A Brief History of Pi

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Note that there's a huge amount about pi that I didn't cover in this video due to time - I didn't even mention proofs of it being irrational and transcendental, or why we call it pi! I chose to focus on the development of its approximation as a hook to teach the broader history of mathematics, rather than make this video an exhaustive list of facts. The wiki is a great place to learn more about the rest of the number's history and applications in maths and physics: en.wikipedia.org/wiki/Pi#History
A few nitpicky things:
- I made mistakes distinguishing between 'digits of pi calculated' and 'decimal points of pi calculated' in some sections, so it is possible that this error is elsewhere without me knowing.
- Archimedes didn't do his approximation with squares, he started with hexagons and then increased the order of the polygon. I chose to present the zeroth order version of his algorithm using squares for simplicity, but note that this is not what he did.
- Something which got lost from the final version of this video is my argument that during the Age of Enlightenment pi shifted from being a physical (measured) constant to a purely logical (theoretical) one. This then embodies the philosophical shift in society at the time. This is hinted at but not fully explained, so I thought I'd put this here.
- Lastly, I am truly sorry for the pronunciations which I doubtlessly completely murdered in this video. At least I spared you my attempt at Chinese.
I am hugely indebted to Alex Bellos and his excellent book Alex's Adventures in Numberland for the inspiration to make this video. There is an entire chapter of the book devoted to a broader but shallower discussion of pi and its history, which I highly recommend.
You can support the channel by donating at / simonoxfphys
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Huge thanks to my supporters on Patreon: Dan Hanvey, David Efird, Elliot Conway, Robert Eldon, Syafiq Kay, Xavier Chesterfield, Jay Wright, Myles Kornfeld, Louis Gillet, Michael Phillips, Neudys Almonte, Fraser Birks, Martin Hermes, Anh Duong, Luca Schumann, Rhys Rickard-Frost, Cameron Matchett, Lachlan Woods, Tim Boxall, Simon Vaes, Gabriele Mozzicato, Jawad Alalasi, Gaia Frazao Nery, Kodzo, Josh Ruby, Claire Anthony, Eve Dillon, Rowan Gow, Matthias Loos, James Bridges, James Craig, Angela, Sanaa Al Derei, Mark Anthony Magro, Liam, Theresa Wang, Kieran Kelly, Wendover Productions, Kendra Johnson, Caitlin Louise.
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[@ajinkya4711]

An interesting fact about Indian Mathematics. Like all other fields, Mathematics in India was documented in the form of Sanskrit poetry ( Easier to learn and remember ). So theorems and formulas including the Madhava infinite series were written as 4 - 8 line 'poems'

[@athulsureshn2866]

is madhava of sangamagrama , a malayali?

[@ananthuraj9973]

@@athulsureshn2866 Yes Irinjalakkudakkaran aanu

[@entitythatyounevermet]

@@athulsureshn2866 No, he was an Indian mathematician.

[@saywhat5034]

Aditya Pant you do know that a malayali is a person from Kerala which is in India.. right?

[@inimacam3945]

@@athulsureshn2866 , no , he was a chinese guy from somewhere north of china near the mongolian border who on his travels adopted india as his spiritual homeland and decided to stay put and get himself an indian name to make his life easier and since his feet was touching the soil which is india , he morphed into an indian guy.......and so on and so forth as the story.. goes .

[@user-lr6xc4jm1c]

I am more amazed and mind-blown when I realized that Archimedes calculated pi using roman numerals. He's a genius and a hardworking person

[@luisricardolozadaamaya670]

Nope, they used greek letters as numbers along with a weird proto-Q for 90. Rome conquered Greece in 212 BC.

[@user-lr6xc4jm1c]

@@luisricardolozadaamaya670 i don't know what that is but I am more amazed anyways

[@fitnesspoint2006]

@@luisricardolozadaamaya670 the Indian/Arab numerals revolutionized math and brought exponential increase in technological advancement

[@thomaskennedy5728]

@@fitnesspoint2006 ok that was random. We are actually talking about how hard Roman number were to calculate a value. Thanks to work of Indian and Arab mathmatics to introduce hindu-arabic numerical

[@janlloyd6138]

Sorry but no one calculated anything memorable using Roman Numerals

[@8BitGamerYT1]

9:40 Sanghamagrama madhavan His aashrama is 30 minutes from our house. Proud to have a mathematics from our small state Kerala.

[@murthykrishna3834]

Indians used the pi for practical purposes only and not for fancy. we have used 22/7 for pi value which works fine for practical use. All our mathematics were application oriented.

[@HarishKumar-0405]

@@murthykrishna3834 yup, even the first tile designs are found in India, that means they clearly had an organised idea of geometry, but just (almost ?) no theoretical standardisation.

[@nikobellic570]

Mathematics is the second best thing Kerala has given the world. No. 1 being black pepper of course.

[@WilliamLi-nd4lz]

@@nikobellic570 Profound!!!

[@TheShipwreckedStoic]

Oh how I love the Ancient Greek legends - "Don't disturb my circles" ... Last words - I love it

[@wandcamilo3989]

yeah before he died

[@maxwellsequation4887]

Archimedes demi god

[@ezekielgordon8852]

I know Im asking randomly but does any of you know a tool to log back into an Instagram account? I stupidly forgot my login password. I love any tips you can give me!

[@zechariahfelipe5909]

@Ezekiel Gordon Instablaster :)

[@justlikethtmrjustliketht1732]

Greeks stole from the egyptians.

