Pi - Sixty Symbols

[grande1899]

How is a right angle pi/2?

[virumoz]

You could mirror this video on your »numberphile« channel, Brady.

[cpovey1]

Pi day arrives soon: March 14th

[PinkCammy]

Pi by 4 or Pi on 4 ...

[makingitsnowy]

I baked you a pi. Oh boy what flavor!? Pi flavor!!

[ZeddZul]

I know Pi out to the 55th decimal place :D

[Nadeeja94]

When we were introduced to Pi at school, we had a hard time containing our laughter. Because Pi means d**k in my mother tongue (Sinhalese).

[Arghira]

2x2x4x4x6x6=2304

3x3x5x5x7x7=11025

2304/11025=0.2089796

pi=3.141592653589

3.141592653589/2=1.57079632679­45

see my confusion??? 0.2089796 it different form 1.5707963267945 Where is my mistake?

[MultiPaulinator]

@Arghira found it:

The long-hand version of this series is actually:

2/1x2/3x4/3x4/5x6/5....

So to get an approximation out of the series, you would need to use one less number in the denominator than you use in the numerator:

3x3x5x5x7 =1575

2304/1575 yields 1.462857.

Looks like this series needs a large number of terms before it starts converging.

[farzyness]

@Arghira to infinity. As to say 2x2x4x4x6x6x8x8x10x10x12x12x14­x14....... so on and so forth. Same for the denominator but for odd integers.

[RikkTheGaijin]

I don't understand anything of this.

[F35Pilots]

The total area under 1/(x^2+1) is pi because the integral of 1/(x^2+1) is tan^-1(x)+C

[my31415]

how about tau...

[aluisious]

I never realized there was an infinite series for pi/4.

[gregiep]

Dude got pi wrong. He wrote 3.141592, when really it should be rounded of to 3.141593. When 3.1515926 gets rounded off, the 2 should go up to a 3 because 6>5. Despite my catching his error, he is still many times smarter than I am, and would whoop the pants off me in any sort of physics/math competition to be sure. I feel a little better, though knowing he is, in fact, human.

[theneonfire]

@gregiep Usually if you memorise digits of pi people don't round off because if he knew the digit as 3, then learnt it was actually 26, it introduces more easy errors. But you're right, strictly speaking he should've rounded.

[tomaskvapil]

I didn't get the end with triangle, can anyone write it in other words please?

[BlueCosmology]

@tomaskvapil A right angle is equal to (pi)/2.

[BlueCosmology]

@ColdHeartedMan86 "If you're dealing with radians."

If you mention pi and don't mention units you are always dealing with radians as radians are dimensionless, and are defined by pi.

[TheMultiSergey]

hm, how infinity of all space depends on pi?(pi depends on time and speed of object)

its my question, can anyone answer me?

[TheUberOmfg12333]

As I write this post, this video has 314 likes which is 3.14 x 10^2. There are also 2 dislikes.

[JRBendixen]

I have learned by experience that if you have any math problem, just divide or multiply whit PI and there is a pretty good chance of getting it right.

[AngieK412]

All I know without looking is 3.141592653589793238

[CrankyCassanova]

3.14159265358979

[TheEnspycelly]

3.1415926535897932384626433832­795028841971693993751058209749­445923078164062862089986280348­253421170679 821480865132823066470938446095­505822317253594081284811174502­841027019385211055596446229489­5493038196 442881097566593344612847564823­378678316527120190914564856692­346034861045432664821339360726­0249141273  724587006606315588174881520920­962829254091715364367892590360­011330530548820466521384146951­941511609

[TheExtractor1]

3.1415923589

Can't remember any more digits :P

[Chickend0ut]

3.14159265358979323

as far as I got in grade school

[GiorgioCapocasa]

How about a Tau video? (: It would be really nice.

[thedevilburnsred]

super smarty pants genius 

[mdiem]

By-the-way, 22/7 is accurate to pi within an error margin of 0.04025%

So, yeah, pretty close..

[01000110I01010101]

@mdiem even 3.1415 is more accurate than 22/7

[mdiem]

@01000110I01010101

It's way more accurate, but 6283/2000 isn't as handy a fraction to use for quick-and-dirty 'back of the envelope' arithmetic. ;-)

I prefer my graphing calculator's pi button regardless.

