I think Ramanujan's formula is the real OG. It converges to 8 decimal places at first iteration n=1. By studying Ramanujan's formula, mathematicians discovered another cousin of Ramanujan's formula which converges even faster. Ramanujan truly opened the door.
❤🎉🎉🎉😊😊😊🎉🎉🎉🎉🎉 Truly truly i say to you all Jesus is the only one who can save you from eternal death. If you just put all your trust in Him, you will find eternal life. But, you may be ashamed by the World as He was. But don't worry, because the Kingdom of Heaven is at hand, and it's up to you to choose this world or That / Heaven or Hell. I say these things for it is written: "Go therefore and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit, *teaching them* to observe all that I have commanded you; and behold, I am with you always, even to the end of seasonal". Amen." -Jesus -Matthew 28:19-20
@@gamer__dud10that's honestly insensitive and disrespectful to people of other religions. Feels like you are forcefully shoving your beliefs down other people's throats. Please apologise to everyone you have offended like this and try your best to be a decent human being
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)
@@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.
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.
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.
@@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.
@@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)
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?
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.
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.
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!!!
YES! BBP type formulas are still the best for all pruposes of computing digits of pi, they are in a sense even better then this new one & Ramanujan's (as unlikely as it sounds).
@@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 ?
@@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.
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 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).
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.
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
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.
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!
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.
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.
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
That's because those achievements were basically rediscovered, so both India and Western nations can claim discovery. India juat did it earlier.@@YoungPhysicistsClub1729
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.
22/7 includes first 3 or 4 digits of pi up to decimal places that's why we conclude it but it is not pi because pi is irrational 22/7 is rational so can't say that 22/7 is pi
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)
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.
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 .
it seems logical to me that n! produces an upper bound for the number of possible combinations of factors of n. Since we are trying to organize them sequentially, we can essentially estimate how many non repeaters and only concern ourselves with the fraction
It is not so bad as you think: (x)n = x(x+1)...(x+n-1). But this negates the fast convergence of 1/n!, so this series is not suitable for calculating pi to very high precision.
If they wanted to compute pi faster, and then the gamma function isn't too fast when used for pi, what difference does it make regarding the computation time? And how does lambda increase the accuracy for pi when set to different values?
While gamma function can be used to calculate pi, it wasn't discovered for that purpose hence not the best way for calculation of pi, but what it was discovered for was to smoothen the graph of y=x! So that it can be used in their physics paper on whatever they were working on and also for other such research purposes.
But just see how Madhava originally invented the way in India our homeland and how it's get lost and somehow transferd to lebnitz That's not a goodthing that Britishers did....
@harshitgiri8199 tldr; Mathematical concepts have been developed and rediscovered across different cultures and times, with many individuals credited for similar work. Arguing over the origins of these ideas is less important than acknowledging that we all benefit from them as a shared human achievement. Many significant contributions from Indian scholars have been rebranded or forgotten, like Sridhar Acharya's formula becoming the Quadratic Formula and Madhava's accurate estimation of pi. Early trigonometric concepts and the binary system also originated in India, among other contributions. The Western world has a history of adopting knowledge from other cultures and integrating it into their own historical narratives, often leading to misconceptions about the origins of these discoveries. This pattern isn't unique to India; mathematicians from China, Egypt, the Arab world, and elsewhere have also seen their work absorbed into Western history. However, it's important to recognize that some legitimate discoveries did originate or were independently developed in the West. In the end we need to acknowledge that the history of mathematics is a collective human endeavor, encompassing contributions from all cultures.
@@_Loki__Odinson_ I honestly don't see how this formula is that novel though. All they did was plug in a number to a formula involving gamma. If they invented this formula that would be great, but if not then it isn't worth publishing.
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?
It seems to me the formula converges at about the same speed for all values of lambda, since (x)_n = x(x+1)...(x+n-1). That is, the 1/n! is essentially cancelled out.
@@sparshsharma5270 Actually, n! Is defined as the number of permutations on n distinct objects. How many ways can you permute 0 objects? There is only one way.