[@danielrutschman4618]

One thing I learned from this video is that Simon finds it easier to pronounce long Indian names than short Chinese or French names. Now, you can diagram those names as n-sided polygons where n is the number of syllables in each name, and fit the polygons inside each other such that the polygons with lower values of n are contained within the polygons with higher values of n. Then, by subtracting the highest value of n from the lowest value of n and dividing that by the number of polygons, you can determine that there is an infinite series in which the ease of pronouncing a name progressively increases in proportion to the number of syllables in the name. So a name containing zero syllables would be impossible to pronounce, whereas a name with infinite syllables is absolutely pronounceable. At least in Simon's case.

[@ishansharma3944]

But he didn't pronounce correctly.

[@goldwink]

😄 That's awesome!!

[@hiro9209]

It wasn't right tho

[@GeertDelmulle]

Ramanujan was pronounced in a way I had never heard before. I’ll stick to the version I heard on Objectivity and Numberphiles.

[@ankitminz5872]

Holy math bruh

[@michlgilbertclements6178]

But wait, the greek letter Pi was first used as a symble to represent the number 3.1415 in 1706 by William Jones. So inthe year 2020, Pi will have been used for 3.14 centuries!

[@Belioyt]

Bookmarking this

[@stroys7061]

👍🏻

[@stevenbrucci]

That's interesting! Were there other symbols used by his predecessors?

[@Goldpenny1]

This calls for some pie and coffee

[@theinacircleoftheancientpu492]

Pi day coming up...

[@monmoymaahdie3177]

Why doesn't this guy have more subscribers This is really good content

[@pizzawithcheese1947]

@@antonchik2371 No you make lego videos.

[@TroyLFullerton]

Simon, I'm not a real math enthusiast, and I only stumbled onto this video tonight and thought I'd stop in and have a look, just out of mild curiosity. But that gleam in your eyes as you talk about all of this and the passionate enthusiasm you exude captivated me, and I had to subscribe to learn more.

[@kryskestrel]

This video was made so well, and was actually nice and engaging throughout the entire lesson! Keep up the good work, Simon!

[@clivelewis3058]

I loved this video. Fascinating and engaging maths with a great dollop of history thrown in! Quite a feat. 10/10

[@Gaiboii-un4sv]

Loved this video! On March 14 of this year, my retired physics teacher who came back to teach in an emergency (long story), gave the class some pie! Food for the brain 🧠

[@barisbilgi8490]

History of PI and some other similar concepts like history of trigonometry, derivative, integral etc. should be taught in ordinary public schools to all the students (no matter which subject they will choose in the future). That will help increase the awareness of importance of math and science. Youth will know why we need to trust science. A common sense can be created that way. That will affect how we see life and even our political choices.

[@BunnyLebowski38D]

But these were ALL invented in India! Didn't you know? And Mr. Modi has demanded some patent rights and payment, or else the "west" stop teaching these disciplines, unless they do it in Roman numerals only!

[@alkamishra9974]

@@BunnyLebowski38D wtf is wrong with u???

[@anirudh177]

@@BunnyLebowski38D wtf, not all of these were Invented in India, many Indian Mathematicians and Polymaths over the centuries have contributed to these subjects, and "concepts" like these do not belong to any country. And where did Modi demand patent rights and payments? please show evidence. btw I am an Indian.

[@atwilliams8]

@@anirudh177 It was an anti-capitalist joke, saying what if India patented its math as "intellectual property" and forced others to pay for it's use like countries today (US). Basically it's not all about education, some problems are without.

[@anirudh177]

@@atwilliams8 oh, I see.

[@KingCulta]

Your science and maths education videos are fantastic, Simon. Can't wait to see what's next!

[@dennisberry9518]

Your enthusiasm is delightfully infectious. I could listen to you speak about anything.

[@mikmop]

Great video. Very interesting. Breaking Pi "π" news. As of 9th June, 2022, Google has set a new world record for calculating Pi "π" to 100 Trillion Digits. It took 157 days to calculate and required 128 vCPUs, 864GB of RAM, and 515 terabytes of storage.

[@v0id_d3m0n]

jesus christ... that much storage just for one number

[@rakeshvemulapalli2196]

Hi Simon, This is the first video that I'm watching of yours and i have watched so many videos who explained π. I can surely say that you explained it pretty much better than many. Really appreciate this video, Well done 👌

[@eccentricorbiter1390]

You make Sir Cumference proud

[@jorgensenmj]

Sir Cul and Sir Cumference should come out of the closet. ...And finally tell us which fits inside the other.

[@donalso]

I am as corny as they get! One of my favourite jokes is "why did the chicken cross the road? It was too far to go around". I get a kick out of your Sir Cumference comment. So much humour to be found in our existence and so little time!!!

[@6977warrior1]

@@jorgensenmj-- After they eat some Sir Loin

[@wholeNwon]

Groan.

[@anandsuralkar2947]

Cum -for -once ohk

[@samkenkaj]

I am terrible at maths and not really that interested in it's history but your videos are slowly making me more and more interested about the history and future progress of mathematics!

[@veroxid]

Some minor updates and trivia some people might find interesting: - While due to the shear size the exact number of digits can vary a smidge, to calculate the circumference of the known universe with the accuracy of a planck length, you only need to know about 65 digits of pi; give or take. - Recently at the time of this post, Google succeeded at breaking the 100 trillionth digit point. - About 3 decades ago, a hexadecimal based formula to calculate every 4th digit of pi was found by three mathematicians, and was named after them: the Bailey-Borwein-Plouffe formula. This formula has been one of the methods used to verify any new calculation. - _Just_ *_last year,_* Plouffe - one of the 3 mathematicians that found the previous formula - found and published a paper on a decimal based formula. This means that we can now calculate any decimal point we wish. With this method it's simply a case of creating an infinite for loop until it runs out of space to fit more digits.