[EducationLover]

@01000110I01010101 yes i did the calculation i got 3.14285..... ! :s

[crazyliclay]

@01000110I01010101 technically speaking no, that's like saying 1/3 is less accurate than .333333333333

[AppleAssassin]

@crazyliclay It is less accurate...

[crazyliclay]

@AppleAssassin um no it's not 1/3is the same as .3333333........repeating to infinity, and is thus more accurate that the decimal that ends

[NiamOfAsuras]

@01000110I01010101 Yet 22/7 gives you 3.14 which is the common value of pi in high schools and elementary schools where it is first introduced to students.

[CheezyMaple]

3.141592654

All I know :P

[wwbraveheart4]

I can remember pi as 3.1415926535897932385, am I a geek?

[cuntylishus]

Never understood why Americans deny themselves meat Pis. It's like vegetarians denying themselves meat :\

[therealTOTOfan]

thumbs up if you checked on the calculator if 22/7 really approximates pi xD yeah, that geeky..

[Tridecalogism]

I like pi. Blueberry Pi.

[madzyadzy07]

Adele called her first albums 19 & 21 because they are numbers that have special importance to her life

Her follow up 3.1415926535897932384626433832­7950288419716939937510 is due out in the summer.

[AndrewTubeWall]

@madzyadzy07 Hey, that's my level of geekiness! PI to fifty places :-)

[Exfenestracide]

@madzyadzy07 I think she'll take a break and make a comeback in 10 years with the album 31.415926535897932384626433832­­7950288419716939937510..

[agus6328]

Hey there virgins

[qwertyp1234]

I see Madhava's name next to the first infinite series...

[X3QT0R]

Each of these videos are guaranteed to form new mural connections in my brain,

[Tullppa]

@X3QT0R Hopefully they'll develop some "neural" connections to the part of brain concerned with spelling

[X3QT0R]

@Tullppa lol :p

[NotGodsCreation]

Because today is 13th of May, i want to wish to all the professors at The University of Nottingham and Brady a Happy ("Pi" π) Day!

Thanks for all the great videos !

[flowertrue]

Liked for pi being a test of geekiness. I agree sir.

[Tinteskou]

A quick chemistry question regarding Pi: The double bond between two carbon atoms, is made up of two bonds (obviously) the first bond is called a sigma bond, and the second is called a Pi bond, (according to my text book anyway) is this just because that as scientists & mathematicians we like to use Greek letters, or is there some special relevance between the ratio of a circle's circumference to it's diameter, that is also apparent in this bond?

[jerommeke69]

@Tinteskou

I can tell you with absolute certainty that is has nothing to do with the mathematical concept (i.e. the ratio of a circle's circumference to it's diameter).

It's because the electrons are in p-orbitals, therefore we call it Pi bonds

[gavyns]

you do have boring activities. but the world record is 67890 and there some one who claims to know the first 30 million but since that take nearly a year non stop I suggest you do it only if your really bored.

[orka16605]

3,1415926535897932384626433832­­7

[y0utuberjosh]

3.1415926535897932384626433832­795028841971693993751058209749­445923078164062862089986280348­253421170679821480865132823066­470938446095505822317253594081­284811174502841027019385211055­596446229489549303819644288109­756659334461284756482337867831­652712019091456485669234603486­104543266482133936072602491412­737245870066063155881748815209­209628292540917153643678925903­600113305305488204665213841469­51941511609

That's all i can remember :(

[DeltaPhi79]

So I'm 14... And I was able to memory 3.14159265358979323486 and I'm trying to memorize 4 more numbers... Am I a geek? XD

[freemakemoneyonline]

Pi is an irrational number. That is why it goes on forever. It cannot be fully understood since it is infinite.

[sbbzy272]

I know 53 digits of pi and i suck at math :D

[csgaylord]

THINK 113355. Now split it into 113 and 355. With a calculator, divide 113 into 355 and get 3.14159292..., correct to six decimal places!

[Films4You]

A Geek test... so this is what pi is really about

[Zee96969696]

here is infinity in the real world, or is Pi never accur in real world, is there no perfect sircles or perfect angles in real world? there probably are, therefore infinity does accur in real world, right?