@@TepsiMorphic No, that is not the formal definition of factorial. I am not denying that 0!=1 but saying that it is justified because of other reasons and not as per the standard definition of the rule. It is justified by conventions of recursive, combinatorics and empty product; gamma function simply justifies it.
fs what does he mean by saying its an exception???????????...ITS PROVED BY GAMMAAA (im just messing...i just graduated hs with considerable advanced math in my courses...gamma function and beta functions were taught)
I request you to prepare a video how Bhaskar II, conceived instaneous speed with Sine difference which encouraged Madhaba of Kerala school to find out Sin , Cos and tan series. It is interesting to note that Bhaskar 1 in early seventh century theorized formula for Sine value for any angle.
For most of the math I use, I just use 22/7 for pi. More precise calculations is not necessary for day to day math. However, I can see such concise accuracy would be required for string theory; as it is, in theory, it is dealing with the smallest possible particles that make up existence.
"Thank you so much for mentioning our Indian mathematicians and scientists who have contributed significantly to various theories. Their work often goes unappreciated, and it's heartening to see them get the recognition they deserve. Your video is a wonderful tribute to their legacy!"
4:43 "So n factorial will be the factorial of the whole numbers less than that number." (That will be just some approximation, it gets more precise when the number itself is included, but that would require more calculation. )
f(λ,N) should be the next logical step. Analytical solution for an optimal λ for every N...and eventually what is the 'global' optima for λ and N to get the best value for π
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
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.
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
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.
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.
If I have to map out the strategy for how to derive "π" or its rational fraction (÷ by 3 or 4), it is do-able, now. The clue is to expand "Cos" or "Tan" in exponential series, via the Euler equation for e^(iθ). A very smart entrant to a graduate course can do it. Trick is to put argument, θ = Arc Cos (π/3) or Arc Tan (π/4) and drag "π" on the LHS (left hand side). I prefer Cos (π/3), as it equals ½ though division by 3 can be tricky for a computer geared to decimal system [best to adapt "dozenal" or "duo-decimal" system instead of radix 10]. One can use it in a Computer algorithm (best to "freeze" it on an embedded data chip, with the number of places of accuracy, "optional"). It is easy now for us. Iterative procedures are much better if done on "digital signal processor" ("dsp" chips are available) which is a take-off from Analog Computers of yore(1960s). But imagine, Aryabhatta or Madhava to "conceive" of a Sine or Arc sine function numerically, meticulously. That is the greatness of Indian Mathematics that the world needs to acknowledge. "Circle"has been a challenge for the last ten thousand years, for intellectuals.
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...
@@art0007i I mean we can mathematically prove the formulas of pi, however, if you mean how do we know how many of the digits calculated are correct then we use formulas specifically meant to calculate the nth digit of pi (which can be proven to always work) and we use that on the last several thousand digits calculated to show how many of those digits are correct.
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 ?
I taught my niece how to create the Pi formula. Made 3 circles, measured perimeter, divided by diameter and we came up with 3 results. Add them up, divide by 3 and we came up with 3.14 With 10 circles, you can probably get the Pi up to 10 numbers after .
Not even close. The accuracy of your measurements is basically random past three digits, you will never get better approximations no matter how many times you average. Basically you get random results after 3 or 4 digits and averaging out random numbers gives a random number.
@@NotYourBusiness-bp2qn wouldn't their errors in measurement be approximately the same above and below the true number? So averaging those errors out would converge on the true number
@@garglebargle69 You cannot create detail by repeated measurements. If we could we would use it to see to quasi infinite distances by averaging multiple telescope images.
How do we test that the ever increasing precision of pi is correct? I would think that we would (perhaps quickly) reach a point of how many angels dance upon the head of a pin. Does the goal become being able to push through the compution or does it real something in the world? Better engineering?
Pi has the potential to unlock nearly unlimited data storage. Rather, the ability to quickly calculate and locate strings of matching digits within pi, as expressed in binary, is where the potential is. Pi, like any other number, can be expressed in binary. Those digits don't repeat. Because they are infinite, the theory is that one could find a matching string for the text of the complete works of Shakespeare, given enough searching. So imagine saving those works in a file that roughly translates like this: _Pi using the Martinez algorithm, v7.02.01, starting at digit 2365433632 and continuing for 29567920 digits.
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.
Yeah, that was nonsensical even for newspaper standards. An approximation formula doesn't change any axiom nor any theorem (unless an axiom/theorem claims the absence of such an approximation but there is no such thing). So this formula has zero chance to change maths in any significant form.
