0001 sec 😂😂😂
Your calculator doesn't really calculate it, it's just a predetermined constant.
Next year:
Calculating pi using the perfect curvature of Matt's bald head. Looking forward to that one.
7:25 27182818 (hmm... seems familiar...)
its the e
John Chessant I noticed that too. Coincidence? ...probably.
I wonder if there's any correlation or if its purely a really unlikely coincidence.
e = 3 = pi
I dont think it is a coincidense considering that 13591409 is the number from the formula. So when they defined this method of calculating Pi, they probably took the half of e and multiplied it by some power of 10.
Or it's really a super (un)lucky coincidense. xD
Love it. I want to see him do this with increasingly sophisticated calculation aids. Like if we granted him a slide rule, how much faster could he go?
11:08 It's an older meme but it checks out.
its never to late for extanded scenes
11:11
@@naxzed_it 11:14
Calculating Pi is such an irrational thing to do.....
Almost transcendental.
approximating it is very rational though
@@IntergalacticPotato Only in 22/7 cases though.
Billions must Pi
Love your work Matt! Strangely nice watching this sort of maths done by hand.
Wow crazy good estimate on sqrt 10,005! The actual answer is 100.02499, getting 100.025 in a handful of seconds off the back of a napkin was impressive.
Na, the approximation was incredible simple - still very accurate though.
ABaumstumpf What's the point of an approximation if it isnt incredibly simple?
KackBon3rdGen ....................
Yeah, no. It is to approximate something. This video even is about Pi - a number that needs to be approximated in most scenarios for the simple reason that it is impossible to show it with 100% accuracy as it is transcendental.
An approximation can be complicated for many reasons - fast convergance, easy hardware synthesis, easy to program, or interesting effects.
In some cases the approximation can be shown to converge to the real value, but when a specific approximation is used it can cancel out with other parts of the equation making it a lot simpler to use the approximation - which you wouldn't see if you used the 'real' value as a symbol.
The method he used is actually equivalent to a differential approximation. The reason that x2 is ignored is because as x tends to zero, d(x2) /dx is zero
In india, Even grade 6 students can do this approximations so its not like out of the box maths lol. Illiterate foreigners !!
I'm impressed that you did all this working out by hand, and more impressed that you made it that far before making a mistake.
Your head shaved look is awesome. Is it pi day special
subhash mirasi it was shaved in a video he did a few weeks ago :)
It was just Parker hair, anyway.
He was trying to find the surface area of a hemisphere
Pi R Squared Channel rest in peace
It's called the Parker hair
Hey Matt, quick observation I wanted to run by you.
Today I went back and watched your old video about approximating pi by rolling dice. I wanted to see how accurate this method could be, so I wrote up some code in python to automate it. I was messing around with the variables, like # of sides on the dice and number of dice rolled, and I was trying to optimize it to give the best answer possible. Something that I noticed was that when increasing the number of sides on the dice, accuracy didn't improve linearly. Instead, a highly-divisible number of sides like 30 was more accurate than 31-35, and 36 sides were more accurate than 37-39 sides, 40 sided dice were more accurate than dice with 41-45 sides, and so on. I thought this was really interesting, and was curious if you had any insights as to why using highly divisible dice might increase the accuracy of the program's estimate of pi?
Great vid as always, thanks for reading!!
It could be related to floating point errors. The highly divisible numbers have a lot of factors of 2, which are more accurately represented by floating point numbers.
Damn both this and the comment are both smart. I’d feel bad not leaving anything smart.
My 10 cents are that code isn’t perfect when doing physical things like dice or even doing anything random. Simulations aren’t perfect with it. Or that could be completely off topic.
