Calculating pi debate, arguement, discussion AND contest...! [Including other maths]

[yauhui]

Here's where we discuss about pi!

I somehow calculated to 8,000,000 decimal places :cool:

but too bad i copied it to notepad and it hanged! :mad:

So i posted it to a friend via msn.. but too bad msn messenger has text limits so here's the txt file my friend sent back to me..

Here:

[Plasma]

Right...
And you foind this number out... how, exactly?

[MrBunsy]

Pi can be expressed as the sum of an infinite series, if I remember correctly. So I presume you can get programmes which sum together a very large number of terms of such a sequence.

[Nugget]

... You are aware that the number you posted isn't Pi? It's just a tiny flick of it. Pi goes on forever, never ends.

[Paul.Power]

... You are aware that the number you posted isn't Pi? It's just a tiny flick of it. Pi goes on forever, never ends.Welll, "tiny flick" isn't quite fair, because of the decimal point after the 3. It's an accurate answer to within 0.0000125%.

(I still prefer e, though :p)

[thomasp]

That document is only Pi to 1098 decimal places. Here's pi to one million: http://3.141592653589793238462643383279502884197169399375 105820974944592.com/index1.html, which is considerably more accurate - especially when you need to do things like work out the circumference of the universe.

[Paul.Power]

That document is only Pi to 1098 decimal places. Here's pi to one million: http://3.141592653589793238462643383279502884197169399375 105820974944592.com/index1.html, which is considerably more accurate - especially when you need to do things like work out the circumference of the universe.

... ya know, I didn't actually think to check his document when I gave my accuracy remark.

Anyway, everyone knows that real astrophysicists take Pi to be the square root of 10. When they aren't taking it to be 10, that is :p.

[Pickleworm]

Pi sucks, I don't believe in it.

[Kelster23]

Why do people spend so much time caculating out pi to x number of decimal places anyway? Is there any instances where people use it to that many decimal points?

[MrBunsy]

Why do people spend so much time caculating out pi to x number of decimal places anyway?
Because we can.

[thomasp]

... ya know, I didn't actually think to check his document when I gave my accuracy remark.

Anyway, everyone knows that real astrophysicists take Pi to be the square root of 10. When they aren't taking it to be 10, that is :p.

I'm surprised you didn't turn that round into an insult against engineers. We always use the "PI" function in Matlab, which gives it to 20dp or something stupid like that. If we're accurate on one thing, it's our pies :p

[SupSuper]

Why do people spend so much time caculating out pi to x number of decimal places anyway? Is there any instances where people use it to that many decimal points?

Mathematicians need something to do.

[farazparsa]

Why do people spend so much time caculating out pi to x number of decimal places anyway? Is there any instances where people use it to that many decimal points?
Short answer: Yes. Pi is a strange constant, but also helpful is solving things like circumferences and areas of prisms like circles, cones, and the like.

[Paul.Power]

I'm surprised you didn't turn that round into an insult against engineers. We always use the "PI" function in Matlab, which gives it to 20dp or something stupid like that. If we're accurate on one thing, it's our pies :p

Mostly because the astrophysics one is true :p. The engineer insults are just jokes: I really have a lot of respect for what engies do, even if your approach to calculation does make me recoil in horror :p.

I'm an astro and a mathmo. It's a strange combination, but it at least gives me a foot in both camps.

[AndrewTaylor]

Mostly because the astrophysics one is true :p. The engineer insults are just jokes: I really have a lot of respect for what engies do, even if your approach to calculation does make me recoil in horror :p.

I'm an astro and a mathmo. It's a strange combination, but it at least gives me a foot in both camps.

Yes, well you could put both feet in the maths camp and call it approximately the astro camp.