[@Haridas991]

Thank you for this informative video. I love your expression of mathematics in such a lighthearted and fun way.

[@edwoodvine6793]

Loved this video Simon. We shall watch your career with great interest.

[@howardman3926]

Despite already having a large chunk of subs, I really think you do deserve more. I feel as though you are one of the few people who are talented in explaining things scientific and mathematical. ; )

[@potawatomi100]

Outstanding video and extremely well narrated. Well done!

[@thomasbrooklyn1820]

Excellent vid, audio, speaking, and content. Moved quickly, no fluff.

[@Sourkid13]

I love these videos, Simon. You're making great stuff, keep it up

[@NickKartha]

9:37 I was so suprised to see my native language of malayalam in this video. I didn't know Madhava did that, thank you!

[@chinmay2910]

I blinked twice, shocked to see Malayalam written in a non Indian video

[@angelabrown6598]

It’s visually a very pretty language 😍

[@adlerdoesstuff1872]

same

[@soorathkaruvatta8383]

He was from irinjalakkuda.theres a temple still there where he used to perform this calculations

[@itsoblivion8124]

His text was in Sanskrit

[@aldemarinfante2600]

You must be really good because my teacher of geometry recommended your video for a homework

[@aayusharya6899]

Dude, lucky moment! It's PI Day and this video has 314k views today.

[@seekandfind5005]

Ayush Arya dear friend, God is with you and numbers!

[@plo8monster113]

#Fortuitivity

[@damirkadric9985]

Happy Pi day bro

[@destinyovbiebo8988]

Really

[@subscribetobanbasstabs2599]

untrue unfortunately 😔

[@ColoredScreens]

Awesome video, but I can't help but to point out one small inaccuracy. At 9:05, you said that "If those contributions keep getting smaller as you go on, then the series converges to a particular value." Though this is often true, there are infinite examples (such as the harmonic series, Σ1/n) where a series consisting of strictly decreasing values diverges.

[@albertolema8583]

Great content! Love the tone and how you connect the dots through historic events. Great narratives!

[@chillouthere4056]

You’re the right in all, your video is most valuable/simple all around!! Big thanks,

[@yourmomlmao8656]

Thanks, I needed this for a project it helped a lot

[@saultube44]

@11:54 Srinivasa Ramanujan, current infinite Pi series of choice, Awesome! Wait, there was Pi Machines? really? wow! I never knew this Dude, you presentation was spotless: interesting, complete, well spoken and explained, well you're British that's a given but you pronounced your 'Ts' and other letters some British people are choosing not to and is harder to understand them, overall awesome, I rarely watch such videos, thank you and keep the quality 100%, Cheerio

[@ornestebuitkute9720]

Brief History of ... :( RIP Hawking. Loved this video and the way you've written the script!

[@SaumyaSagarVishwakarma]

Born of ALBERT EINSTEIN...

[@C.J.80]

Loved the narration! Thank You!!

[@anandsuralkar2947]

The way u brought it up was so awesome and inspiring

[@gakaface]

Good video Simon. Brings back memories for me. For me, it was the benchmark in mathematics and computer programming. 37 years ago, I programmed a mainframe computer to calculate Pi to 1,000 decimal places - my formula was 4(arctan(1/2) + arctan(1/3)) which converges at a rate of two decimal places per iteration. In those days, it took a whole weekend of the core CPU time. These days, this can be done in a matter of minutes on a laptop.

[@lifewithdylan]

This is my revision for the day then!

[@naz42009]

Student Vlogs - ayyy its dylan 😉

[@NganNguyen-zz6vk]

THANK YOU SO MUCH! This is such an amazing video. I was desperate on my assignment of pi until I watched this video!

[@kalpanarohitnain7938]

Hi! You have explained very well to us. Really, it is an interesting and amazing video.

[@claudiajade624]

Literally no one ever told me that that's what pi is...I just thought it was like an arbitrary number that worked for things. I also thought 'sequences and series' was the most boring topic in maths...I do kinda wish they gave more explanations about things along the way for why different mathematics was important/useful. I was pretty happy to just accept it and do the work, but I certainly would have found it more interesting (and I think would have motivated a bunch of other ppl), to know the context and significance.

[@yosefmacgruber1920]