Your oldest historic assertions about discovery of PI value are incomplete and there for inaccurate. The concept of Pi (\(\pi\)) has been referenced in ancient Indian texts, particularly in relation to geometry and calculations involving circles. One of the earliest references comes from the **Shulba Sutras** (800-500 BCE), which are ancient Indian texts on geometry. The Shulba Sutras are part of the broader corpus of the Vedic scriptures and are primarily concerned with the construction of altars for religious rituals. In the Shulba Sutras, there are approximations of the value of Pi used in the context of calculating the circumference and area of a circle. For example, in the work attributed to the sage Baudhayana, Pi is approximated as \( \frac{25}{8} = 3.125 \). While this is not the precise value we know today (\(\pi \approx 3.14159\)), it reflects an early attempt to understand the relationship between a circle's circumference and diameter. Another notable reference comes from the mathematician and astronomer **Aryabhata** (476-550 CE). In his work **Aryabhatiya**, Aryabhata provides an approximation of Pi as \( \frac{62832}{20000} = 3.1416 \), which is remarkably close to the modern value. These references indicate that the concept of Pi was understood and used in ancient India, particularly in the context of religious and mathematical practices.
When europeans discover the (already discovered) things,they tell the whole world that they have discovered those things.But when Indians discover something,Europeans tell the whole world that indians have discovered this accidentally. You people don't have any right to call the discovery accidental.
Presh, is your formula at 1:05 correct? You have a "4+" term before the Sum, which is not present in the Formula shown on Indian Physicist's Blackboard at 0:05.
Well spotted, but the initial 4 probably corresponds to n=0. On the blackboard, the summations starts from n=0, in the formula later in the video the summation starts from n=1. (I did not check whether the n=0 term is indeed 4.)
@@ronald3836 well spotted on the differing n starting points, that probably explains it. For n=0 the first parenthesis yields ~ -4 depending on Lambada. But I don't see how the second parenthesis gives -1 to give the resulting +4.
@@russhellmy for n=0 the part with the subscript is a bit awkward, which is probably why in the video the n=0 part is separated out. I have no time now, but I'll try to check it tomorrow.
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.
In the history of calculating pi, you failed to mention Newton's role. Not only did he use area for the calculation, he came up with a scheme to make the infinite series converge "faster" by integrating only a portion of a circle because he removed a triangle. (That triangle required calculating the square root of 3, which Newton also optimized). The infinite series has only even terms not alternating in signs. This is explained in this video: th-cam.com/video/gMlf1ELvRzc/w-d-xo.html
Credit goes to those physicist and not to the country {Indi/Bharat}. Country couldn't manage to conduct a single exam without leak and problems. Great job those guys did solving another problem but stumble to something great. Great for inspiration ❤❤❤
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!!
Can’t believe we got a new formula for pi before gta6
Everybody else: we can!
Nice one
and hytale
after GTA 6 releases be like...
cant believe we got GTA 6 before this
@@robuu5890 cant belive we are gunna get gta6 before hytale
I think Ramanujan's formula is the real OG. It converges to 8 decimal places at first iteration n=1. By studying Ramanujan's formula, mathematicians discovered another cousin of Ramanujan's formula which converges even faster. Ramanujan truly opened the door.
gg's on it.
❤🎉🎉🎉😊😊😊🎉🎉🎉🎉🎉
Truly truly i say to you all Jesus is the only one who can save you from eternal death. If you just put all your trust in Him, you will find eternal life. But, you may be ashamed by the World as He was. But don't worry, because the Kingdom of Heaven is at hand, and it's up to you to choose this world or That / Heaven or Hell.
I say these things for it is written:
"Go therefore and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit, *teaching them* to observe all that I have commanded you; and behold, I am with you always, even to the end of seasonal". Amen."
-Jesus
-Matthew 28:19-20
@@gamer__dud10i 'd like to choose hell.
@@gamer__dud10that's honestly insensitive and disrespectful to people of other religions. Feels like you are forcefully shoving your beliefs down other people's throats. Please apologise to everyone you have offended like this and try your best to be a decent human being
@@gamer__dud10Sir, this is a Wendy's...
Meanwhile, engineers have discovered a new way to calculate 4.
It's like 3, but more...
They haven't published yet, because they are still ..... checking their calculations! 🤣😂🤣😂
But five is right out.