[quakerworm]

Pi can be expressed as the sum of an infinite series, if I remember correctly. So I presume you can get programmes which sum together a very large number of terms of such a sequence.
by far the simplest algorithm is pythagorean one. start with a regular hexagon with a side = 1. inscribed in a unit circle. perimeter of that hexagon is 6, which is your first estimate of circumference of unit circle, or basically of pi*2. add segments from center of the circle to each vertex, giving you 6 triangles. now, bisect each triangle from center, and extend each bisector to the circle. connect the points of intersection with circle and the vertecies of the hexagon. you now have a regular do-decagon. you can use pythagorean theorem to get the length of each side, giving you a new perimeter, which is a better approximation of 2*pi. keep subdividing, and you will have a polygon with more and more sides, giving you closer and closer approximation.

the problem with this algorithm is that it does not converge very well. there are better algorithms for computing pi, but they are less geometrical and more mathematical. i have been told that there is even an algorithm that directly gives you an nth digit of pi. of course, the number of steps still depends on n, but not as bad as if you wanted to get all of the digits up to that point as well.

[yauhui]

what are the differences between different algorithms? like Chudnovsky, Gauss-Legendre, Borwein, etc etc etc. They still give the same answer, dont they?

wait... pi to 8million places is coming up! (my notepad hanged again)

[quakerworm]

speed. some algorithms are fast for first few hundred thousand digits, but then slow down. others start out slower, but they don't slow down quite as fast later, so that's what you typically want if you want a few million digits. stuff like that.

[yauhui]

which is fastest when calculating to 100 million? (damn notepad.)

[_Kilburn]

I have done a quick C program that could calculate up to 1 million places. When you wanted to calculate more, it started to be really slow, though.

[Paul.Power]

which is fastest when calculating to 100 million? (damn notepad.)

Use Wordpad, then. It's common knowledge that Notepad can only handle files that are so big

(Also, have fun with your 100MB+ file)

by far the simplest algorithm is pythagorean one. start with a regular hexagon with a side = 1. inscribed in a unit circle. perimeter of that hexagon is 6, which is your first estimate of circumference of unit circle, or basically of pi*2. add segments from center of the circle to each vertex, giving you 6 triangles. now, bisect each triangle from center, and extend each bisector to the circle. connect the points of intersection with circle and the vertecies of the hexagon. you now have a regular do-decagon. you can use pythagorean theorem to get the length of each side, giving you a new perimeter, which is a better approximation of 2*pi. keep subdividing, and you will have a polygon with more and more sides, giving you closer and closer approximation.

Aha! So our second-order approximation for π is 30934

(or 3.1058... if you want to be crude and boring about it)

Good old Archimedes :)

EDIT: Third-order approximation for π: 30935

(or again, 3.1362... if you want to be crude and boring about it)

I think I'm spotting a pattern here...

EDIT: Yyyep. Definite pattern. Here's the fourth-order one: 30936

(For the boring, crude people: 3.13935...)

Looks like I should be able to prove this by an induction of some kind.

EDIT: Yeah, here we go: http://img401.imageshack.us/img401/50/piproofru2.th.jpg (http://img401.imageshack.us/my.php?image=piproofru2.jpg)

Here, have an algorithm:

Input n
x = 1
For i = 1 to n
x = √(2 + x)
Next i
y = √(2 - x)
Answer = 3 * 2^n * y

Let's see what Excel makes of it:

http://img250.imageshack.us/img250/6603/piexceldy0.th.png (http://img250.imageshack.us/my.php?image=piexceldy0.png)

... yeah, it breaks down after a while due to rounding errors. That's the toughest bit about it: finding nice variables that can cope with silly numbers of digits.

[yauhui]

wait.. what's a radix? e.g. calculate pi to 8 million radix 10 digits

[AndrewTaylor]

It's the same as a base. So calculating pi in base 10 gives 3.1415... but calculating it in base 2 might give 11.00101... (I just did that in my head so it might be wrong).

Of course, calculating pi to 8 million radix pi digits is easy: it's 10.0 recurring. It's not very helpful, mind.

[yauhui]

Use Wordpad, then. It's common knowledge that Notepad can only handle files that are so big

Whoa. wordpad didnt lag a bit!

p.s. :( the file turned out to be 7 megs.

it is 3megs after compression.

right now i am uploading the 8 million decimal places pi text file to FileFactory AND WillHostForFood.