Ironically, π does appear to be slightly arbitrary. While it is cool that it is a natural property of mathematics, and not arbitrarily defined, however, why π and not tau, which is 2π? Why base-10 π? Why not binary π or hexadecimal π or base-12 π? About the same value obviously, but not at all written with the same digits. Infinite series seem to be very important, because transcendental numbers can not be calculated by normal algebraic expression. Many functions can not be calculated by simple algebraic expressions, but rather take some sort of infinite series approach, in which you start with a "guess" answer and then calculate and recalculate, and the result slowly converges towards the correct answer. The process is stopped when it reaches sufficient accuracy. We want to minimize such calculations, in algorithms that need to be fast, such as in drawing 3-D computer graphics. I think that the trigonometric functions such as sine, cosine, tangent are of this nature - painfully slow to calculate. Thus, I was curious how 3-D graphics work, and I wanted to find a way to rotate my points while minimizing my use of trigonometric functions. Thus, taking the arc-tangent of a point's position, calculating its distance from the center of rotation, and adding my rotation angle to it, then recalculating the position of the point, is a serious no-no, because it is not computationally efficient. If I could work it out as a simple algebraic expression in terms of multiplication and addition, that would be much more computational efficient, because computers can do those calculations very fast. I worked it out by thinking about it geometrically, and found out how to do it, the only trigonometric functions I had to use was to calculate the sine and cosine of the desired angle of rotation, only once per rotation. Not on a per-point basis. To test my solution, I plotted a set of random points onto the screen. I then rotated them little by little in 2-D, without bothering to erase them, and sure enough, the points smeared into concentric circles going around the center of the screen. Cool. It works! I later found that I had geometrically re-discovered a angle A + B identity while in high school, that was already well known and indicated in a (later) college level mathematics textbook of mine. I never had the time to expand and try my own hand at 3-D graphics. I seriously think that the old 2-D computers could have drawn 3-D graphics games, provided that they did not attempt too much complexity that would bog down their old slow CPUs. We could have walked through 3-D mazes of hallways and rooms and such. As there were no graphics processing units back then on typical home computers, the number of vectors and shape fills of the regions, or polygons drawn, would have to be limited. No complicated textures on surfaces, like we see now. No complicated "in the distance" fogging effects. The floor and walls could be of different colors, but making the walls of complicated surfaces such as individual bricks, likely would not have been possible with those old slow computers. Way too many polygons to calculate for them. Well unless a frame rate of several seconds per drawing of each frame, was acceptable? I think that the old computers of the 1980s, could have achieved maybe a frame or 2 per second in 3-D, had the 3-D graphics subroutines been properly written for them. But back then, they were struggling just to make memory cheap enough to do decent 2-D graphics. Now why do 3-D graphics need to be rotated? Well because if they are not, then we have x and y coordinates, and the z direction is perpendicular to the screen, thus it disappears. Because the screen is actually 2-D, we have to rotate everything into view to make it seem to be 3-D. Well unless _Zaxxon_ video game fake 3-D is what you want, which is really more like 2-D? 2-D graphics were getting sort of boring, and in 2-D most everything on the screen is very little, or else your room size itself is very limited. In 3-D, distant objects appear very small, but become much bigger and more detailed when they are approached. Much like real life, and it makes video games seem a lot more interesting and detailed. Even a 3-D mathematics graph of an equation needs to be rotated, to get a good perspective onto it. Too many regions would be hidden from the wrong viewing angle. And I hardly have any idea how to remove "hidden" portions that are blocked by a surface in front of them, from the graph. Would you draw the farther away portions first, and then let the graph overwrite and erase whatever might be behind it, as it then draws the closer regions? BTW, modern 3-D graphics I think are calculated using quaternions. Even more complex than complex numbers, as there are 3 imaginary number components rather than just 1. Still just 1 real number portion. It is more computational efficient and avoids gimble lock, whatever that is? Something I will want to study more into.

[@abowla7187]

As with all forms of math in public schools. All they want is better test scores for more funding from the government.....

[@yosefmacgruber1920]

@@abowla7187 Government monopoly schools seem to neglect the joy of learning and the process of learning and discovering truth. Too much cramming of stuff without very good mastery of it. Students should proceed at their own pace and be encouraged to explore. Wait, that sounds a lot like home-schooling. Where is the government-monopoly-promoting benefit in that?

[@almostfm]

My favorite sequence is the Fibonacci sequence, where the next number is found by adding the two previous numbers, so 0,1,1,2,3,5,8,13,21... It's found in a lot of places in nature, but it's also a "quick and dirty" way of converting between miles and kilometers. If you're in miles, the next number up is kilometers (so 2 miles is 3 kilometers, 13 miles is 21 kilometers, etc.). You go to the next smaller number in the sequence to go from kilometers to miles.

[@yosefmacgruber1920]

@@almostfm The first 3 Fibonacci numbers > 1 are the first 3 primes as well. I think that fractals are so beautiful. A YT video calculated the fractional dimension of the Sierpinski triangles at 1.58. Did you know that 2 and 5 might not be quite as prime as we were led to believe? They have factors in the complex numbers. How weird is that? Did they forget to look in the complex numbers? (1 + *_i_* )(1 - *_i_* ) = 2 (2 + *_i_* )(2 - *_i_* ) = 5 And these factors would seem to the the complex version of integers.

[@peorakef]

simon clark: ah sorry can't pronounce the easiest of chinese words. also simon clark: proceeds to pronounce persian and indian names.

[@user-zl5cv6vw2m]

Lmao

[@nachiketh.d5356]

😂🤣

[@cpasr8065]

The Indian pronunciations weren't great either.

[@peorakef]

@@cpasr8065 exactly

[@dynamo429]

@@peorakef probably because Persian and Indian languages are Indo europian...

[@leanonymous486]

You are brilliant Simon, Nice website too , and by the way I subbed and would definitely buy your merchandise once released. hats off for your effort .

[@tomaszstarzZz]

Very passionate and well researched video. Outstanding

[@biplabkar8737]

Wow, what a great presentation! You are an inspiration for inquisitive minds...

[@raulgil7389]

I must watch this video 2 or 3 times so that on the 4th time I may start taking notes. Math is good for the senses and the senseless. It’s almost emotional! It’s for the ages of enlightenment... Good for sharing.

[@Roberto-REME]

Excellent video, Simon, and expertly narrated.

[@Stephen_Lafferty]

I'm glad that I found this on PI Day 2020! Thank you for summarising this amazing history!

[@Imakeeeeeno]

It's almost as if you planned this to be uploaded on the 3/14...