Meanwhile, Terrence Howard has discovered a new way to calculate 2.
you mean 5?
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
it's not actually news, it happens all the time, especially in theoretical physics.
its not even close to pure math
String theorists are closer to mathematicians than physicists anyway
@@BOTNPC Seriously, elegant math is the only reason to waste time on string theory anyway.
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)
Science/Math Headline Writers Understand What The Heck You’re Writing About Challenge
Impossible
bhai aise likhoge toh humlog rude lagenge (translation: brother if you write like this, we'll look rude)
@@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.
@@RavenMobile It's just some BJP IT Cell Troll, let it be. The less attention they get, the better.
@@rajeshgajwelly9035 bro delete it, learn to stay humble.
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.
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.
That’s what I was wondering. I’m confused why someone would go to this for pi if they have the gamma function.
He used gamma in the spreadsheet. But if you look closely, you can use integer parameters and switch to factorials.
@@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.
@@Mathguy1729 actually it's a falling factorial. You don't need gamma to calculate it at all
Does this mean I don’t have to go to work tomorrow?
Yes, work is now optional.
Don't worry very soon ai will replace u in job, then u would be happily unemployment 💪
@user-ty1vy3yx1j Ai told me to eat 1 small rock a day.. not sure were there yet.
It does if you're Canadian.
😂😂
even Maths is still getting updates. What say you, Gabe Newell?
1,2,....4,5
@@jaypolas4136 bleem
At least you haven't been waiting for 500 years like chess players...
Unlike chess you onky had to endure bots for a few years
@@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)
Still trying to identiπ this new formula.
Haha
This happens all the time. It is an oft repeated claim.
Identiф*
@@Vsevolodbochkovexactly
use the sign of work function.
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?
Exactly! Waiting for somebody to answer this. Should see which lambda values they reference in the paper and why...
I wanna know too
I imagine it just blows up at infinity. You're approaching ∞, not at infinity.
also wondering
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.
Damnmit, I thought they came up with a new flavor of pie.
Oh well, back to rhubarb.
Yah, I had my fork ready too, I was ready to dig in!
Haha
😂
Oh, we're now entering the field of Bistromathics
quantum pie tastes the bestest.
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.
Bro it's ramanujan
Bro has a thing for infinite series
Ramanujan was him
"It was revealed to me in a dream"- Srinivasa Ramanujan
yes , he is diff , he is unconventional .
Waaaah... Something useful has come out of String theory... I'm overwhelmed.
I had a similar reaction
Its not useful though, way better algorithms exist.
Lots of mathematically useful things have come out of string theory.
@@LagMasterSam it's true. But I still find the joke funny
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!!!
My favorite is the Bailey-Borwein-Plouffe formula, which allows to compute the value of the n-th digit INDEPENDENTLY of the previous one.
sadly, hex
@@notyourfox or base 256, or ...
Unfortunately it's not computationally more efficient than calculating all the previous digits though.
YES! BBP type formulas are still the best for all pruposes of computing digits of pi, they are in a sense even better then this new one & Ramanujan's (as unlikely as it sounds).
This group is from IISc, Bangalore. Feeling proud to be an IIScan.
are you a UG student ?
@@devesh..... Alumni, PhD
@@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 ?
@@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.
@@bedabyasbehera2058 thanks...
Indian mathematican Srinivasa Ajangar Ramanudžan has the most acuracy formula for Pi on 3 trillions places with very fast calulation
3 trillions 😭
Ramanujan - 104 trillion decimals
@@kokaix9 ramanujan - 104 undecillion decimals
Well to be honest he's formula is the inly best
Sir Presh Talwalkar, greetings from a medical student from India!
Your content is so satisfying for my mathematical interests.
Hello, do you study maths as hobby?
@@johnbrooks6243 Yes!
@@johnbrooks6243 Yes!
@@johnbrooks6243 Yes!
@@johnbrooks6243 Yes!
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
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.
@@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).
@@ronald3836 I don't think you know what "exactly" means
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.
@ethanbottomley-mason8447 you can read their comment. They were talking about decimal precision.
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
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.
Please write in sentences.
No surprise indians found new ways to write pi😂😂😂...i think it was actually given by them some named aryabata
You're Heisenberg
How uncertain of u Heisenberg
@@Giveup00 PERFECT LMFAO
Wya heisenberg, ik you can't run for me :>>
I'm impressed by the fact that the formula works for any value of lamba!
