Scientists Just Discovered A New Formula For Pi Accidentally

While studying high energy physics in quantum theory, Indian physicists developed a formula that surprisingly provides a way to calculate the digits of pi! What's more, the formula relates to the first ever known infinite series formula for pi discovered by Madhava hundreds of years before Newton or Leibniz was born.
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iisc.ac.in/events/iisc-physic...
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Sabine Hossenfelder video
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references
www.iflscience.com/physicists...
phys.org/news/2024-06-physici...
www.indiatoday.in/science/sto...
www.msn.com/en-in/entertainme...
www.ynetnews.com/health_scien...
mathoverflow.net/questions/47...
math.stackexchange.com/questi...
en.wikipedia.org/wiki/Leibniz...
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[@Qermaq]

Meanwhile, engineers have discovered a new way to calculate 4.

[@alistairmackintosh9412]

It's like 3, but more...

[@nobodyknows3180]

They haven't published yet, because they are still ..... checking their calculations! 🤣😂🤣😂

[@BrianMelancon]

But five is right out.

[@jay31415]

Meanwhile, Terrence Howard has discovered a new way to calculate 2.

[@miendust9659]

you mean 5?

[@johnnydepp4866]

Can’t believe we got a new formula for pi before gta6

[@ivocanevo]

Everybody else: we can!

[@slothik1]

Nice one

[@siddarthan.s7749]

its not news that we found new way to calc pi, its news for the fact physicists to discover something so close to pure math, lol

[@TheDelwish]

it's not actually news, it happens all the time, especially in theoretical physics.

[@a.f.mashrafi2496]

its not even close to pure math

[@BOTNPC]

String theorists are closer to mathematicians than physicists anyway

[@FreemanPresson]

@@BOTNPC Seriously, elegant math is the only reason to waste time on string theory anyway.

[@ChannelMath]

A physicist usually knows more math than a mathematician I've found (to the extent that this is measurable). Not just because we specialize in a tiny subarea while every physicist knows all kinds of mechanics stuff, ODEs, PDEs, and ways to solve and numerically estimate their solutions, etc. In math, we stop ACTUALLY DOING math somewhere during undergrad. Mathematicians don't "do" math in the way most people think the word "do" means there. We INVENT math that other people COULD do, if they find it useful. Then investigate what kinds of things would or could happen if one were to do that math we invented, invent methods to solve problems in the math we just invented, and demonstrate that these methods for solving problems work and how well (again, IF anyone ever decides to use the methods we just invented for doing the math we just invented)

[@bergamt]

Science/Math Headline Writers Understand What The Heck You’re Writing About Challenge

[@NabPunk]

Impossible

[@zeeshanrabbani8125]

bhai aise likhoge toh humlog rude lagenge (translation: brother if you write like this, we'll look rude)

[@RavenMobile]

@@rajeshgajwelly9035 You went from supporting Indians to racism real quick ("superior intellect of us indian"). If you are intelligent, just be intelligent. No need to go around telling everyone you're intelligent.

[@SaumyaBhati]

​@@rajeshgajwelly9035 डिलीट कर दो भाई 🙂🙏

[@NabPunk]

@@RavenMobile It's just some BJP IT Cell Troll, let it be. The less attention they get, the better.

[@someone._.5333]

Still trying to identiπ this new formula.

[@FreshCamps-tw9co]

Haha

[@jacobsnider7304]

This happens all the time. It is an oft repeated claim.

[@Vsevolodbochkov]

Identiф*

[@Ephemeral_EuphoriaYT]

​@@Vsevolodbochkovexactly

[@padmalochandash_9873]

use the sign of work function.

[@iansragingbileduct]

So lambda = 10 gives us pretty good accuracy per term, lamdba = 50 gives us better accuracy, and lamdba = infinity gives us pretty bad accuracy. What's the optimal value of lambda, and why?

[@caesarinchina]

Exactly! Waiting for somebody to answer this. Should see which lambda values they reference in the paper and why...

[@nashh600]

I wanna know too

[@EdwardCurrent]

I imagine it just blows up at infinity. You're approaching ∞, not at infinity.

