Today is Pi Day!

[Trickiert 150]

Happy Pi day. Have some Pi.

http://pi.ytmnd.com/ 

[SasQ 1,376]

I'm pretty sure pi is infinite. It just goes on and on, like my hatred for math.

But.... Pi is infinite.

Pi is infinite, which is why it's hard to put up the number.

Meh, it's finite.

 

Take a can of beer and put it on a table. Mark a spot on its rim and on the table at the same place. Start rolling the can until the spot goes one full circle and touch the table again. Then mark a spot on the table at this place. Now put as many cans in a line as you can before touching that other mark, and see how many you can fit in the whole distance the can traveled across the table. You'll get around 3 times and a bit.

You can as well take a piece of string and wind it around the can one full turn. Then straighten the string and see how many cans of beer you can put on it in a line. Again, you'll get around three.

"Around three" is not much infinite, isn't it?

 

It's just the number of decimal digits after the decimal point which is infinite. Not the number pi itself. This alone isn't anything extraordinary. Even the number 1 has infinite number of decimal places after the decimal point: an infinite number of zeros: 1.000000... or 1.0 (where the underline marks the digits which repeat without end). Similarly 1/9 has infinite number of decimal digits in its fractional part: 0.1111... or 0.1. That's because when you try to measure it, you'll fit 0 units in it, so you break your unit into 10 equal parts (1/10) and try with that, and you can fit one tenth in it, but you still have some little piece left, so you break your tenth into ten more pieces (1/100) and try with this, and you get another 1 (one hundredth) and still some little piece left. No matter how many times you repeat it, you'll always fit only one of your pieces in what's left and still have some little piece left. That's how 0.111111... comes to place.

 

But with 1 = 1.0, or 1/9 = 0.1, or 1/7 = 0.142857, or any other fraction, these digits will start to repeat somewhere, making a pattern of digits. This is not the case with pi or any irrational number which is not a fraction. Those are numbers "in between of fractions", and if you tried to express them as fractions, you would need fractions with infinite number of digits.

 

The decimal expansion is also just a fraction written in a compact way. Instead of writing e.g. 1234/1000, you write 1.234, which is:

1 + 2/10 + 3/100 + 4/1000

But if you wanted to express pi this way, it would be:

3.14159265... = 3 + 1/10 + 4/100 + 1/1000 + 5/10000 + 9/100000 + 2/1000000 + 6/10000000 + 5/100000000 + ...

or, if you tried with just one fraction, you'd get:

314159265.../1000000...

but you would have to put down infinite number of zeros in the denominator, and infinite different digits in the numerator. That's why pi (and any other irrational number) cannot be expressed as simple fraction.

 

BTW why do you hate math? Bad memories from schools?

Then I tell you something: What they taught you in schools is NOT math! It's some bastardized piece of gibberish they made from it to make you hate it for the rest of your life and never figure out the beautiful patterns of how Nature and the whole Universe works. Because mathematics is all that: it's the language of Nature itself, expressed by every little and big piece of it, a beautiful symphony of life.

 

 

Once I hated math too, and learning it in schools was a nightmare for me, since I didn't get it. But one day I was looking at these:

 

 

in my bathroom and noticed something intriguing: that they all spiral in the same freakin' direction! It bothered me, and I started digging the Internet, finding more and more evidence that they all turn this way. There's only one species of snail on this planet, in India, whose shell turns the opposite direction, and it's so rare that Hindu people supposedly praise it as a sacred animal. I was curious why Nature choses this particular pattern, and why does it look so beautiful and is so efficient in space. And that's how my adventure with REAL mathematics has started.

Edited March 14, 2014 by SasQ

[Wind Chaser 4,768]

I just found Pinkie Pie's number!

 

8.53973422267

[Zyla Fae 5,405]

Meh, it's finite.

Pi is infinite, it goes on and on forever, it may not be infinitely BIG, but it's infinitely long, which in a way is what you said, though you don't seem to want that to be true from the way you said it...

Pi is infinitely long, just not infinitely big.

[SasQ 1,376]

Pi is infinite, it goes on and on forever, it may not be infinitely BIG, but it's infinitely long, which in a way is what you said, though you don't seem to want that to be true from the way you said it... Pi is infinitely long, just not infinitely big.

I know what I said, and I still hold it.

 

The "pi is infinite" thing is a common misconception repeated over and over by people who don't understand what they repeat. It's not the number pi which is infinite. It's its decimal expansion which is infinite. The number pi itself is finite, and I even proposed a simple experiment which you can do on your own to convince yourself that it's true. Have you done it? Or you just repeat what someone told you?