Thank you for sharing this string piece of news
"The technique has come full circle." Brilliant!
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!
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.
You put the exponent of 2 in the wrong place. [Gamma(1/2)]^2 = pi.
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.
No need to compute gamma function since only n! Require gamma function and n is integer .
@@minamagdy4126 You're right. It is unfortunate that the video shows the Gamma(a+b)/Gamma(a) formula (and apparently uses Excel's Gamma function).
Great explanation, Presh. I was waiting for somebody to shed some light on this new formula for pi.
Always knew Madhavas theorem as lebinitz
well, most indian math achievements are known by western names, what can you do
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
That's because those achievements were basically rediscovered, so both India and Western nations can claim discovery. India juat did it earlier.@@YoungPhysicistsClub1729
@@YoungPhysicistsClub1729 "Lebinitz" is a Western name?
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.
Meanwhile, Terrance Howard is shaking all of the math community up by bringing "1+1=2" to the forefront.
Hail whoever discovered 22/7
Al-Khwarazmiy
*if I am not mistaken
22/7 includes first 3 or 4 digits of pi up to decimal places that's why we conclude it but it is not pi because pi is irrational 22/7 is rational so can't say that 22/7 is pi
@@Tyson23576 ok genius but it's easy for calculation
Yeh respect but honestly it ends at high school
The headlines are so hilarious!! 😂
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)
Just like every aspect of String Theory, there's always a more difficult and ridiculously complex way to express basic ideas. Great job!
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.
Indian Institute of Science (IISc) ❤
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 .
Wasn't the paper from IISER pune?
@@Axenvyy10:00 See under the "Physicists"
@@Kuldeep0404 yes I looked it up, Thank you!
makes me remember fourier series discover while solving heat equation.
it seems logical to me that n! produces an upper bound for the number of possible combinations of factors of n. Since we are trying to organize them sequentially, we can essentially estimate how many non repeaters and only concern ourselves with the fraction
"One last video before sleep"
*proceeds to optimize pi generator for the rest of the night after the video*
That n-1 subscript is a gamma function. So good luck solving that
It is not so bad as you think: (x)n = x(x+1)...(x+n-1). But this negates the fast convergence of 1/n!, so this series is not suitable for calculating pi to very high precision.
Haha
Clever pun there, Presh. "Madhava-cation"...
It's good to see Indian mathematicians are being recognized 🙌🙌
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 😉
I meditated on this issue one time and eventually found it to be transcendental
It does have exact value
@ rjones6219 -- Your post is being reported, because you are posting misinformation.
um.. no sweaty. did you check your facts today? this has been debunked.
@@robertveith6383
The ratio is exactly pi. The value of pi is just as exact as the value of the number 123.
Important to note that the desmos graph shows the Pi function, which is the Gamma function with an offset of 1 to make it connect with the factorial
If they wanted to compute pi faster, and then the gamma function isn't too fast when used for pi, what difference does it make regarding the computation time? And how does lambda increase the accuracy for pi when set to different values?
While gamma function can be used to calculate pi, it wasn't discovered for that purpose hence not the best way for calculation of pi, but what it was discovered for was to smoothen the graph of y=x! So that it can be used in their physics paper on whatever they were working on and also for other such research purposes.
But just see how Madhava originally invented the way in India our homeland and how it's get lost and somehow transferd to lebnitz
That's not a goodthing that Britishers did....
@harshitgiri8199 tldr; Mathematical concepts have been developed and rediscovered across different cultures and times, with many individuals credited for similar work. Arguing over the origins of these ideas is less important than acknowledging that we all benefit from them as a shared human achievement.
Many significant contributions from Indian scholars have been rebranded or forgotten, like Sridhar Acharya's formula becoming the Quadratic Formula and Madhava's accurate estimation of pi. Early trigonometric concepts and the binary system also originated in India, among other contributions. The Western world has a history of adopting knowledge from other cultures and integrating it into their own historical narratives, often leading to misconceptions about the origins of these discoveries.
This pattern isn't unique to India; mathematicians from China, Egypt, the Arab world, and elsewhere have also seen their work absorbed into Western history.