[@abdelghafourfid8216]

also wondering

[@dark3031]

I think that's not quite an accurate statement. As how I understand it, when lambda is infinity, it still gives us an accurate value of pi, the problem is that you need to take 5 billion terms to get it accurate to 10 digits.

[@thegunsofficial5857]

even Maths is still getting updates. What say you, Gabe Newell?

[@jaypolas4136]

1,2,....4,5

[@pranjalsrivastava4260]

@@jaypolas4136 bleem

[@Kiririll579]

At least you haven't been waiting for 500 years like chess players...

[@inqizzo]

Unlike chess you onky had to endure bots for a few years

[@dwacheopus]

​@@Kiririll579actually, there has been an update. About castling. It is now allowed to do horizontally only (there was a scandal, i believe, where castling should've been allowed to do with brand new passed pawn transformed into a rook in order to get a checkmate)

[@javastream5015]

My favorite is the Bailey-Borwein-Plouffe formula, which allows to compute the value of the n-th digit INDEPENDENTLY of the previous one.

[@notyourfox]

sadly, hex

[@trueriver1950]

​@@notyourfox or base 256, or ...

[@abebuckingham8198]

Unfortunately it's not computationally more efficient than calculating all the previous digits though.

[@stanleydodds9]

If you're allowed to use the gamma function in your calculation of pi, then instead of this infinite series we can simply compute pi = gamma(1/2)^2. To even determine if this is a practically useful formula, you need to know exactly how much time it takes to calculate the gamma function to a given precision. In practice, computing the gamma function is way harder than just computing and summing up rational values, which is all the other common pi series do, and they have faster convergence aswell.

[@rtc9]

This is a good comment. But it also seems to open the door to estimating Pi through methods of estimating the gamma function. So is there really much to be gain using the infinite series which includes gamma? There are a lot of different ways to estimate integrals.

[@sharkysharkerson]

That’s what I was wondering. I’m confused why someone would go to this for pi if they have the gamma function.

[@tolkienfan1972]

He used gamma in the spreadsheet. But if you look closely, you can use integer parameters and switch to factorials.

[@user-po2oi5yq7q]

@@tolkienfan1972 Although you can freely choose λ, you need to make sure that for all n≥1, there exists positive integer k such that λ = (1+4n-4nk)/4(n+k), so that you can say (2n+1)²/4(n+λ)-n = k. But I don’t really see many good λ satisfies it though.

[@tolkienfan1972]

@@user-po2oi5yq7q actually it's a falling factorial. You don't need gamma to calculate it at all

[@fenixfp40]

Does this mean I don’t have to go to work tomorrow?

[@bobamu]

Yes, work is now optional.

[@user-ty1vy3yx1j]

Don't worry very soon ai will replace u in job, then u would be happily unemployment 💪

[@Orange_96]

​@user-ty1vy3yx1j Ai told me to eat 1 small rock a day.. not sure were there yet.

[@davidnewell3232]

It does if you're Canadian.

[@surojpaul14]

😂😂

[@hotdogskid]

I love how the journalists are trying their hardest to make people think we've finally "cracked" pi or something like we didn't know what it was before

[@Kyle-nm1kh]

Well we don't know what pi is. It's transcendental. But yeah we do know 105 trillion digits at least. Don't think we need to know more tbh.

[@ronald3836]

​@@Kyle-nm1kh we know exactly what pi is. We just don't and can't fully know its decimal expansion, since it is neverending with no repeats, but that is the same for sqrt(2).

[@Kyle-nm1kh]

@@ronald3836 I don't think you know what "exactly" means

[@ethanbottomley-mason8447]

It depends very much on how you are using the word "exaclty". If by saying "we know exactly what pi is" you mean that we know all its decimal digits, then we don't. If instead you mean that we know it's definition, then indeed we do. You could mean that we know how to compute pi to arbitrary precision, in which case we also know exactly what pi is.

[@Kyle-nm1kh]

@ethanbottomley-mason8447 you can read their comment. They were talking about decimal precision.

[@hm5142]

Is Ramanajin's approach in finding his extremely strange formula for pi understood? He seems to have been working in a slightly different universe than everyone else.

[@marinoceccotti9155]

Waaaah... Something useful has come out of String theory... I'm overwhelmed.