<uploading......>

Server 1:

WillHostForFood
http://www.willhostforfood.com/files/185257/pi.txt
http://www.willhostforfood.com/files/185257/pi.txt.png (http://www.willhostforfood.com/access.php?fileid=8217)

Server 2 (if WHFF fails)

FileFactory
http://www.filefactory.com/file/10ed70/

[AndrewTaylor]

I wonder how we could check this result.

[yauhui]

take your time ;)

[tal05]

Pi sucks, I don't believe in it.

lol
thats like saying "i don't believe in 3 because it looks like an ass when turned sideways":o

[thomasp]

I wonder how we could check this result.
Matlab. God knows how many DP of pi that evil thing has. Or write a script to accurately work pi out.

[Akuryou13]

I wonder how we could check this result.I'll explain the mathematic formula in a quick 2 step method:

1. calculate the circumfrence of the head of the nearest sledge hammer.

2. apply directly to the forehead.

[Paul.Power]

Y'know, really I should have called that "stuf²"

[AndrewTaylor]

Matlab. God knows how many DP of pi that evil thing has. Or write a script to accurately work pi out.

Well it doesn't have 8 million digits, does it? It only runs 32-bit arithmetic.

(Sure, you could write a script to calculate digits beyond that, but I'm not going to, and I'm certainly not going to sit there while it runs the damn thing.)

[quakerworm]

... yeah, it breaks down after a while due to rounding errors. That's the toughest bit about it: finding nice variables that can cope with silly numbers of digits.
just engineer your own high precision class with custom sqrt function, and run it in c++. you'd probably want to machine code the algebra, though, or you will be pretty far from peak performance.
Of course, calculating pi to 8 million radix pi digits is easy: it's 10.0 recurring. It's not very helpful, mind.
any base where 1+1 gives you a number that you have no way of writing tends to have problems.

[yauhui]

anyone wish to check my answer? www.8-million-pi.tk :cool:

[Paul.Power]

you'd probably want to machine code the algebra, though, or you will be pretty far from peak performance.You're forgetting something: mathmo.

I've just proved that the thing can calculate pi, so why should I test it? A solution exists, that's all I need to know.

[AndrewTaylor]

any base where 1+1 gives you a number that you have no way of writing tends to have problems.

Not if you're an astrophysicist. Just approximate it to one. Or pi. Or zero. Or a cat. They just don't care.

[robowurmz]

Because we can.

Aperture science...we do what we must, because, we can.
[/song]

Pi is very interesting, but it's hardly ever used beyond about 12 decimal places...why didn't we just stop at about a million?

[quakerworm]

Pi is very interesting, but it's hardly ever used beyond about 12 decimal places...why didn't we just stop at about a million?
some people are still trying to derive a simple formula for pi, despite the fact that it is a transcendental number.

[Pickleworm]

anyone wish to check my answer? www.8-million-pi.tk :cool:

One of your 5s should be a 6. Other than that, perfect.

[Paul.Power]

Aperture science...we do what we must, because, we can.
[/song]

Pi is very interesting, but it's hardly ever used beyond about 12 decimal places...why didn't we just stop at about a million?

Because quite a few people genuinely find it fun.

I have to admit, I can't see the point. π is π. We already have an accurate way of expressing it: π.

(Saying that, I can remember that e starts out 2.718281828459045... but only because the mnemonic is dead easy)

[thomasp]

Dare I ask what the mnemonic for remembering e is?

[Paul.Power]

Dare I ask what the mnemonic for remembering e is?

2.7
1828
1828 <-- same bit repeats twice
45
90 <-- twice 45
45 <-- 45 again

EDIT: Speaking of repeats, how come we haven't brought up the Feynman Pi Joke yet?

[Plasma]

I have to admit, I can't see the point. π is π. We already have an accurate way of expressing it: π.
I agree. The only two things you need to remember about it is that it's equal to 3.14 or 22/7, the latter should be only used when there is a question regarding multiplying pi by seven and if you don't need to have it accurate.