However, it's important to recognize that some legitimate discoveries did originate or were independently developed in the West. In the end we need to acknowledge that the history of mathematics is a collective human endeavor, encompassing contributions from all cultures.
@@harshitgiri8199 But Leibnitz was German... why was it the fault of the British?
@@_Loki__Odinson_ I honestly don't see how this formula is that novel though. All they did was plug in a number to a formula involving gamma. If they invented this formula that would be great, but if not then it isn't worth publishing.
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?
It seems to me the formula converges at about the same speed for all values of lambda, since (x)_n = x(x+1)...(x+n-1). That is, the 1/n! is essentially cancelled out.
"The *exception* that 0! = 1"
Oh boy, you are about to be chewed out for calling that an exception
Nah, that's an exception.
Cause n!=product of all numbers from 1 to n.
@@sparshsharma5270 The empty product is used to be defined as 1.
@@sparshsharma5270 Actually, n! Is defined as the number of permutations on n distinct objects. How many ways can you permute 0 objects? There is only one way.
@@TepsiMorphic
No, that is not the formal definition of factorial.
I am not denying that 0!=1 but saying that it is justified because of other reasons and not as per the standard definition of the rule.
It is justified by conventions of recursive, combinatorics and empty product; gamma function simply justifies it.
fs what does he mean by saying its an exception???????????...ITS PROVED BY GAMMAAA (im just messing...i just graduated hs with considerable advanced math in my courses...gamma function and beta functions were taught)
I request you to prepare a video how Bhaskar II, conceived instaneous speed with Sine difference which encouraged Madhaba of Kerala school to find out Sin , Cos and tan series. It is interesting to note that Bhaskar 1 in early seventh century theorized formula for Sine value for any angle.
For most of the math I use, I just use 22/7 for pi. More precise calculations is not necessary for day to day math. However, I can see such concise accuracy would be required for string theory; as it is, in theory, it is dealing with the smallest possible particles that make up existence.
Meh. You can have more fun with 355/113.
@@saveddijon true, it is just a question of your requirement of accuracy and preference if you want to remember 3 debits or 6.
"Thank you so much for mentioning our Indian mathematicians and scientists who have contributed significantly to various theories. Their work often goes unappreciated, and it's heartening to see them get the recognition they deserve. Your video is a wonderful tribute to their legacy!"
coincidentally chefs discover a new formula for Pie at the same time... ;)
Great work Arnab and Aninda🎉🎉
4:43 "So n factorial will be the factorial of the whole numbers less than that number."
(That will be just some approximation, it gets more precise when the number itself is included, but that would require more calculation. )
I wonder what Sabine Hossenfelder is making of this!
Some type of cynicism, probably
1900 :We will have flying cars by 2000
2024:Scientists discovered a new formula for Pi
0:58 I don't want to waste your time, so let me repeat the headline for the 4th time.
f(λ,N) should be the next logical step. Analytical solution for an optimal λ for every N...and eventually what is the 'global' optima for λ and N to get the best value for π
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
Amazing how much free time he had to work since there was no internet or teevee
@@billcook4768 That applied to everyone back then, but there was still only one Archimedes.
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.
@@KerrySoileauimagine how ahead we would be if that monk didn’t write over Archimedes paper
Well you would be suprised to know about the BCE Indian mathematicians!
"There are no accidents."
- Master oogway
I've seen this elsewhere. The thing in parentheses with a subscript is called a Pochhammer symbol.
Why is it that important to find a lot of digits of pi?
It isn't. It throws some light
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
To confuse us
By the way , it is used for accurate calculations in large numbers like solar system ,or in universe
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.
@@abebuckingham8198 Toy problem? You mean a benchmark problem.
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?
It’s a function.
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.
Why are you Presh Talwalker tho?
Who else would he be? He can't be donwald3436, you're already doing that.
If I have to map out the strategy for how to derive "π" or its rational fraction (÷ by 3 or 4), it is do-able, now. The clue is to expand "Cos" or "Tan" in exponential series, via the Euler equation for e^(iθ). A very smart entrant to a graduate course can do it. Trick is to put argument, θ = Arc Cos (π/3) or Arc Tan (π/4) and drag "π" on the LHS (left hand side). I prefer Cos (π/3), as it equals ½ though division by 3 can be tricky for a computer geared to decimal system [best to adapt "dozenal" or "duo-decimal" system instead of radix 10].