[@tolkienfan1972]

I had a similar reaction

[@julianbruns7459]

Its not useful though, way better algorithms exist.

[@LagMasterSam]

Lots of mathematically useful things have come out of string theory.

[@tolkienfan1972]

@@LagMasterSam it's true. But I still find the joke funny

[@chriskennedy2846]

Correct! A rare case where string theorists actually discovered something real and useful. After all of the decades spent - collectively using millions of labor hours, along with billions in grant money and graduate level tuition costs - they can now claim that it wasn't a total loss. Despite the fact that they never effectively quantized gravity - at least they can now claim victory in discovering a novel way to derive the value of a mathematical constant that was already known for hundreds of years. Bravo!!!

[@knowwhey7559]

Damnmit, I thought they came up with a new flavor of pie. Oh well, back to rhubarb.

[@ThomasDrish]

Yah, I had my fork ready too, I was ready to dig in!

[@yippee8570]

I'm just astonished by Archimedes, because I know that in the same situation, I'd never be able to do that. He had so very little to work with and he still figured it out. That's the most impressive, to me

[@billcook4768]

Amazing how much free time he had to work since there was no internet or teevee

[@LagMasterSam]

@@billcook4768 That applied to everyone back then, but there was still only one Archimedes.

[@KerrySoileau]

IMHO Nobody was ever as far ahead of his time as Archimedes was. He basically invented integral calculus more than a thousand years before Newton and Leibniz.

[@aswinganji7870]

@@KerrySoileauimagine how ahead we would be if that monk didn’t write over Archimedes paper

[@Jee25-]

Well you would be suprised to know about the BCE Indian mathematicians!

[@fretzT_T]

That n-1 subscript is a gamma function. So good luck solving that

[@adityaagre1461]

Always knew Madhavas theorem as lebinitz

[@YoungPhysicistsClub1729]

well, most indian math achievements are known by western names, what can you do

[@gigachad6844]

Skill issue, proof or does not exist. We have proof of Bhaskara, Varahmiria, Aryabhatta and few others. But a lot of other claims are fake and propoganda like Vedas knew about Aeroplane, Vedas knew about Black hole, Vedas knew about Hawking radiation, Vedas knew about C++ Java blah blah... All baseless claim.​@@YoungPhysicistsClub1729

[@jameschristenbury2625]

That's because those achievements were basically rediscovered, so both India and Western nations can claim discovery. India juat did it earlier.​@@YoungPhysicistsClub1729

[@RavenMobile]

@@YoungPhysicistsClub1729 "Lebinitz" is a Western name?

[@jannegrey593]

There are 2 replies here that kind of miss the point. It is great if someone independently discovers something. Both Madhava and Leibniz did do it on their own and it isn't wrong to call it Leibniz formula. It just would be nicer to give Madhava some recognition as well. Madhava himself "discovered" things that were known in other parts of the world for centuries or millenia - it doesn't make them less important, because locally people benefited from it. India has long history of mathematical achievements, but it is wrong to assume malice or some sort of wrongdoing on part of 17th Century European mathematicians. And it's not like all mathematical discoveries were made first in India. And yes, Leibniz is a western name, I guess. German at least.

[@linforcer]

"The *exception* that 0! = 1" Oh boy, you are about to be chewed out for calling that an exception

[@peterkoch3777]

I have no idea about these chinese names, but you butchered "Leibnitz" totally😂🎉❤

[@kamilrichert8446]

I don't think anything beyond 40 digits of pi will be needed in the future. 40 digits gives basically precision for a circle the size of the observable universe up to a diameter of a single hydrogen atom. Anything beyond that is just fun musings (which is ok but I don't think it to be as groundbreaking)

[@mathematicalbiologist154]

Sir Presh Talwalkar, greetings from a medical student from India! Your content is so satisfying for my mathematical interests.

[@johnbrooks6243]

Hello, do you study maths as hobby?

[@mathematicalbiologist154]

@@johnbrooks6243 Yes!

[@mathematicalbiologist154]

@@johnbrooks6243 Yes!

[@mathematicalbiologist154]

@@johnbrooks6243 Yes!