[@raney150]

Joe Reed which is interesting since he lives in the UK, and over there it is 14/3

[@Imakeeeeeno]

raney150 I live in the UK myself - today is the only day it’s acceptable to embrace the M/D system (in my opinion, I prefer the British way but hey I was brought up on it)

[@non-inertialobserver946]

Its pi day here in italy too (even tho its 14/3)

[@thatoneguy9582]

raney150 31/4

[@pulakdeyashi]

Absolutely

[@user-ov8ei2ep8o]

9:33 totally incorrect, the indian mathematicial Acharya Pingal has given Fibonacci series formula in ~200 bc, so infinite series is way older concept than 13 cen, given to world like most of the important mathematics by india

[@nathanwhitten8950]

Well done. If I were to undertake a description of the discover of pi, I'd do something like you did. I have a bit of experience with infinite series. 120 hours of math, 72 of them in grad school. Series were of great interest to me. Thanks for this.

[@miles6875]

Great work, Simon. Ton of value in this video

[@soraaoixxthebluesky]

Circle is a result of anti-aliasing switched ON. Linus told me this.

[@anandsuralkar2947]

Lol🤣🤣🤣🤣

[@samplebrandaccount7166]

Ah, i see you're a Man of Culture as well

[@ZahidAli-oy4lk]

@@anandsuralkar2947 ukkukukukukukukiukkukukukukumu7u7

[@williammcdonald5086]

Pi is approximately 3 which means most circular equations use pi, which is close to 3. In music, most dance pieces are written in 3 time or multiples of such as 3/4, 3/8 or 6/8 times. Many dances such as waltzes use circular motion.

[@supersaiyangoku1495]

This is the best explanation of pi I have ever seen 😊

[@tariq729me1]

awesome video. History and methods of calculations beautifully explained.

[@6977warrior1]

I'll give you the brief history of PI...my Italian grandmother made one every week since she was 10 years old. Usually apple.

[@kilroy1964]

Mine made one the first week, then 4 the second week, 1 on the third, 5 on the fourth, 9 on the fifth...

[@kienhachi1068]

Good pun! But I like chocolate PI more.

[@rawnanle]

I bet it fed atleast 3 people and then some

[@stroys7061]

Make it pumpkin pi and I’m all in!

[@MrKmanthie]

You're thinking of PIE. Oh, wait, I get it. You were trying to be funny.

[@michietn5391]

6:43ish "modern decimal notation" should have noted that India showed us zero (represented by an empty ring, ie no digit in it), and the place value derived from creating symbols to represent beads inserted into an abacus.

[@alvienbautistabautista6485]

im not good in english but ilike math. im only carpenter here in the philippines, I always use pi to calculate square meter very usefull. thanks to you bro.now i know that there are more.

[@supersaiyangoku1495]

This is the best explanation about pi in the world luv this channel

[@stroys7061]

“Because they CAN!” With an Irish accent. Perfect!

[@fernandosantosviana7971]

cool

[@robbes7rh]

Michael Collins - it wasn’t a Scottish accent?

[@stroys7061]

robbes7rh It might be. I confuse the accents when they aren’t very strong.

[@nikhilnrao]

Great Video. Thanks! I think you got the picture of Madhava wrong at 9:43. The picture in the video is that of the philosopher - Madhwacharya and not the mathematician - Madhava

[@errolfellows409]

Excellent! Most entertaining. I did basic maths at school, but I was not good at it. The teachers were dreary and boring. However, I was damned outstanding at English, History, and, at a stretch, Latin - because the teachers were masters of their subjects, were EXCITED to impart knowledge and the methodology of learning, and HAD FUN in class! I understand the concept of Pi, but I will never need to know the value to any more than 5 numbers - and that's simply because I can be a smart-arse! If this dude had been my maths teacher, things might have been different.

[@mehulturakhia1958]

mind blowing . Very nice done . well documented chronologically

[@mikehawk4583]

Do that about number e

[@NewCalculus]

The following number explains how we got the incommensurable magnitude e. There is no number that describes the measure of e: kzbin.info/www/bejne/h3_EeWeIjpuMnM0

[@stopthecrazyguy9948]

@@NewCalculus That is not the history of e.

[@fanimeproductionst.v.3735]

*E*

[@jamesarthur67]

5:35 to do calculate?

[@jeffwells1255]

A great video, especially since you pronounced Ramanujan's name correctly ;) One mathematical advance that still needs to be done, however, is to lose our clumsy decimal system and switch to duodecimal or "dozenal" counting by twelves instead of tens, mainly because of its factorability. Ten is only evenly divisible by 2 and 5, whereas twelve has even factors of 2, 3, 4, 6 and almost by 8 and 9. We got stuck with tens because we have ten fingers, but if we used the three segments on each of out four fingers we can easily count to twelve (or 24) that way. The symbols for base twelve are the usual 0,1,2,3,4,5,6,7,8,9 plus X and E for ten and eleven, so 10 in dozenal represents twelve, 20 is twenty-four, 100 is 144 and so on. The names proposed for X, E and 10 are currently dek, el and do (rhymes with so). Twelve is why we have twelve months of three seasons each in our calendars and 24 hours in a day, but finer divisions don't fit once weeks, hours, minutes and seconds are randomly crammed in to make decimalizing time a real pain to calculate. This could have been implemented during the French Revolution of 1789 but the chances of it happening now are practically zero, less even than if the United States finally decided to adopt the full metric system.

[@v0id_d3m0n]

No! Seximal is better! - this post was made by the Jan Misali crew

[@emanuelkokovics]

The video was amazing !!! I really enjoyed watching it !!!