 

The string going around the can of beer is not infinitely long, nor infinitely big. Even in comparison with the diameter of the can. But when you try to express pi with digits, then you will go into an infinite process.

 

Don't confuse the infinitude of the process of measuring some thing with that thing itself. You can measure any finite number with an infinite number of steps, getting infinite number of digits as well. For example, you can take a wooden stick of unit length and try to measure it with 1/10 stick. You will fit 9 such stick there, and instead of putting the remaining tenth stick, you can break it into 10 smaller pieces and try with these, fitting another 9 hundredth parts there, and so on, getting 0.99999... and so on into the infinity, even if the stick has finite length of 1.

 

Don't let the digits deceive you!

 

 

There was a guy in Ancient Greece called Zeno of Elea, who invented a clever "paradox" to show this exact error people made with digital notation. He showed that one can take a unit distance (say, one step long) and walk only half of it (half a step), and then half of the remaining half (1/4), and another half (1/8), and so on, which will turn into an infinite process of halving and you'll never get to the end of your road. But the road is finite. You can just walk one full step right away. You can see this as expressing 1 in binary notation: 0.111111 (which means: 0 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + ...), an equivalent of 0.9999... = 1 trick in decimal notation. (Yes! Binary digital notation long before computers, in Ancient Greece! Want more? Check out I-ching code from Ancient China, on which Leibniz based "his" binary digital system.)

 

People call it "paradox" to this day, and even call Zeno unfamiliar with modern math (the notion of limit from Calculus), but it's them who don't understand numbers, confusing them with their digital notation. Zeno was not stupid. He wanted to show those "digit lovers" (yeah, digital freaks were already there, long before digital computers) that there's something more in numbers than their digits (this something is geometry). And one can escape the apparent "paradox" by understanding this fact. This "paradox" was an eye-opener, similar to Koans of Zen.

Edited March 14, 2014 by SasQ

[Vinyl Scratch. 604]

Just because I wanna be "that guy" the first 2000 digits of pi are: 

3.141592653589793238462643383279502884197169399375105

82097494459230781640628620899862803482534211706798 
21480865132823066470938446095505822317253594081284 
81117450284102701938521105559644622948954930381964 
42881097566593344612847564823378678316527120190914 
56485669234603486104543266482133936072602491412737 
24587006606315588174881520920962829254091715364367 
89259036001133053054882046652138414695194151160943 
30572703657595919530921861173819326117931051185480 
74462379962749567351885752724891227938183011949129 
83367336244065664308602139494639522473719070217986 
09437027705392171762931767523846748184676694051320 
00568127145263560827785771342757789609173637178721 
46844090122495343014654958537105079227968925892354 
20199561121290219608640344181598136297747713099605 
18707211349999998372978049951059731732816096318595 
02445945534690830264252230825334468503526193118817 
10100031378387528865875332083814206171776691473035 
98253490428755468731159562863882353787593751957781 
85778053217122680661300192787661119590921642019893 
80952572010654858632788659361533818279682303019520 
35301852968995773622599413891249721775283479131515 
57485724245415069595082953311686172785588907509838 
17546374649393192550604009277016711390098488240128 
58361603563707660104710181942955596198946767837449 
44825537977472684710404753464620804668425906949129 
33136770289891521047521620569660240580381501935112 
53382430035587640247496473263914199272604269922796 
78235478163600934172164121992458631503028618297455 
57067498385054945885869269956909272107975093029553 
21165344987202755960236480665499119881834797753566 
36980742654252786255181841757467289097777279380008 
16470600161452491921732172147723501414419735685481 
61361157352552133475741849468438523323907394143334 
54776241686251898356948556209921922218427255025425 
68876717904946016534668049886272327917860857843838 
27967976681454100953883786360950680064225125205117 
39298489608412848862694560424196528502221066118630 
67442786220391949450471237137869609563643719172874 
6776465757396241389086583264599581339047802759009

[Surface 115]

Here is some music on SoundCloud. xD

[Totally Ducklett 181]

YAAAAAAAAAAAAAAAAAAAAAAAAAY! Pi Day! Piiii! π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π π !

 

PIIIIII!

 

Hey, anypony gonna go do something special? I'm going to go get some pie to eat :3

 

http://25.media.tumblr.com/047bf9b6d894126e442d3cc4c2caf2f4/tumblr_mjoexowtCt1r7jepho1_1280.jpg

Edited March 14, 2014 by Ducksquack

[~Silver Essence~ 2,625]

It's pie day? Nice.