[@mathematicalbiologist154]

@@johnbrooks6243 Yes!

[@akumaryoshi5341]

makes me remember fourier series discover while solving heat equation.

[@vanholloman9918]

Thank you for this amazing video. This was my fist video that I watched of yours. I really like how this really help me have a better perspective of this formula and the history behind it.

[@YouTube_username_not_found]

The headlines are so hilarious!! 😂

[@LunarcomplexMain]

Should have added in the knowledge of Pi by ancient Babylonians in 1900 - 1680 BC and in ancient Egypt 1650 BC...

[@angeluomo]

Great explanation, Presh. I was waiting for somebody to shed some light on this new formula for pi.

[@arkexplorer9328]

Awesome stuff, getting closer every day, well done guys!

[@vinko8237]

I'm impressed by the fact that the formula works for any value of lamba! Thank you for sharing this string piece of news

[@utuberaj60]

Quite a nice way you have told us the Math and the history of pi. I understood most of the stuff (being an engineer with a strong Calculus background). Trying to figure out the 'lambda' computation, hopefully in a few days. I liked the historical perspective you gave, especially the Indian connection. No highschool student in India ( I am from India) even from elite schools even know anything about the historical background of pi, because there are any Math teachers who, know this, or even care. Few even know the famed Math wizard Ramanujan- the man who knew infinity!

[@denelson83]

Clever pun there, Presh. "Madhava-cation"...

[@user-po2oi5yq7q]

This formula involves the Gamma function multiple times, but computing Gamma function is even more difficult than computing π since Γ(1/2)² = π. There is still so much to do with this formula to make it actually useful. But anyway, this formula is not just “a formula”, it’s like a formula generator.

[@robertveith6383]

You put the exponent of 2 in the wrong place. [Gamma(1/2)]^2 = pi.

[@minamagdy4126]

Well, the fact that the subscript is a non-negative integer means that, using a property of the gamma function, that part of the expression is fairly simple to transform to an iterated multiplication that doesn't need a proper evaluation of the Gamma function at all. In fact, that is the inspiration for this notation in the first place. It will specifically become k terms being multiplied, where k is the subscript. This makes the formula much more feasible to use than you made it out to be.

[@jboss1073]

"But anyway, this formula is not just “a formula”, it’s like a formula generator." Exactly, it's what I said above - this is not a formula but an algorithm. There can be no formulae for infinite processes like irrational numbers.

[@motherisape]

No need to compute gamma function since only n! Require gamma function and n is integer .

[@thialfi2289]

Thanks for the TLDW. I wan't planning on watching past learning why it was significant but you peaked my interest so I ended up sticking around after all.

[@tevaum]

Thanks for this video it saved me a lot of time. I was planning to read a bunch of articles to see if I could grasp the subject lol

[@nobodyknows3180]

"The technique has come full circle." Brilliant!

[@huzefa6421]

Should have uploaded this video on 22nd July ... (22/7 in DD/MM system ) 😅

[@zzzaphod8507]

That's apparently the date when this video goes in everyone's recommendations (for everyone in countries where the date is written that way)

[@alihms]

That sort of made-up coincidence thing suits mostly the Matt Parker's Stand-up Math crowd, not the Presh Talwaker's Mind Your Decision crowd.

[@zzzaphod8507]

@@alihms What fraction is in both crowds?

[@alihms]

@@zzzaphod8507 Beats me. But I reckon there's a huge overlap.

[@pierreabbat6157]

I've seen this elsewhere. The thing in parentheses with a subscript is called a Pochhammer symbol.

[@rjones6219]

I always found it strange, that the relation between the diameter of a circle and its circumference, has no exact value. That seems irrational to me 😉

[@zzzaphod8507]

I meditated on this issue one time and eventually found it to be transcendental

[@abhir7823]

It does have exact value

[@robertveith6383]

@ rjones6219 -- Your post is being reported, because you are posting misinformation.

[@McCarthy_Was_Right]

um.. no sweaty. did you check your facts today? this has been debunked. @@robertveith6383

[@wesleydeng71]

It is very interesting that you can plug any lambda in this formula to get the same value of pi.