[@nishatiwari9212]

I like his videos so much.

[@uthkarshdatt1070]

Really deep Research. Nice video👍

[@walteralter9061]

Lively, interesting presenter. Wish I had this guy for my high school geometry and trigonometry classes.

[@MyMathTeachingOnline]

I love your video, very interesting for all of learners. thanks

[@PujaMallUSA]

GREAT VID AND GLAD U MENTIONED THE ANCIENT SAGES OF INDIA, Paadi panchaka Yadyashtaka Kshah sunyam” Meaning: Kaadi Nava Starting from ka, the sequence of 9 letters represent 1,2,..9 Similarly Taadi Nava , starting from ta Paadi panchaka (1-5), starting from pa Yadyashtaka (1-8) starting from ya And ksha represents 0 In detail it is as follows: ka (क) - 1, kha (ख) - 2, ga (ग) - 3, gha (घ) - 4,gna (ङ) - 5, cha (च) - 6, cha (छ) - 7, ja (ज) - 8, jha (झ) - 9 ta (ट) - 1, tha (ठ) - 2, da (ड) - 3, dha (ढ) - 4,~na (ण) - 5, Ta (त) - 6, Tha (थ) - 7, Da (द) - 8, Dha (ध) - 9 pa (प) - 1, pha (फ) - 2, ba (ब) - 3, bha (भ) - 4,ma (म) - 5 ya (य) - 1, ra (र) - 2, la (ल) - 3, va (व) - 4, Sa (श) - 5, sha (ष) - 6, sa (स) - 7, ha (ह) - 8 kshah (क्ष) - 0. Based on this code there are many slokas in mathematics., e.g., the following is a sloka for Pi value: गोपीभाग्- य मधुव्रातः श्रुंगशोदध- ि संधिगः | खलजीवितखा- ाव गलहाला रसंधरः || gopeebhaagya maDhuvraathaH shruMgashodhaDhi saMDhigaH khalajeevithakhaathaa- va galahaalaa rasaMDharaH ga-3, pa-1, bha-4, ya -1, ma-5, Dhu-9, ra-2, tha-6, shru-5, ga-3, sho-5, dha-8, Dhi -9, sa-7, Dha- 9, ga-3, kha-2, la-3, jee-8, vi-4, tha-6, kha-2, tha-6, va-4, ga-3, la-3, ha-8, la-3, ra-2, sa-7, Dha-9, ra-2 3.141592653589793238462643- 3832792… The above sloka has actually 3 meanings 1. In favor of Lord Shiva 2. In favor of Lord Krishna 3. The value of Pi up to 32 decimals. There were many inventions in the field of science and technology in ancient India, we just have to sift through the sands of time to find them.

[@kienhachi1068]

Oh that is a good way of remembering Pi But I'm not an Indian

[@amarjotsingh9676]

legendary mathematician SRINIVASA RAMANUJAN

[@anna-marie4035]

Amarjot SIngh

[@Satya_Golu]

@DARK HateMaN 😂😂😂

[@danimtions7964]

Maybe i should correct ya all it's euclid and newton

[@HariomSir]

@DARK HateMaN In 1910, the Indian mathematician Srinivasa Ramanujan found several rapidly converging infinite series of π, including {\displaystyle {\frac {1}{\pi }}={\frac {2{\sqrt {2}}}{9801}}\sum _{k=0}^{\infty }{\frac {(4k)!(1103+26390k)}{(k!)^{4}396^{4k}}}}{\frac {1}{\pi }}={\frac {2{\sqrt {2}}}{9801}}\sum _{k=0}^{\infty }{\frac {(4k)!(1103+26390k)}{(k!)^{4}396^{4k}}} which computes a further eight decimal places of π with each term in the series. His series are now the basis for the fastest algorithms currently used to calculate π. See also Ramanujan-Sato series.

[@HariomSir]

In 1989, the Chudnovsky brothers computed π to over 1 billion decimal places on the supercomputer IBM 3090 using the following variation of Ramanujan's infinite series of π

[@yxyvyc]

Well done mate, first time watching you, now subbed

[@geraldmanley1816]

Excellent and you speak so well.

[@natefcod9361]

This has increased my appreciation for pie

[@anoopantony5072]

Actually I'm a Keralite and I'm very proud to say this....The Jyesthadeva's Ganita-Yukti-Bhasa (1530 CE) written in Malayalam that contains the proofs given by Madhava the first book of calculus even before Newton... After the Portugese came to Kerala and they passed the work into Europe. Unfortunately the Kerala school of Mathematics came to an end because of European invasions of Portugese, Dutch and English. Thus all the mathematical works were destroyed or we can say that the kings were in constant fight with these powers. It is said that at that time of 1400s the father malayalam language Ezhuthachan move to other part of Kerala as the place he lived was having constant fights for European forces.

[@brajabasisahu5281]

Beautiful, Brief, Interesting summary.

[@dcterr1]

Very interesting presentation of the history and math behind the calculation of pi.

[@indiansrk9997]

I am Indian Muslim.. And proud to have so many scientists

[@gauravsrivastava3252]

Simon clark. The idea of algebra and linear equation as well as quadratic was very much common in ancient india... the arabic mathematician came india and he translated the algebra and trigonometry in arabic. And after that it travelled to europe. In india it was known as jayamiti and it getting translated and got its name in english as Geometry. Trikonamiti as trigonometry which was developed in india independently long before pythagoras and greek mathematicians. Algebra had name beejganit which is now algebra! Literal meaning is mathematics of numbers.. i hope u understand it now... in 11th century AD. Two indian mathematician developed limit as a sum technique in a diffrent way. It clearly shows that indian mathematics had an approach and understanding of infinity. But later on newton and lebnitz developed diffrential calculus. Which he patented. Ancient Indian mathematician never believed for the patent mechanism! Because here it was developed just to understand the world for better. 0 was discovered in India. I hope u get everything well! And still if u want reference of everything.. i can surely provide every reference to you!