 

And as a hooray for today, enjoy the whole complete section of pi!

 

[Lightwing 12,970]

What kind of Pi Day is a Pi Day without its exclusive animation?

 

[Zyla Fae 5,405]

I know what I said, and I still hold it.

 

You know, I've always loved a good debate...

 

First thing's first, I've heard of Zeno and his paradoxes, and I've always had fun with those, but the problem with what you're saying is that infinity doesn't always mean extremely big. For instance, in the paradoxes that you just referenced, the distance that an infinitely long sequence leads you to (the limit) is 2, which although it required an infinity to get to, it's not infinitely big.

But another problem with what you're saying is that infinitely doesn't just mean "Bigger than anything else" it means endless, and π has no end, you can't stop at a finite number of digits, meaning that it's infinitely long, and is endless.

[CMQuickfireTK 751]

So's who going to treat themselves to a Raspberry Pi this 3.141592 day?

[Zyla Fae 5,405]

So's who going to treat themselves to a Raspberry Pi this 3.141593 day?

Why would I eat a computer?

 

I prefer chocolate chess pie to raspberry actually

Edited March 14, 2014 by Somepony

[CMQuickfireTK 751]

Why would I eat a computer?

 

On the contrary, the Computer will eat chur knowledge!

[Discordian 6,015]

It's pie day? Nice.

 

And as a hooray for today, enjoy the whole complete section of pi!

 

I have nothing to add to this topic now. I came here to post this.

 

Still one of the most entrancing songs I've ever heard.

 

Oh wait, I CAN contribute!

 

Walmart has these minipie things for about a dollar. For about $3.14 one can buy about 3.14 minipies. The universe, and Walmart, loves Pi.

[Starbound 150]

Happy PI day everyone!

 

I've memorized about 450 digits of Pi so far, but scientists and mathematicians have teamed up to calculate it up to the 5 trillionth digit!

 

3.141592653589793238462643383...

[ninjamon102938 222]

We had cookies in class today to celebrate

[Starbound 150]

 

But don't forget Phi! Say January 6th if you know about Phi and the Golden Ratio.

[UltimaX 63]

Today is Pie day

Its also Albert Einstein's Birthday

 

But  the least important  of today events and birthdays would be my sister's birthday.

[SasQ 1,376]

You know, I've always loved a good debate...

Me too There are some things which are debatable (e.g. opinions), but there are also those which aren't: the scientific truths. One doesn't debate about 2+2=4. It's a fact, which can be easily verified (that is, proven to be true). Same with the number pi being finite. (I proposed a simple experiment above. Have you done it already?)

 

First thing's first, I've heard of Zeno and his paradoxes, and I've always had fun with those, but the problem with what you're saying is that infinity doesn't always mean extremely big.

I know that, but I don't know how it follows from what you said about Zeno's paradoxes (classical non sequitur). Infinity doesn't say anything about being big or small, since it's not a number or magnitude: it's a way of telling that some process never ends; that one can continue it at will. As with the process of generating the digits of the decimal expansion for pi.

 

But it's that process which is infinite, not the number itself. You seem to confuse those two.

 

"3.14159..." is not pi, at least from the fact that it isn't complete yet: lots of digits are missing in place of the "...". One cannot put down all the digits, but one can put down a piece of string of length pi: just make a circle of unit diameter, wind a string around it (one whole turn), and unwind it. Its length will be to the diameter as pi is to 1 (notice how numbers are always relative: any length can be a circumference of the circle; it is equal to pi only in comparison to some unit, when this unit happens to be the diameter of that circle). And this length will be finite.

 

Again, don't confuse the digital notation of some number with the number itself. There are more numbers than you can express with digits. Actually, you can express only fractions in a finite way, and only if the denominator consists only from factors of 10 (that is, 2 and 5), if you want to use the decimal system. Otherwise, your computing algorithm will fall into an infinite loop. Even for number 1/3, if you try to express it digitally in binary or in decimal.