[@SPYros101_]

This is so useful. I was always wandering how to calculate 4 quickly and now I have it thanks to those two incredible mathematicians. Truly incredible 👏🏽

[@prav077]

Presh seems extra excited.

[@bedabyasbehera2058]

This group is from IISc, Bangalore. Feeling proud to be an IIScan.

[@devesh.....]

are you a UG student ?

[@bedabyasbehera2058]

@@devesh..... Alumni, PhD

[@devesh.....]

@@bedabyasbehera2058 sir i am not interested in corporate world.... i offers of both iit and iisc for my bs ms course should i join iisc or iit madras , can you guide ?

[@bedabyasbehera2058]

@@devesh..... If you are interested in research, the best place in India is IISc. It has world-class facilities, an excellent research environment, and top-notch professors in their fields. After graduation, you can go for further research abroad. Even if you choose not to continue, you will get an attractive package. The only thing is that research needs a more mental space and you have to work very hard here. My best wishes.

[@jakesto]

If increasing lambda causes the formula to approach PI more quickly, how come taking the limit as lambda approaches infinity yields the Madhava series? What is the optimal value of lambda?

[@pradipkumarhansda9353]

i tried to find this new method to determine of 'pi' explained video 😊😊 thank you for uploading.

[@OhAncientOne]

Love this sort of stuff about pi. I've always thought it's interesting that between a circle's diameter and it's circumference, you can only ever know the exact length of one of those properties. You can create a circle with a 1 inch diameter and not know the exact length of the circumference or you can take a 1 inch length of string and create a circle that has a diameter that cannot be exactly calculated.

[@cypress1337]

Why do we need more than trillion digits, let alone 100 trillion..

[@Ozymandi_as]

Why do we need it to 10 digits? That's a much higher accuracy than any engineering application, at 1 part in 10 billion. Pure maths is not really concerned with purpose, although uses are constantly being found for maths that began as pure abstraction. That said, I believe the calculation is used to test new microprocessor architectures and innovative software algorithms for speed and accuracy, since there is an agreed value and any errors can be easily identified. With clock speeds at GHz levels, and multi core CPUs, and the work on P v. nP constantly improving the efficiency of raw computation you need to have some big verifiable tasks, and π fits the bill. So not needed in a deterministic sense, but it has it's uses. Also, π. People have been trying to extend the accuracy for millennia, and I guess that tradition continues. As with many things, it's not the destination but the journey.

[@Kyle-nm1kh]

​@@Ozymandi_asyeah an infinite journey into the void of nothingness

[@chharlessweeney]

@@Ozymandi_as Thanks for taking the time to make this considered reply.

[@rjsegedin7116]

The guy who has memorised pi to a trillion digits says he's bored and wants a real challenge.

[@gothmog2441]

Might be useful if we need to accurately calculate the circumference of a really big circle. Like the orbit of Pluto to the nearest cm.

[@Furkan-yv5ew]

Why is it that important to find a lot of digits of pi?

[@paperclips1306]

It isn't. It throws some light

[@hikari1690]

The techniques we discover along the way ends up being useful in other stuff too. Like the weird limits formula. It's used in neural networks quite a bit for the loss function. Also, there's a rumour that once we find out pi is rational after all our tutorial simulation will finally end amd we can start level 1

[@7yamkr]

To confuse us By the way , it is used for accurate calculations in large numbers like solar system ,or in universe

[@Dr.Kraig_Ren]

Pure maths

[@abebuckingham8198]

It's not. It's typically used as a benchmark for hardware and algorithm analysis since it's common and we have multiple ways to calculate it. So it gets used as a toy problem frequently.

[@janami-dharmam]

the formula at 3:25 is expansion of arctan(1); it converges so slowly that you will need thousands of terms to get 5 significant digits of pi. there are simple modifications that converge the series more efficiently but I have forgotten them

[@charlesmrader]

If you made a plot of the approximation versus n, now would see it oscillating between two curves. One curve is all terms which are larger that pi, getting closer and closer to the limiting value for an infinite number of terms. This curve passes through every other term of the infinite series. The other curve is all the terms which are smaller than pi, getting closer and closer to the limiting value for an infinite number of terms. That curve passes through terms missing from the first curve. That suggests always taking the average between any two successive terms of the original slowly converging formula. This is super easy to do, and it gets you many digits of accuracy in just a few dozen steps. It's far from the best formula mathematicians have found, but it's so easy to create from the Madhava formula.