@@Treviisolion wonder if he used an arbitrary precision module what it would be
considering your using the "math" library, thats the problem it can have more errors deviding more. the true way to simulate this is expressing it in a geometrical manner, you can start with an axis and find your way into a circle(which is what we are looking for anyways), this might be the case of the light beam reflection calculating pi(if you dont know what this means, there is a great video about by 3blue1brown i think), but again i might be wrong as im not familiar with this concept. well you commented 4 years ago, so i guess you alrdy solved this so yea gday
Happy pi day!!
I’ve only just discovered this channel and I’ve been binge watching everything up to now. It’s so nice to have math be fun again ^u^
Hey Matt, it would be a great video to show (to some extent) why is there e at 7:25. I reckon it's connected with how the algorithm was conceived. j-invariant and all that
"This is why I pay you the (slight pause) medium bucks!"
that cracks me up XD
Always love these Pi day videos
Thanks for the exact 2 year anniversary of the last video that we did or you did to be exact exact exact about this pi calculating video
Well let's just call it parker pi
How long did it actually take for the working out? I was impressed with the 3.1415927 on the very first term. That is on the order of 1 millionth of a percent error, which is well within enough precision for many practical applications. The square root approximation was great, too.
Compared to that first infinite series video done a few years back, this is a wonderful demonstration of how two different series converge on the same constant at different speeds. Incredible how the Chudnovsky gives you that many digits in just two terms!
This is good stuff! Keep up the good work!
Love the new haircut. Looks great! ;-)
There’s a reason why you’re my favorite mathematician, Parker.
OH YES BEEN WAITING ALL YEAR FOR THIS
This needs more likes. Love this dude. Thanks for the mind blow
10:53
What you have written down id the correct aproximation of pi to 7 decimal places as the next digit is a 5...
7:25 WTF?? y is e on the board?????
ron raisch woah, nice observation
I've learned enough mathematics to know that it's probably not at all a coincidence, and there's a valid reason that one of the "magic numbers" used in the series work out to a multiple of e/2. But I haven't learned enough mathematics to know what that reason is XD
I think it has something to do with the fact that e ^ (pi * √163) ≈ 262537412640768000 + 744. Someone smarter and less lazy than me can probably figure out why.
I'm... pretty sure that's an 8. Unless you're not talking about the glyph on the top row, 4th from the right.
Naturally it's there ;)
Great vid, as usual. A few genuine LOL moments, like your approximating a sphere.
This video holds surprisingly high value in the meme economy, good work!
I see why they used this for a computer. They are especially amazing at division and subtraction. Binary makes it easier.
Tristan Ridley mainly because it’s pretty much the fastest converging equation for pi (about 14 digits per iteration!)
why is he writing decimal points like dot multiplication and dot multiplication like decimal points?
It's a british thing, I know sometimes it may be confusing
?
Dharsono Hartono, well in my country we use a comma as decimal separator, so 8·56 would be 8,56 (or 8.56) for example. And for multiplying we commonly write this symbol (·), for instance 5.6=30 would become 5·6=30.
I'm British and that's not a thing. Multiplication dot is in the middle and decimal point is at the bottom. Also, he's from Australia so that may be why.
Morgan Mitchell hmm, weird, not sure about multiplication sign but middle dot is still used as a decimal separator, usually when handwritten.
Source: www.quora.com/Whats-this-punctuation-·-How-can-I-type-it-on-my-computer-What-is-it-used-to-do
Matt, that was awesome!
Thanks for the ridiculous and ridiculously amazingly pi day video
6:22 "42... 69..." and then it cuts away lol 😂
And now I know the Parker sphere.
Nicely done!
The mindblow and the sound of silence bits are the quality Standup(maths) this channel is worth watching
So sad Stephen Hawking died on Pi day. RIP a great mind :'(
WazzupKMS Einstein was born on pi day.
RIP Stephen Hawking, hold one fist in the air tonight :(
Yeah, he died today 😪
A damn good run for a sufferer of ALS. He provided us with such tremendous advances in physics that we must be forever grateful, but let it not be said that he was hindered from his goals by his horrible disease. The man will be a legend from now to the end of our species, like Archimedes before him!