[@asmasm9736]

To say Algebra was invented in India would be wrong. Indian mathematicians contributed to the “invention” or “discovery” of Algebra as did other mathematicians from other civilizations from the period of antiquity. Knowledge always flows and a lot of that knowledge eventually ended up on the desks of Arab and Persian mathematicians. These Arabs and Persians, given their geographical location, were able to advance work done on countless sciences and topics and had access to a treasure trove of knowledge from both the West and the East - from the ancient Greeks and Romans to the knowledge enmassed by the people of India. There is still an ongoing debate as to who holds the title of “Father of Algebra”. On the one hand we have the Greek mathematician Diophantus who has traditionally been known as the "father of algebra" and on the other hand we have the Persian mathematician al-Khwarizmi. India is not considered the birthplace of Algebra though the Indian mathematician Brahmagupta did advance many of the concepts needed for its eventual discovery by al-Khwarizmi. Also Brahmagupta lived after Diophantus so if one was to consider Diophantus as the father of Algebra then once again we cannot state that Algebra was invented in India.

[@gauravsrivastava3252]

@@asmasm9736 diophantus and brhmagupta independetly developed there notion for algebra brother.... still u agree on the rest of evidence its good... its not that i m claiming about that it is ours... i just wanna express that though many of theories originated in india still indians never petented it... its not because we are foolish.. its just we dont believe in patent mechanism! Its all about we just believe in sharing knowledge without royalty.. even some years before marconi, jagdish chandra basu developed radio transmission technology.. its clear evidence.. but due to british rule it was tough to get a patent... so marconi after some later years put his name fixed to radio transmission. Even bose Einstein condensate, bose-einstein statistics and bosons were independetly developed by satyendranath bose.. but it was very hard to publish as british govt. Refused. So he wrote a letter to einstein to give a reference and publish his works in german! That's whole story... idea of limit as a sum was also developed in india during 11th centuary AD. And i hope u well know srinivas ramanujan! Who knew lots of stuffs beyond the thoughts. I m not counting achievements.. its just facts... we Indians don't want any fight about claiming anything. We just want the respect we deserve. 🙏 namaste!

[@gauravsrivastava3252]

And still u donot value the 15000 years old culture.. then its my failure to make u aware of Indian culture!

[@asmasm9736]

@@gauravsrivastava3252 yeah we Arabs know how great Indian culture is, and we adore it, my mom studied hindi last year 😭😂😂, arabs also invented many things that the west claim as theirs or don't give credit arab/Persian creators, like the airplane, glasses, cameras, soap, surgery, medicines, university, the wheel system that's used in trains, cars, ect, they claim it to be theirs when it was stolen from Arabs after invading them All of us Asians and north African have many discoveries that were stolen and claimed to be discovered by Westerners and we should raise awareness about it and reclaim it, but most importantly to discover and invent new stuff instead of being attached to the past

[@gauravsrivastava3252]

@@asmasm9736 i agree!😂😁

[@PhillipJames100]

An excellent presentation...thank you.

[@altareggo]

LOVE this chap's accent!! Reminds me of my grandfather and Scotty from TOS....

[@the_sophile]

9:43 surprised to see that he is a keralite , a malayalee like me

[@poetrylover6511]

I am sending you 1π! Pi is a new digital currency developed by Stanford PhDs, with over 9 million members worldwide. To claim your Pi, follow this link minepi.com/Wolverine006 and use my username (Wolverine006) as your invitation code.

[@anoopantony5072]

Ha that too in 1400s

[@oskarhenriksson]

Hmn, I'm not sure Archimedes and Euclid would have agreed that their methods were any less rational, theoretical or based on reason than what the 17th century Europeans were up to :) I guess it fair to say that Leibniz, Gregory et al. had a slightly more abstract and symbolic approach to mathematics -- and they certainly had some really sophisticated concepts (like the notion of a series) that the Greeks didn't have -- but when it comes to theoretical rigor, my impression is that the Greeks had just as solid ground under their feet as the 17th century Europeans, if not more! I haven't read Leibniz's original proof of the series formula, but the way I understand it, it involves quite a lot of infinitesimals being thrown around, which (especially at that early time in the development of calculus) must have been much less clear/rigorous and much more based on intuition/common sense, than the very strict and precise arguments within (an extension of) the Euclidean axiomatic framework that Archimedes made in his "Measurement of a Circle."

[@shivbajpai3826]

This is the best thing that I watched today.

[@PerpetualBass]

This was exactly what I was looking for, thank you

[@41-Haiku]

"It's Brilliant!" No, Simon, it's SquareSpace.

[@AbdullahSalimalig]

The catch words by Archimedes: "Don't disturb my circle."

[@theshoulderofgiants]

what the fuck is catch words??

[@barbarannop1799]

Nishchal Bhat google it moron.

[@archieryan9015]

Interesting how that same logic of infinity was applied thousands of years later by Newton when he invented calculus. Just really does emphasise the universality of maths.

[@juanitaalyozha848]

Zizi Alyozha Brilliant! Loved this! Thank you Simon.