[TardisGeek]

I once said to my maths tutor that if Pi and pie were the same by definition then Pi would equal the whole of circle rather than the ratio of C:D of the circle. But if it is the ratio of the C:D of a circle then why arn't pies served as half circles? At least that way we wouldn't get fat!

[wowrobs]

3.1415926535897932384626433832­795028841971... 40 significant figures :P

Oh no I'm a geek :P lol i got bored at work one day and memorised pi... i don't regret it!

[liamdot]

@wowrobs Thats only 2 significant figures. The other 38 are insignificant...

[cryodragoon]

3.14

I lose :(

[alexandre220011]

Ok, i always thought i'm geeky, now i'm sure i am! 3.14159265358979...

Just wanted to thank you for all these you add on youtube, it's really interesting, some more than other but it depends of our own interest. Thanks!

(and sorry if i made any english mistakes :p i come from Belgium)

[0Banjo0]

It's the marker guy! Yay

[IB4EAtheistConspiraC]

I guess I'm pretty high on the geek scale. I know 145 places thanks to a memorization contest in high school for Pi Day. I only managed 3rd place

[yamborghini3]

I know its 67, learnt it from y6 to y8

[ConnorXV]

@ Hnaef83

Funny cos i get one more number than you from memory! It's 2!! Mwahaha! Totally destroyed..you are powerless to me now mortal.

[ConnorXV]

@ Lilreaper1010

He didn't say it was pi he said it's a relatively good approximation of pi, when the exact value of pi is not necessary, shortcuts can be made by simply writing 22/7.

[1993gandy]

pi r square and pi r cubed :S thats not right :P pi r round

[okuma0kuma]

@1993gandy u r wrong divisions of Pi chart:

Pi (π) = ●=■=▲=▬=∞

:p

[LilReaper1010]

22/7 isn't pi.....if you look at the numbers after the sixth decimal place in 22/7 you will see that they aren't the same as pi!!!

[noxure]

@LilReaper1010 Off course not, it's a rational approximation and pi is an irrational number. People used those approximations because it's easier to make quick calculations without a calculator if you write pi as 22/7.

Pocket calculators were as expensive as a desktop computer in the 70's, so not many people started to use them before the 80's.

[odysseus9672]

You gotta be careful with how you write that product expansion for pi/2. If you just go off and start doing it the way it appears: (2 * 4 * 6 * 8 / (3 * 5 * 7 * 9))^2, you'll have an answer that appears to converge to zero. You actually have to do it this way: 2*2 / (1 * 3) * 4*4/(3*5) * ...

That the answer changes when you rearrange how you do the product reveals that the product converges conditionally, not absolutely.

MathWorld has a neat page on expansions for pi if you're curious.

[vivisilas666]

Beautiful Voice...

[TehNewV]

pi~~=22/7

[hnaef83]

Hmm... from memory, 3.14159265358979323846... Does that make me a geek?

[ausanibadisa]

i know 121 decimals lol!

[VanillaShoelace]

So is there then no way to define Pi as a series? The professor showed how to do it for Pi/2, Pi/4 and Pi^2, but what about plain old Pi?

[uut0]

i know some1 who knows 65 decimals of pi omg

[chrisofnottingham]

Does anyone else get annoyed that pi is defined as the ratio of circumference to diameter rather than circumference to radius?

If it were the radius, all those equations to do with rotation and frequency would just be pi, rather than 2pi all the time, and there would be pi radians in a circle. Simple.

Plus the radius is a more fundamental aspect anyway, since it relates the centre of a circle to its edge and is how we construct a given circle in a given position.

[Commentator732]

The diameter is more fundamental when it comes to size... pi relates the linear distance to the circular distance.

The radius is also very important, and 'fundamental' in the sense of construction, but the diameter expresses the apparent 'size' of a circle.

[chrisofnottingham]

I know what you mean but surely a radius defines size as much as a diameter but in addition it also defines the centre, which is one end of the radius. Actually the standard form of equations for volume & area of spheres & circles are all in terms of the radius.

But this isn't really the point. Virtually every equation you meet after GCSE level that involves pi, actually involves 2pi, basically because there are 2pi radians in a circle. There is even 'h bar' for planks constant divided by 2pi

[RonnnieBuckley]

The 137 annotation ended at 1:37. I wonder if that was intentional.