One can use it in a Computer algorithm (best to "freeze" it on an embedded data chip, with the number of places of accuracy, "optional").
It is easy now for us. Iterative procedures are much better if done on "digital signal processor" ("dsp" chips are available) which is a take-off from Analog Computers of yore(1960s). But imagine, Aryabhatta or Madhava to "conceive" of a Sine or Arc sine function numerically, meticulously. That is the greatness of Indian Mathematics that the world needs to acknowledge.
"Circle"has been a challenge for the last ten thousand years, for intellectuals.
Should have uploaded this video on 22nd July ... (22/7 in DD/MM system ) 😅
That's apparently the date when this video goes in everyone's recommendations (for everyone in countries where the date is written that way)
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.
@@alihms What fraction is in both crowds?
@@zzzaphod8507 Beats me. But I reckon there's a huge overlap.
Hey! The authors of this article actually shouted you out on a numberphile interview!!
i find fuckin scary that ive been watching presh for so long that the videos are begining to make sense to me.
*Stop* with your major cursing! It is ignorant and needless.
This is impressive how good your explanation is for a 10 min video ! Thanks
I have no idea about these chinese names, but you butchered "Leibnitz" totally😂🎉❤
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...
I am glad to share that I have studied a maths course from prof. Aninda Sinha. ❤
the "powered by caffeine" t-shirt💀
Frr I just noticed lol
Just ramanujan things ..
8:35 just wondering, how do we determine if the "actual" value of pi is actually "actual"?
yeah thats my question too 😅
We know the first 105 trillion digits of pi from other formulas.
@@DendrocnideMoroides how do we know the "other formulas" are actual too
@@art0007i I mean we can mathematically prove the formulas of pi, however, if you mean how do we know how many of the digits calculated are correct then we use formulas specifically meant to calculate the nth digit of pi (which can be proven to always work) and we use that on the last several thousand digits calculated to show how many of those digits are correct.
I thought Newtons integration of the area under a circle from 0 to 1 was a milestone in pie calculations
It was, but that was still long after Madhava. Madhava set a record, and many years later Newton outdid him.
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 ?
i cant wait to learn this at school
Now string theory will be a prequisite for school children learning plane geometry
Madhava-cation of formula😅
I discovered a whole new way of looking at a mathematical system but don't know how to publish it 😂😂😂😂
I taught my niece how to create the Pi formula.
Made 3 circles, measured perimeter, divided by diameter and we came up with 3 results. Add them up, divide by 3 and we came up with 3.14
With 10 circles, you can probably get the Pi up to 10 numbers after .
Not even close. The accuracy of your measurements is basically random past three digits, you will never get better approximations no matter how many times you average. Basically you get random results after 3 or 4 digits and averaging out random numbers gives a random number.
@@NotYourBusiness-bp2qn wouldn't their errors in measurement be approximately the same above and below the true number? So averaging those errors out would converge on the true number
The error is likely to be proportional to √n where n is the number of trials.
You are basically using Monte Carlo sampling.
@@tolkienfan1972 1/√n, I would think
@@garglebargle69 You cannot create detail by repeated measurements. If we could we would use it to see to quasi infinite distances by averaging multiple telescope images.
How do we test that the ever increasing precision of pi is correct? I would think that we would (perhaps quickly) reach a point of how many angels dance upon the head of a pin. Does the goal become being able to push through the compution or does it real something in the world? Better engineering?
Pi has the potential to unlock nearly unlimited data storage. Rather, the ability to quickly calculate and locate strings of matching digits within pi, as expressed in binary, is where the potential is.
Pi, like any other number, can be expressed in binary. Those digits don't repeat. Because they are infinite, the theory is that one could find a matching string for the text of the complete works of Shakespeare, given enough searching. So imagine saving those works in a file that roughly translates like this: _Pi using the Martinez algorithm, v7.02.01, starting at digit 2365433632 and continuing for 29567920 digits.
Should have added in the knowledge of Pi by ancient Babylonians in 1900 - 1680 BC and in ancient Egypt 1650 BC...
if Lambda -> inf is slow converging but increasing Lambda from 10 to 50 reduces error shouldn't there be lambda with maximum convergence speed?