[@DranPan]

3:58 Truly, the right spelling (enenekontakaihexagon) is a tongtwister even in greek!

[@arielfuxman8868]

How did that Indian guy discover the formula for the arctan? Without calculus? Absolutely amazing

[@jobsonjames3810]

He done it with the help of calculus. Some of the first discoveries of calculus

[@LowellBoggs]

A fun video, well presented. Thank you!

[@martebest]

Interesting and deep explanation. Thanks a million. Then maybe you will understand. Please consider it. We have some tricky formulas to use to calculate the value of Pi. In my opinion, the value of Pi can be calculated in a much easier way. We have the formula Pi = Phi^2 + RC . Phi is the golden number, RC (royal egyptian cubit) is Pi/6 so we have Pi = Phi^2 + Pi/6 and hence Pi - Pi/6 = Phi^2 and then 5*Pi = 6*(Phi^2) so Pi = 6*( Phi^2)/5 We know that we can get a good approximation of Phi by dividing the largest possible values ​​of the Fibonacci series. The values ​​of the sequence can be calculated using the formula: f(n)=f(n-2)+f(n-1) so let's take this notation let's substitute it to calculate Phi, so Phi = f(n) / f(n-1 ). I substitute these values ​​into the formula and we have Pi = 6 * ( f(n) / f(n-1) )^2) / 5 So this is another and rather new formula for calculating the value of Pi. Do you understand? There was no such formula before to calculate the value of Pi. Maybe you should nominate me for the Abel Prize? 😁 Maybe aliens will come to shake my hand after all... 😜

[@anupthomas4345]

9:40 "samgramagramamadhavan".its what that weird writing says and its malayalam.

[@sachinnandakumar1008]

Malayali aanalle

[@BangMaster96]

Here is another fact. There is no such thing as a perfect circle in nature. Basically, circles as we describe in Math, do not exist in nature. It's an entirely human made concept, and has allowed us to advance so much as well, both Mathematically, and technologically.

[@carlosalexandreFAT]

The association of the main numbers in the field of mathematics with each other, reflects numerical sequences that correspond to the dimensions of the Earth, the Moon, and the Sun in the unit of measurement in meters, which is: 1' (second) / 299792458 m/s (speed of light in a vacuum). Ramanujan number: 1,729 Earth's equatorial radius: 6,378 km. Golden number: 1.61803... • (1,729 x 6,378 x (10^-3)) ^1.61803 x (10^-3) = 3,474.18 Moon's diameter: 3,474 km. Ramanujan number: 1,729 Speed of light: 299,792,458 m/s Earth's Equatorial Diameter: 12,756 km. Earth's Equatorial Radius: 6,378 km. • (1,729 x 299,792,458) / 12,756 / 6,378) = 6,371 Earth's average radius: 6,371 km. The Cubit The cubit = Pi - phi^2 = 0.5236 Lunar distance: 384,400 km. (0.5236 x (10^6) - 384,400) x 10 = 1,392,000 Sun´s diameter: 1,392,000 km. Higgs Boson: 125.35 (GeV) Phi: 1.61803... (125.35 x (10^-1) - 1.61803) x (10^3) = 10,916.97 Circumference of the Moon: 10,916 km. Golden number: 1.618 Golden Angle: 137.5 Earth's equatorial radius: 6,378 Universal Gravitation G = 6.67 x 10^-11 N.m^2/kg^2. (((1.618 ^137.5) / 6,378) / 6.67) x (10^-20) = 12,756.62 Earth’s equatorial diameter: 12,756 km. The Euler Number is approximately: 2.71828... Newton’s law of gravitation: G = 6.67 x 10^-11 N.m^2/kg^2. Golden number: 1.618ɸ (2.71828 ^ 6.67) x 1.618 x 10 = 12,756.23 Earth’s equatorial diameter: 12,756 km. Planck’s constant: 6.63 × 10-34 m2 kg. Circumference of the Moon: 10,916. Gold equation: 1,618 ɸ (((6.63 ^ (10,916 x 10^-4 )) x 1.618 x (10^3)= 12,756.82 Earth’s equatorial diameter: 12,756 km. Planck's temperature: 1.41679 x 10^32 Kelvin. Newton’s law of gravitation: G = 6.67 x 10^-11 N.m^2/kg^2. Speed of Sound: 340.29 m/s (1.41679 ^ 6.67) x 340.29 - 1 = 3,474.81 Moon's diameter:: 3,474 km. Cosmic microwave background radiation 2.725 kelvins ,160.4 GHz, Pi: 3.14 Earth's polar radius: 6,357 km. ((2,725 x 160.4) / 3.14 x (10^4) - (6,357 x 10^-3) = 1,392,000 The diameter of the Sun: 1,392,000 km. Numbers 3, 6 & 9 - Nikola Tesla One Parsec = 206265 AU = 3.26 light-years = 3.086 × 10^13 km. The Numbers: 3, 6 and 9 ((3^6) x 9) - (3.086 x (10^3)) -1 = 3,474 The Moon's diameter: 3,474 km. Now we will use the diameter of the Moon. Moon's diameter: 3,474 km. (3.474 + 369 + 1) x (10^2) = 384,400 The term L.D (Lunar Distance) refers to the average distance between the Earth and the Moon, which is 384,400 km. Moon's diameter: 3,474 km. ((3+6+9) x 3 x 6 x 9) - 9 - 3 + 3,474 = 6,378 Earth's equatorial radius: 6,378 km. Orion: The Connection between Heaven and Earth eBook

[@rohanleslie4004]

Very good young man! Good presentation; enjoyed it very much. Thanks.