(alright, so the only real time you have to use the latter is if you ever get asked 'is 7pi an integer?', and a variation of that did actually come up in a non-curricular maths test I did a few weeks ago)

[yakuza]

anyone wish to check my answer? www.8-million-pi.tk :cool:

Care to share how did you find out? I'm a bit confused after you asked what the difference was between different algorithms, your concern being, that how can they be different when they share the same response, you also seemed to ignore what a radix is, don't take this as an accusation please, I'm only curious.

[Shadowmoon]

What is this thread about?:confused: Maths?
i don't understand what its about

[MrBunsy]

What is this thread about?:confused: Maths?
i don't understand what its about

Then read the thread or don't post.

[Shadowmoon]

I have. Not everybody understands what the thread is about.

[Plasma]

I have. Not everybody understands what the thread is about.
Here's a tip:
'Calculating pi debate'

[Shadowmoon]

But what is calculating pi debate? i know the name, but what is this thread about?

[MtlAngelus]

It is about calculating pi.

If you don't know what pi is, then: http://en.wikipedia.org/wiki/Pi

[Shadowmoon]

So it is maths.... okay thats weird.

[MrBunsy]

So it is maths.... okay thats weird.

Not really. For someone who claims to be 27, I don't believe you don't know what pi is, even if you don't know how it can be used.

[yakuza]

He's 12 .

[MrBunsy]

Then why does his profile say he was born in 1980?

And if he's 12, he should definitely know roughly what pi is.

[Paul.Power]

12-year-olds should know what pi is. I knew what it was when I was 12 (even though I thought it was 22/7 :p)

[yakuza]

I was just saying how old he is, by no means I'm trying to justify his ignorance with his age.

[MrBunsy]

I was just saying how old he is, by no means I'm trying to justify his ignorance with his age.

Fair point, I shouldn't have directed that at you.

[Kelster23]

I didn't learn about pi until I was 13.
And my teacher was retarded. I almost failed math 2 years in a row.
Then I almost bombed the Grade 10 Provincial exam. His fault.

[quakerworm]

EDIT: Speaking of repeats, how come we haven't brought up the Feynman Pi Joke yet?
you mean the feynman point at the 762nd decimal place? here is a quick math problem: compute pi as a fraction assuming that after feynman point the last digit really did keep repeating. shouldn't take you more than a few seconds to figure it out.

[Pickleworm]

Iguana, please go away :(

[yauhui]

One of your 5s should be a 6. Other than that, perfect.

yay.

Yauhui and his whole class spent weeks (since there's nothing else to do once the exam finished) calculating pi. all they assumed was 22/7, and all they did was 22/7. on many pieces of large papers stuck together. but the class refused to take credit for it. and they gave it to yauhui. because he was the one who had that stupid suggestion.

[Shadowmoon]

It says 1980 because the person that told me about here said 12-16 year olds aren't allowed on the forum. Thats why i put in 1980 I am not 27, i am 12. And i am going to turn 13 next year. I haven't learn about pi yet, so i don't know what it is. But i will probably find out next year or something.

[Paul.Power]

you mean the feynman point at the 762nd decimal place? here is a quick math problem: compute pi as a fraction assuming that after feynman point the last digit really did keep repeating. shouldn't take you more than a few seconds to figure it out.

Oh, that's easy enough.

First we observe that if the nines did go on forever then it'd round up the previous digit (since 0.9 recurring = 1 and if people start denying that then they'll get more than they bargained for)

3. 1415926535897 9323846264338 3279502884197 1693993751058 2097494459230 7816406286208 9986280348253 4211706798214 8086513282306 6470938446095 5058223172535 9408128481117 4502841027019 3852110555964 4622948954930 3819644288109 7566593344612 8475648233786 7831652712019 0914564856692 3460348610454 3266482133936 0726024914127 3724587006606 3155881748815 2092096282925 4091715364367 8925903600113 3053054882046 6521384146951 9415116094330 5727036575959 1953092186117 3819326117931 0511854807446 2379962749567 3518857527248 9122793818301 1949129833673 3624406566430 8602139494639 5224737190702 1798609437027 7053921717629 3176752384674 8184676694051 3200056812714 5263560827785 7713427577896 0917363717872 1468440901224 9534301465495 8537105079227 9689258923542 0199561121290 2196086403441 8159813629774 7713099605187 0721135