[sixtysymbols]

@RonnnieBuckley I'm not that geeky!!!

[RonnnieBuckley]

lol, Funny coincidence, though.

[smeghead666]

@sixtysymbols Lies!

[budman533]

@RonnnieBuckley I see 137 ALL THE TIME in my life...thanks for adding to it.

[TigerSlashX]

aw-sum

[Alphasys]

22/7 is a bad and crude approximation. I personally prefer 355/113 Which I also find easier to remember odd enough.

[TanksSkool]

3.1415926535897932384626433832­795028841971693993751058209749­445923078164062862089986280348­253421170679

[w1ngzer0]

I was hoping you would talk about the unit circle. Pi is very confusing.

[johnmacward]

Mmmmm.... mince pie.

[johnmacward]

When I get pi on a calculator: 3.142857142857143

That's different from his pi.

That's when I divide 22 by 7, like einstein above said!

Wonder what the number for mince pie is...

[PinkMEeTwo]

Really, only 90? I know 160! Beat that! HA!

[WasTechnology]

@PinkMEeTwo can you beat Daniel Tammet? he learnt pi to about 22 500 decimal places in only 1-2 weeks!!

[DaDaWgLLS]

I know 90 digits of pi. My geek level is OFF THE CHARTS!

[CoolKidAceSpade]

3.142 for circle.

[desiredusername]

This video has now shown up in my New Items box: 15 times

[desiredusername]

Sixteen

[desiredusername]

Seventeen.

[filipebr20]

Funny

[Hunnter2k3]

I personally prefer the Pi/2 version, such a nice way to express it, and explain to people as well.

[idiotatwack]

3.1415926535897932384626433832­795

[LWStupidus]

3.1415926535897932384626433832­795028841971693993751058209749­445923078164062862089986280348­253421170679821480865132823066­470938446095505822317253594081­284811174502841027019385211055­596446229489549303819644288109­756659334461284756482337867831­652712019091456485669234603486­104543266482133936072602491412­737245870066063155881748815209­209628292540917153643678925903­600113305305488204665213841469­51941511609...

[nospam671]

Ok... I like the numerical patterns created here... but what does it mean? My construction friends don't know math at all, but calculate these things on a daily basis without even blinking. Help me out here. There MUST be an easier way to figure all this out without knowing that Pie is something other than an awesome dessert at thanksgiving meal???

[sparxwil]

He said at the beginning, its the circumference/diameter.

[festmax]

It is stated very directly! ~ +++

[culwin]

This blew my mind

[oxygenownz]

boring :(

[x246869]

The 3'rd calc can't have the last /(nxn), just /(n) if multiply out the parts.

After 1000 calcs the values I got in excel for the 3 methods were all about the same and not as accurate as I thought they would be.

3.140592654

3.140638056

3.140807746

22/7 = 3.14285714

355/113 = 3.14159292

[thucydides01984]

The power series converge very slowly. I tried them in Excel. Also, his PI/2 formula (product of even numbers squared divided by product of odd numbers squared) doesn't seem to work. The first "term" is 2*2/3*3 = .889, much less than pi/2. More terms would only make it smaller. An error?

[TheReigningSupreme]

i would supposed as the number goes on by infinity, that you would have to do the calculations as a whole rather than by parts

but, i did the calculations in a scientific calculator, and got 2x2/3x3=4.

[ppzrjah]

(2x2)/(3x3) = 4/9 = 0.44444 etc... You have to be careful typing this into a calculator. What the calc did was 2x2 = 4, then when you divided by 3, it did 4/3= 1.333, then you multiplied that answer by 3 to give 1.333*3 = 4. Use the brackets on the sci calc "(2x2)/(3x3)"

[gobaskof]

There is an error. The first term should be

(2*2)/(1*3), the next is (4*4)/(3*5) then (6*6)*(5*7). And by the time you have 2 million numbers on the top and bottom you get

pi = 3.1415918682

[ghuegel]

gobaskof, that works. The series as shown in the video keeps shrinking from 0.444 at the start.

Thanks.

[NerdGradeA1]

3.1415926535897932384626433832­795028841971693993751058209749­445923078164062862089986280348­253421170679821480865132823066­470938446095505822317253559408­128481174502841027019385211055­596446229489549303819644288.