:(
PS: It would be interesting, if it has even one more digit of accuracy, if you used a more exact estimation of the square route of 10005.
The great thing is I always get a present from Matt for my birthday, can't wait for the next one. :D
Meeting you at the “Curious Incident” was such an amazing day- how can you make maths so much fun?!
Matt's Pi day video - 90% of comments about his hair :)
But seriously - whay happened?
He noticed a trend and decided to extrapolate.
Parker Cancer, it is harmless
Pi R Squared Channel
RIP....
Ivan Mazeppa congratulations, you're the first person in history to make a Parker Square joke that's actually funny
He's powering his brain using performance-enhancing radium injections
MIND ≈ BLOWN
As someone who's also follicly challenged and had to get rid of it's hair roughly one year ago, I commend you to your desicion to approximate the sphere-shape a little bit quicker. It's a tough step but you"ll have to admit that you look so much better afterwards!
i'm 15 and i'm impressed that i understood the whole video (and the k=2 one in the second channel)
It hurts that he puts his decimal in the middle.
Is there a GIF version of 11:12 yet, and if not, can I make one?
not sure of an equivalent phrase but you shouldn't have a problem using it. Im austalian and it just means that the preceding statement is very straight forward and easy,
"Bob's your uncle is an expression of unknown origin, that means "and there it is" or "and there you have it.""
Thats a better definition
Great effort, nice work
Fantastic hair and the best possible way to celebrate pi day!
Can someone tell me what discovery show does Matt parker do?
Outrageous Acts of Science, wikipedia says and imdb confirms it
Do your long division in binary, you can avoid all this "how many times does x go into y" and just have "does x go into y"
re: the approximation, that IS stunningly fast; re: the hair, I just thought "oh thank god he finally bit the bullet and did it" but sounds like you thought "thank god I finally got to do it" haha :). and it looks good!
i never saw your videos with hair so you look great
k=0 is probably good enough to get you to the moon within a few yards of error.
nberedim I heard somewhere that 30 digits is more than enough for any practical purpose we will ever need. If I remember correctly, this is because it is approximate enough to be precise down to an atom’s width for the circumference of the observable universe...
@@vibaj16 I don't know if it's 30 or 40 digits, but yes that's the idea.
@@vibaj16 37, if I remember correctly.
And that's quite a bit more than any practical purpose will ever need.
Matt... great to see you using the same tricks I have been using for decades, including the massive division...
And yes, it is sad that it is both Einstein's birthday and Hawking's event-horizon day. Yet another tie between two great individuals.
i feel like this would be an AMAZING way to practice reducing mistakes
You look so much better with your new hair(less) style!
Strangely enough I think your shaved head accentuates the hair you still have while your unshaven head accentuates the thinning hair/bold spot.
355/113 is about as good as this first term. Probably easier to divide by hand as well. :)
That isn’t part of the chudnovsky algorithm, so yeah a little irrelevant
@@cringeSpeedrunner bro replied to a 5 year old comment trying to correct something that didn't need to be corrected
@@doppled Bro tried to correct a correction to a 5 year old comment
how can you calculate how many digits are certainly right without already knowing pi? is that possible?
Assuming you know it goes to pi, but you didn't know pi's value. If the difference between the approximation of pi including the k'th and (k+1)'th term is less than 0,000 000 000 5 (5 at the end as you might round up), you know the k'th term has 10 correct digits
the easiest way is keep going and going. so if say first run we get 3 second 3.15 third 3.14159......
you start seeing which numbers stay the same farther and farther. and those must be accurate. thats the easiest way but of course means your last calculation you wont know how many digits are correct but youll know most.
it also helps when you prove your formula actually gets pi
Happy Half Tau Day Matt!
I've never seen that way of doing division before. And I'm glad we can fairly call it Parker Division after that little off-by-one..