Now we multiply the whole thing by 10^761

31415926535897 9323846264338 3279502884197 1693993751058 2097494459230 7816406286208 9986280348253 4211706798214 8086513282306 6470938446095 5058223172535 9408128481117 4502841027019 3852110555964 4622948954930 3819644288109 7566593344612 8475648233786 7831652712019 0914564856692 3460348610454 3266482133936 0726024914127 3724587006606 3155881748815 2092096282925 4091715364367 8925903600113 3053054882046 6521384146951 9415116094330 5727036575959 1953092186117 3819326117931 0511854807446 2379962749567 3518857527248 9122793818301 1949129833673 3624406566430 8602139494639 5224737190702 1798609437027 7053921717629 3176752384674 8184676694051 3200056812714 5263560827785 7713427577896 0917363717872 1468440901224 9534301465495 8537105079227 9689258923542 0199561121290 2196086403441 8159813629774 7713099605187 0721135

Now stick a "/10^761" underneath.

31415926535897 9323846264338 3279502884197 1693993751058 2097494459230 7816406286208 9986280348253 4211706798214 8086513282306 6470938446095 5058223172535 9408128481117 4502841027019 3852110555964 4622948954930 3819644288109 7566593344612 8475648233786 7831652712019 0914564856692 3460348610454 3266482133936 0726024914127 3724587006606 3155881748815 2092096282925 4091715364367 8925903600113 3053054882046 6521384146951 9415116094330 5727036575959 1953092186117 3819326117931 0511854807446 2379962749567 3518857527248 9122793818301 1949129833673 3624406566430 8602139494639 5224737190702 1798609437027 7053921717629 3176752384674 8184676694051 3200056812714 5263560827785 7713427577896 0917363717872 1468440901224 9534301465495 8537105079227 9689258923542 0199561121290 2196086403441 8159813629774 7713099605187 0721135/10^761

[yauhui]

i am 12.

you're the same age as me! (tip: select "Hide age and date of birth" or something like that in your Profile (User CP > My Profile) and no one'll know)

And if he's 12, he should definitely know roughly what pi is.

I havent learn about pi you know. all we did was 22/7.

[Paul.Power]

tip: select "Hide age and date of birth" or something like that in your Profile (User CP > My Profile) and no one'll knowInstead, they will assume that you're 16+ and mentally subnormal. Your call.

[Akuryou13]

(tip: select "Hide age and date of birth" or something like that in your Profile (User CP > My Profile) and no one'll know)yauhui, you haven't fooled anyone yet, so how can you give advice on the subject? :p

[Plasma]

Alternatively, you could send a pm to Volcadmin and claim that your date of birh had changed.

[yauhui]

yauhui, you haven't fooled anyone yet, so how can you give advice on the subject? :p

I havent fooled anyone because i already said that i was 12 when i first came to this forum.

[Akuryou13]

I havent fooled anyone because i already said that i was 12 when i first came to this forum.my point was more that none of us really have to check the profile to know, regardless of you stating it at any point :p

[Run]

it explains this travesty

[MrBunsy]

I havent learn about pi you know. all we did was 22/7.Really? Where do you go to school? We did pi and the golden ratio and such in Year 6.

[pilot62]

I can't remember when I learnt about pi (nor do I particularly care, for that matter), probably year 7, but maybe later.

I never learnt any of this 22/7 stuff though, I'd never heard anyone use that as pi until this thread. We just used the button on our good ol' 'scientific' calculators. ;)

[Shadowmoon]

What year do you do pi in? Year 9?

[yakuza]

The same year you learn about circles, squares and maybe triangles.

[Paul.Power]

What year do you do pi in? Year 9?