[@robertveith6383]

Please write in sentences.

[@ra4san404]

the "powered by caffeine" t-shirt💀

[@donaldhoot7741]

Pi are squared? NO! Pi are round! Nyuk-nyuk!

[@meberg500]

For reals! CORNBREAD are squared!

[@vibrablox]

i cant wait to learn this at school

[@okaro6595]

7:41 On such series there the result osculates between the correct one can get a much better estimate by taking the average of the two last ones.

[@garyhundt]

Now string theory will be a prequisite for school children learning plane geometry

[@Kuldeep0404]

Indian Institute of Science (IISc) ❤

[@PluetoeInc.]

small people talk people , events , places . real people talk ideas , throw that university worship mentality away , grow a pair of balls weakling . Don't forget it's the subject , don't get too carried away in worshipping the institute . Its the people , principles , ideas .

[@Axenvyy]

Wasn't the paper from IISER pune?

[@Kuldeep0404]

​@@Axenvyy10:00 See under the "Physicists"

[@Axenvyy]

@@Kuldeep0404 yes I looked it up, Thank you!

[@Wilkins_Micawber]

Wow. Just what I need I’ll use it for my maths test next week.

[@rupamghosh2020]

Wow..... Very nice and precise

[@trucid2]

So is there an optimal value for lamba that leads to the quickest convergence for pi?

[@harshojha6231]

I am glad to share that I have studied a maths course from prof. Aninda Sinha. ❤

[@KeithAllen-pg8ep]

So we've "progressed" from C/d to this? String theory has a lot to answer for!

[@Soulful_Pizza]

Any being happen to notice the subtle nod to Terrance Howard ? 😆

[@jimdenzler389]

I discovered a new addition for pi over a year ago! By substituting one quarter of the regular floor with whole wheat flour, it still bakes fine, but it adds a new dimension to the flavor!!

[@mistec34]

Have they estimated how many terms of this new formula get us to today's accuracy? And is there like a formula representation of the fraction of computing power needed now before and after?

[@milos_radovanovic]

if Lambda -> inf is slow converging but increasing Lambda from 10 to 50 reduces error shouldn't there be lambda with maximum convergence speed?

[@donjoe7529]

at 8:32 when mathematicians compare any given method's approximation of pi with the 'actual value of pi' to determine the error, what method is used to generate the officially accepted correct series of pi's digits (this 'actual value of pi') which all approximations get compared to ?

[@aluacage1054]

so many cute mathematical expressions pop out studying scattering amplitudes, I love to see it! I don’t work on string theory but it was the paper was a nice quick read

[@dhhfkkjb6891]

Hail whoever discovered 22/7

[@kingki1953]

Sir, you didn't explain what is Lambda in the video. 😅 You just explain n is representation of all natural number, but what about lambda?

[@devjock]

Every scientific discipline is linked at some level. That is a reassuring feeling.

[@NOBODY-toxic]

Cant wait for a European to do the same in a few years and name it after the said European

[@usamaizm]

This could be beneficial for compute and games.

[@studymagic197]

Physics combined with other logical subj is just op !!! Btw which music ! End?

[@johnpiggott7426]

Math major: Pi r squared. Baker: Pie are round.

[@Kumurajiva]

holy cow, truly amazing!

[@nehalkalita]

What was the other formula used by Madhava to calculate value of Pi till 10 decimal places?

[@notyourfox]

"One last video before sleep" *proceeds to optimize pi generator for the rest of the night after the video*

[@YoungPhysicistsClub1729]

finally Madhava of Sangamagramma gets his rightful recognition for the arctan series

[@jpopelish]

So, is the choice of lambda arbitrary, a free choice? If so, what value gives the fastest convergence with this pi formula?

[@mehmeteminconkar2590]

Madhava-cation of formula😅

[@bhgtree]

Thats why maths is the the most wondrous and key to all other human knowledge, we''ll never reach the end of its mysteries.