205 digits. I used to know 254 for a pi contest, which I lost. by like, 10 digits. dammit.

[Ezplain]

second place loses the hardest=P

[NerdGradeA1]

failz! :p.

[OhYeahMilkIt]

extreme geek

[NerdGradeA1]

and damn proud!

[kebabsallad]

Are you associating the space gaps after 30?,60,60 digits to easier remember what follows in a bunch. clearly easier for the brain to understand, ? maybe its some random spaces, but would be cool if I noted that :P

[NerdGradeA1]

i break it up into groups that are easy to remember if that is what you are asking.

[kebabsallad]

yeah exactly :)

[bb0ss]

pi suks wats so cool about it!!!??

[mantas1111000]

its nubers. look at comment wich is above yours. 205 DIGITS!!! AND POSSIBLY EVEN MORE!!!

[Paxmax]

I like pi ! makes my mouth water!  =o)

[kebabsallad]

In a methaphorical way?, of making you hunger for more knowledge about mathematics ;O ?

[Paxmax]

kebabsallad said: In a methaphorical way?

No, I like Pi spelled wrong! =o)

[solomsolomol]

And that's exactly why they invented scientific calculators !

[G3org3Master]

I agree.

[pin3appel]

i dont even like math, but i liked this video

[bng44270]

3.1415926535897932384626433832­795028841971693993751058209...

I memorized it in the 8th grade and can't forget it (dang it)

[jarjarbinks77]

wow pi is so long there even a space in it. :)

[SoronII]

Why memorize it :P?

[G3org3Master]

omfg? you lie? or do they teach you pointless things (hey should teach you to use a scientific calculator)

[blenderpanzi]

@bng44270 I never understood what it is good for to memorize such things. I does not give you ANY insight about it and you NEVER need it to this precision (if you then only in the context of doing science and you use a computer anyway).

[BasherCoon]

@bng44270 The song helps..

[holsson85]

Cool! But is Pi exactly 22/7 or round about 22/7?!!

[deathbyninjastar]

lol i am a teenager and I have ... about 120 or 130 digits in memoyry :( lol

[NerdGradeA1]

254 last few months, but I dropped down to about 205.

[JaksProductions]

proffessors fav. number is 137... .LEET!

[Forssa1]

Pi equals exactly three!!

[seanbrockest]

how year one of you!

[jtdreisb]

Pi can equal three. In 3 dimensions Pi can vary in value from 2-3.14158... Thusly you may have a ellipsoid where Pi is 3. Pi is only 3.14 in two dimensional planar geometry.

[Fordi]

"Thusly you may have a ellipsoid where Pi is 3"

Pi is the ratio between the circumference and diameter of a circle*. An ellipsoid does not meet the criterion for "circle".

Pi is never ever 3.0

* As defined as the curve inscribed a fixed distance from a point.

[Fordi]

(Ellipsoids are also not spheres, as defined as the surface inscribed a fixed distance from a point - it doesn't change in three dimensions either.)

[nitronixasd]

awesome, I love maths, its so cool. Even basic maths is good for everyday stuff, but remember one thing kids, algebra is useful and so is trigonometry. Remember the basics of those and you are set up for life be it a mechanic, carpenter, bricky, warehouse worker...you name it! Maths is only hard cos the person teaching you makes it hard!

[ReallyPsilly]

I was born on Pi day!

[seanbrockest]

Last spam, i promise

pi . ytmnd . com

[koolitaliano]

i like pie too!!!

[seanbrockest]

and dont forget 3.1415926535897932384626433832­795028841971693993751058209749­44592 . com

[seanbrockest]

3.1415926535897932384626433832­795028841971693993751058209749­445923078164062862089986280348­253421170679821480865132823066­470938446095505822317253594081­284811174502841027019385211055­596446229489549303819644288109­756659334461284756482337867831­652712019091456485669234603486­104543266482133936072602491412­737245870066063155881748815209­209628292540917153643678925903­600113305305488204665213841469­51941511609

Sorry i had to

[Kev888]

You're still missing a few digits :p

[RupertsCrystals]

Now, you rounded that off, didn't you? ;-)

[djunior874]

@seanbrockest and then..?

[RookieStudios]

makes u think off pi in a new way. good video :)