Pi comes up as soon as you do anything quantitative with circles.

Heck, I remember questions about pi on my Year 6 Maths Extension SAT (Really complex questions too, as it happens: calculating the area of a circle with a bit of the circle lopped off by another circle, you know, like in an eclipse. I still don't think I've found out how to answer a question like that. Needless to say, I didn't actually pass the extension paper and I ended up with 5, 5, 5 as my Year 6 SATs scores)

[SupSuper]

For me it was probably when we learned to calculate areas.

[quakerworm]

Oh, that's easy enough.
indeed. i just didn't want to do all the copy-n-pasting. :p
]First we observe that if the nines did go on forever then it'd round up the previous digit (since 0.9 recurring = 1 and if people start denying that then they'll get more than they bargained for)
now take that proof, and apply it to ...9999999.0 and get -1. what went wrong?
Really complex questions too, as it happens: calculating the area of a circle with a bit of the circle lopped off by another circle, you know, like in an eclipse. I still don't think I've found out how to answer a question like that.
you should have no trouble doing it now by integration. it is almost trivial to construct an integral that takes an intersection of two circles.

[Pickleworm]

Hey I don't get why .999=1 OR .999!=1 please explain using axioms and theorems also is n/0 undefined or infinity thanks in advance

-pickleworm

[Paul.Power]

Hey I don't get why .999=1 OR .999!=1 please explain using axioms and theorems also is n/0 undefined or infinity thanks in advance

-pickleworm

Here's a good few (http://en.wikipedia.org/wiki/0.999...#Proofs): keep reading until you see one you're happy with.

now take that proof, and apply it to ...9999999.0 and get -1. what went wrong?Come again?

[Run]

Hey I don't get why .999=1 OR .999!=1 please explain using axioms and theorems also is n/0 undefined or infinity thanks in advance

-pickleworm

Here's a good few (http://en.wikipedia.org/wiki/0.999...#Proofs): keep reading until you see one you're happy with.

fakepost ruined

[quakerworm]

Come again?
how do you usually prove 0.9999...=1? the most direct method is to use the same method as deriving formula for infinite geometric sums.

x=0.999...
10*x=9.999...
10*x-x=9*x=9.999...-0.999...=9
x=1

right? now take ...999.0, or sum 9*10^n for n=0 to inf., an obviously infinite number, right?

x=...999.0
10*x=...9990.0
10*x-x=9*x=...9990.0-...999.0=-9
x=-1

and so, happily, we conclude that -1=inf. and grab another 0.473l of beer.

[AndrewTaylor]

See, now you have a problem.

Because you'd better not actually believe that rubbish, but damn sure you'd better not be trolling.

[Run]

If he was trolling i'd suddenly have a new appreciation for him

[Akuryou13]

maths postuh....I know very little in the way of math, and I don't really try to normally, but I decided to actually read through that one....perhaps I'm just ignorant here, but that makes no sense...

edit: guess I'm not the only one then...

[yakuza]

I don't understand how a fixed value X can have two values.

[quakerworm]

Because you'd better not actually believe that rubbish, but damn sure you'd better not be trolling.
paul started the 0.999...=1 thing. let him get out of this one. sure, i know why there is a difference in these proofs, in that sense it is trolling. with maths, yeah. but i prefer to look at it as puzzling a fellow math enthusiast in interest of mutual enlightenment. at any rate, there is a key mathematical concept hidden there, and it's worth pointing out.
also is n/0 undefined or infinity thanks in advance
undefined. the limit as the denominator approaches zero can be infinity. that is, for any positive n and N, i can pick d>0 such that n/d > N, no matter how big N is. so as denominator gets smaller, the n/d gets closer and closer to infinity. but if d=0, it is undefined.

one of the simple ways to see this is to ask if it is n/(+0) or n/(-0). as you get close to zero from either side, you can get +inf or -inf. so which is it when it is exactly zero?

[MrBunsy]

I don't understand how a fixed value X can have two values.

Depends whether it's a variable or a constant. In proving 0.999.. = 1 letting x be 0.999... is the same as letting x = 1, as the proof shows that the two are identical.