[@Darisiabgal7573]

Think about what you are saying, Madhava is adding fudge factors, the Summation is using gamma that is arbtrarily added. 10, why 10, why not zero. Of course you are going to get you to the answer you already know the fastest. Here is a no BS way to get Pi, it’s called a Markov chain, per 13 iterations you get 8 digits. It’s not hard or involves hideous integrals. This is an no a priori. You have a ruler of length 1. You measure out 2 lengths. Next at the middle push out an orthogonal creating 2 new triangles, calculate the hypotenuse and multiple by 2 Next from radius push out new radius (=1) that bisects the new hypotenuse creating new triangle and calculate the length of its hypotenuse and multiply by 4. Where h = desired hypotenuse a g = previous hypotenuse h = SQRT((g/2)^2 + (1-SQRT(1-(g/2)^2))^2) So in the first example g is initial starting = 2 h=SQRT((2/2)^2 + (1-SQRT(1-(2/2)^2))^2) h=SQRT(1+(1-SQRT(1-1))^2) h=SQRT(2) est based on 2 chords = 2*SQRT2 h-> g h =SQRT((SQRT(2)/2)^2 + (1-SQRT(1-(SQRT(2)/2)^2)^2 h=SQRT((1/2 + (1-SQRT(1/2))^2) h=SQRT((1/2 + (0.292893218813452^2) h=SQRT(0.5857864376269047) h= 0.76536686473018 @ 4 --> 3.0614 Yada, yada, yada.

[@ioioi_prx4639]

The thumbnail looks like the two guys are being "Lmao" "Now what"

[@rustyfox81]

I thought Newtons integration of the area under a circle from 0 to 1 was a milestone in pie calculations

[@xinpingdonohoe3978]

It was, but that was still long after Madhava. Madhava set a record, and many years later Newton outdid him.

[@alien_0_0_7]

I really like Ramanujan's series for π and Ludolph van Ceulen's method of using 2⁶² sided polygon 😂 he even engraved value of π on hi tombstone

[@MikhailFederov]

There's not a single math creator on this entire site who can mention factorials without proudly explaining it. Like wow you're so clever you have to milk factorial definition for all its worth

[@hemantishwaran5741]

If it’s based on n! that value gets exponentially large which may cause numerical issues when calculating. Don’t see how this can beat the world record. Definitely cool though

[@QuentinStephens]

I wonder what Sabine Hossenfelder is making of this!

[@ivocanevo]

Some type of cynicism, probably

[@chem7553]

That's super cool!😊

[@JanBruunAndersen]

Which value of Pi is good enough for governmental work?

[@2_Elliot]

I believe that your error calculation for the spreadsheet section is off by a order of magnitude.

[@roberthuntley1090]

Fun fact - 355 divided by 113 is Pi to six decimal places (shortcut dates back to the early days of calculators, before scientific calculators became affordable to up plebs).

[@Dominic018]

Terrance Howard punching the air rn

[@ErAdventure]

Another half year of college for this one

[@user-fp9kz6xv6l]

Cool video 👍👍

[@sgdg7777]

this is what happened when physicists had too much alcohol

[@Nanobits]

I love when science comes from accidental discovery.

[@RussellFlowers]

What method is used to calculate "standard pi"? We see methods that say, "it will give you the correct digits of pi up to the 10th." What is the calculation of pi that tells us how we know that?

[@bober1019]

on social media, everything is 'accidentally' found. monetization to the max!

[@divyeshbhattacharya3875]

The harmony between physics and mathematics is truly amazing.I always thought that math helps physics move forward; today I saw, for the first time, physics help maths! I wonder how many times this has happened, and will happen...

[@Amit_Pirate]

Liked for giving real credit to my goat Madhava

[@mitaskeledzija6269]

I think I might discover a new way to represent logarithms

[@the_master_of_cramp]

so which lambda is the best ? if we set lambda to infinity, we have the Madhava series, so higher lambda is not better, but does that mean lambda = 0 is best or are there multiple local optima for lambda, or does it depend on how many digits of accuracy you want ?

[@donwald3436]

Why are you Presh Talwalker tho?

[@Qermaq]

Who else would he be? He can't be donwald3436, you're already doing that.