11:05 - 11:20 - I want to certify this section as an official dank meme.
Parker hair
Well done Matt
I cant describe the beauty of this video. Its 100% funny material! Parker is no longer Michael Palin doppelgänger, but still amazing.
Bald Parker square 😎
A treat, as every year, sir.
So I spent a few hours working it out, but I discovered that if you take a regular polygon of N sides with a perimeter of 2pi the percentage of the way from the verticy to the midpoint so that you have a distance of 1 from the center very very quickly approaches about 18.35%. I find it very interesting that not only does this number converge, but it also converges very quickly! It took a while because I had to use the COH trig identity, the law of cosines, and the quadratic formula, in addition to a fair amount of algebra.
So he finally shaved his hair.
HAPPY PI DAY!!! But let's face it, it's no longer happy... RIP Stephen Hawking T_T
YeahH Awesome video great upload!!
I love your hair!!!
Hello there. Happy (sad) π day! We'll remember you, Stephen Hawking.
Hoo yun zhe also those kids from Florida
Yeah:(
Anyone notice e at 7:25?
[Mind Blown Clip]
Is it a coincidence?
Tazer I would tend to say probably as e and pi appear in lots of places, however, on the second iteration, it doesn't go to e (although it could after lots of iterations)
oh
Where is the e?
Next year, calculate pi using the packing fill ratio of a bcc structure (sqrt(3)pi/8). Pack a box with oranges in a bcc structure and calculate the fill ratio. Basically, calculate pi using some fruits and a box
Wooohoo for the new look!! Happy Pi Day. RIP Dr. Hawking. Happy Birthday Einstein!
I can guess any number you are thinking!
1) Choose any number
2) +1
3) minus the number you chose!
4) BOOM!! The answer is 1.
*cries in spanish*
lets chud it up rq
sharty rise up
I had forgotten that today was Pi day (I remembered yesterday, but forgot today). I was working on a table of probabilities yesterday and kept making little mistakes, after four hours I had to call it quits because I kept making new mistakes. Anyway, I know how it feels to think you've completed something only to see an error toward the very beginning. I've never seen Pi worked out like this before, and I'd love to see how that Chudnovsky algorithm came about. Anyway, thanks!
The actual square root of 10005 being 100.0249969, so really quite a good approximation. Considering you got 6 digits of pi and your only difference is at the 6th digit that's a really fantastic sequence!
Should be the Bloodnovsky algorithm, sounds scarier.
happy π-day!
Cr42yguy Stephen hawking has died (RIP his soul) so it is a day of mourning
Mythic IQ I know, I just didn't want to mention it in my post. I think the whole scientific community is quite sad about his passing.
Could you explain how you come up with these equations for pi. I spend a lot of time in my early college days trying to find one, but with now luck. I was able to come up with a couple of equations that as x approaches infinity y=pi, but I could never find anything else, despite many hours of work. My approach was an old one that I’m sure has been done before but I did do it independently. I calculated half the perimeter of a regular polygon with N number of sides and a distance from the center to any verticy, equal to 1, and then the same but the distance from the center to the midpoint of each line segment equal to one. Both equations approach pi as N (or even x since the equations are continuous for x>3) approaches infinity but from opposite sides. I also found that as N approaches infinity one equation approaches being twice the distance from pi as the other one, but after looking at my proof of that closer it turned out to be trivial unfortunately.
your hair looks amazing
What happened to your hair?
A freak shoe shining accident.
15:40
Breaking Bad
where did his hair go?
parker square of a haircut
15:40
This is the stuff.
I would love to see (maybe I have to try?) what kind of accuracy you would get by using a slide rule to do the division (and square root).
Love your new haircut! I should try it out too!
Welcome to the Scott Manley club!
Because I was curious I looked up how many decimal places of accuracy you get and it's practically linear with ~15 per term. Ten terms is accurate to 155 places. The version in this video must be somewhat simplified as it's getting about half that many.