Cant wait for a European to do the same in a few years and name it after the said European
People say 22/7 is legendary but in reality physics is very fond of π as it is infinitely more accurate
Why do we need more than trillion digits, let alone 100 trillion..
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.
@@Ozymandi_asyeah an infinite journey into the void of nothingness
@@Ozymandi_as Thanks for taking the time to make this considered reply.
The guy who has memorised pi to a trillion digits says he's bored and wants a real challenge.
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.
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.
"could change maths forever" the whole point of maths is that it does not change, which is why we still learn stuff Pythagoras thought about
101 of math is, some simple things just stay.
Yeah, that was nonsensical even for newspaper standards. An approximation formula doesn't change any axiom nor any theorem (unless an axiom/theorem claims the absence of such an approximation but there is no such thing). So this formula has zero chance to change maths in any significant form.
Your oldest historic assertions about discovery of PI value are incomplete and there for inaccurate.
The concept of Pi (\(\pi\)) has been referenced in ancient Indian texts, particularly in relation to geometry and calculations involving circles. One of the earliest references comes from the **Shulba Sutras** (800-500 BCE), which are ancient Indian texts on geometry. The Shulba Sutras are part of the broader corpus of the Vedic scriptures and are primarily concerned with the construction of altars for religious rituals.
In the Shulba Sutras, there are approximations of the value of Pi used in the context of calculating the circumference and area of a circle. For example, in the work attributed to the sage Baudhayana, Pi is approximated as \( \frac{25}{8} = 3.125 \). While this is not the precise value we know today (\(\pi \approx 3.14159\)), it reflects an early attempt to understand the relationship between a circle's circumference and diameter.
Another notable reference comes from the mathematician and astronomer **Aryabhata** (476-550 CE). In his work **Aryabhatiya**, Aryabhata provides an approximation of Pi as \( \frac{62832}{20000} = 3.1416 \), which is remarkably close to the modern value.
These references indicate that the concept of Pi was understood and used in ancient India, particularly in the context of religious and mathematical practices.
When europeans discover the (already discovered) things,they tell the whole world that they have discovered those things.But when Indians discover something,Europeans tell the whole world that indians have discovered this accidentally.
You people don't have any right to call the discovery accidental.
accidental discoveries are cooler
It is very interesting that you can plug any lambda in this formula to get the same value of pi.
Al Kashi ~1400 got pi to 16 decimal places.
Presh, is your formula at 1:05 correct?
You have a "4+" term before the Sum, which is not present in the Formula shown on Indian Physicist's Blackboard at 0:05.
Well spotted, but the initial 4 probably corresponds to n=0. On the blackboard, the summations starts from n=0, in the formula later in the video the summation starts from n=1. (I did not check whether the n=0 term is indeed 4.)
@@ronald3836 well spotted on the differing n starting points, that probably explains it.
For n=0 the first parenthesis yields ~ -4 depending on Lambada. But I don't see how the second parenthesis gives -1 to give the resulting +4.
@@russhellmy for n=0 the part with the subscript is a bit awkward, which is probably why in the video the n=0 part is separated out. I have no time now, but I'll try to check it tomorrow.
Three, take it or leave it.
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.
In the history of calculating pi, you failed to mention Newton's role. Not only did he use area for the calculation, he came up with a scheme to make the infinite series converge "faster" by integrating only a portion of a circle because he removed a triangle. (That triangle required calculating the square root of 3, which Newton also optimized). The infinite series has only even terms not alternating in signs. This is explained in this video: th-cam.com/video/gMlf1ELvRzc/w-d-xo.html
Newton is the most overrated mathematician of all time. He deserves nothing.
finally Madhava of Sangamagramma gets his rightful recognition for the arctan series
Credit goes to those physicist and not to the country {Indi/Bharat}.
Country couldn't manage to conduct a single exam without leak and problems.
Great job those guys did solving another problem but stumble to something great. Great for inspiration ❤❤❤
Superpower 2050
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!!
The formula is pretty easy, actually: boat + tiger
They could discover new formulas, but I haven't found a new t-shirt shop yet.
We engineers use pi= 4 for a reason 🐸
It's not closer to 3?
Truly a e=2, pi=2e moment
@@JaneAustenAteMyCat They need the security factor to be around 50 (in a regular building) so...
I don’t know any engineers that use pi=4
As an actual engineer: no, we definitely do not.