 

Remember Zeno. He knew the limitations of digital computing long before computers were made

 

For instance, in the paradoxes that you just referenced, the distance that an infinitely long sequence leads you to (the limit) is 2

Now I see clearly that you're repeating knowledge without thinking about it, since in my example the limit was 1, contrary to the example usually presented on Wikipedia or in books

 

I know that the limit is finite (1), and Zeno know that too. That's exactly the point of his "paradox": you have a finite number (unit distance) in hand, but the process you use to express this number with digits turns out to fall into infinite loop of generating the same sequence of digits over and over. You can get this effect with any number whatsoever (e.g. try to express 1/7 in decimal). But with irrational numbers, such as pi or root(2) or the golden number Phi = root(5)/2 + 1/2, the sequence of digits is assured to not repeat (since if it started repeating somewhere, one could convert it to some finite fraction).

 

The point of Zeno's paradox was to show to the "digital freaks" that the sequence of digits and the algorithm used to generate it for some number is not the number itself. A number can be finite, but still can cause an infinite loop in digital processing. That's because this tool (digital computing) has some limits. No digital computer will ever capable of storing irrational numbers. They can only store their approximations by binary fractions, written with finite number of digits. Zeno knew that, and he wanted to open the eyes of his fellows too, and that's what he invented these paradoxes for.

 

Paradox is a way to show the error in one's thinking, because there are no paradoxes in Nature; only in our theories, when the theories are wrong. You start with false assumptions, perform the stream of logical thought, and you come to a paradox (or contradiction). What does it tell you? If the whole deduction was correct, this can mean only one thing: that your assumptions were wrong. And the only way to escape from paradox is to change your assumptions. That's exactly the exit from Zeno's paradoxes too: As long as you confuse numbers with their digital notation, you'll be going in circles (pun intended ;J it's a Pi Day after all). But when you notice your mistake and change your assumption that "pi is 3.14159..." (that is: that the number is the digits we use to denote it) to something else: that number is NOT the same as its notation, then your eyes are opened and the paradox disappears

 

I like to see digital notation as an algorithm (a computer program to generate numbers according to some pattern -- this pattern is the long division). And this algorithm is good for some numbers (rational numbers, that is, fractions, when they have common factors with the base of the numerical system), but it fails for others:

It fails for fractions which don't have any common factors with the base of the numerical system (then it repeats the same sequence of numbers again and again in an infinite loop).

It fails for irrational numbers (then it generate a sequence of numbers which doesn't repeat anywhere, and it can generate it over and over without any end).

Knowing these limitations you can use this algorithm wisely for these types of numbers it applies to, and stop wasting your time using it for numbers it doesn't apply well. There are other algorithms, better suited for those types of numbers, which can express them in finite way. Geometry is one of them.

 

which although it required an infinity to get to, it's not infinitely big.

That's exactly my point.

Now apply it to pi: although it requires an infinite number of steps to get all the digits of pi (which in practice means that you won't get them all in any time, since you don't have unlimited time), it doesn't mean that the number pi itself is infinite. It's only its digital notation and the algorithm used to generate it which is infinite. The number itself is a bit more than 3, and obviously less than 4. It's finite, as I've already said.

 

But another problem with what you're saying is that infinitely doesn't just mean "Bigger than anything else" it means endless

I know that.

 

and π has no end

Not pi, but its digital notation.

Can you see the difference yet?

 

Which of these numbers is the number one?:

1 (or 1.000000...)

0.9999999...

 

The answer may surprise you (judging by what you wrote so far): none of them. They're all different notations (or "names") of the number one. But is your name the same as the actual you? Is the English word "dog" the same as the actual dog? Recall that in different languages this dog can be represented with different words. Eg. "chien" in French, "hund" in German, "pies" in Polish etc. Different names for the same dog. The same goes with "1", "one", "1.0000..." and "0.9999...": they're all different names for the actual number one, but they're not the number itself. You can invent some algorithm for generating those names in a structured manner, and if your algorithm is not perfect (as with long division), sometimes it can fall into an infinite loop and generate infinite sequences of characters as a name. But it won't mean that the object with that name is infinite itself.

 

I hope it cleared the matters for you.

Edited March 14, 2014 by SasQ

[Scootalove 10,689]

What a wonderful Pi day, where we celebrate the day that Pi was introduced.

[Fantasma Phantasm 673]

Its awesome to know that Pi is the infinity number in physical form. HAPPY PI DAY! Pi apparently is an interesting concept.,.

[SparklingSquirrels 21,341]

I know 3.1415926535, off the top of my head. I probably knew more at one point, but I forgot XD

[Ihei 713]

Who else baked a Pi pie today? Heh, next year it's going to be 3.1415.

Edited March 15, 2014 by Shaymin

[Commander Bubbles 1,343]

Pi day is also my sister's birthday!