In y=mx, (m=constant, x and y = variables) it's about the relationship between the two variables. As you vary the temperature, say, you also vary the pressure (or something, can't remember much about gases). You can also specific limits for x.

In quakerworm's post, he's got two different values of x because he's talking about two separate situations, thus re-defining x about halfway though. He could have used a different letter.

[Shadowmoon]

The same year you learn about circles, squares and maybe triangles.

I learnt about them in year 2, and we didn't do pi. I think we will probably do pi next year.

[Plasma]

x=...999.0
10*x=...9990.0
10*x-x=9*x=...9990.0-...999.0=-9
x=-1

and so, happily, we conclude that -1=inf. and grab another 0.473l of beer.
Right...

Well, no. Not right at all! You completely ignored that ...9990.0-...999.0 would result in 9000.....00009.0! That's a pretty big screw-up you just made there, Quakey. Man, God would be so screwed if he hired you to create a universe...

[quakerworm]

i think you completely missed the part about the dots.

...999.0 =/= 999. it is the infinite sum of powers of ten times 9. there is no terminating nine. they keep going on to the left forever.

just as a rule of thumb, plasma, if you think i'm wrong, read what i wrote again, think about it carefully. odds are, you just missed something. i do occasionally make errors, of course, and i appreciate you pointing them out, but only when they are actual errors.
I don't understand how a fixed value X can have two values.
it doesn't. x=0.999... we show that it means that x=1.0. it only has one value, so 0.999...=1.0. they are the same value. the fact that x only has one value is the whole point of the proof.

[thomasp]

I don't understand how a fixed value X can have two values.
Technically, every number is made up of two "numbers" - a real part and an imaginary part.

So 3 is actually 3 + 0i, and SQRT(-9) is 0 ± 3i. And then there's the weird ones which have both real and imaginary parts which I can't think of off the top of my head.

[Paul.Power]

how do you usually prove 0.9999...=1? the most direct method is to use the same method as deriving formula for infinite geometric sums.

x=0.999...
10*x=9.999...
10*x-x=9*x=9.999...-0.999...=9
x=1

right? now take ...999.0, or sum 9*10^n for n=0 to inf., an obviously infinite number, right?

x=...999.0
10*x=...9990.0
10*x-x=9*x=...9990.0-...999.0=-9
x=-1

and so, happily, we conclude that -1=inf. and grab another 0.473l of beer.Except that that's a diverging series, not a converging one. So you can't really conclude anything from it.

It's like saying:

1 + 1/2 + 1/3 + 1/4 + ... = infinity
1 + 2/3 + 3/4 + 4/5 + ... = infinity
Therefore
1 + 1/2 + 1/3 + 1/4 + ... = 1 + 2/3 + 3/4 + 4/5 + ...

Doesn't really work. Infinity = infinity, but you can't really extend that to the two diverging series.

It works with a converging series, though. Which is what 0.999... is. ...999.0 is not, though, it's diverging.

[Plasma]

i think you completely missed the part about the dots.

...999.0 =/= 999. it is the infinite sum of powers of ten times 9. there is no terminating nine. they keep going on to the left forever.
Well, if you were going to follow that theory, then infinity plus/minus/divided by/multiplied by anything other than infinity is still equal to infinity. In which case, you'd be better off to say:
(inf) = (inf) + 1
Therefore,
0=1

But no, that's not the case. There is a 9 at the end, you just will never be able to reach it because there's an infinite amount of 0s in the way.

[*Splinter*]

TechnicallySo 3 is actually 3 + 0i, and SQRT(-9) is 0 ± 3i. And then there's the weird ones which have both real and imaginary parts which I can't think of off the top of my head.
sin or cos of theta > 1 gives values of theta with real and imaginary parts

[Paul.Power]

Well, if you were going to follow that theory, then infinity plus/minus/divided by/multiplied by anything other than infinity is still equal to infinity. In which case, you'd be better off to say:
(inf) = (inf) + 1
Therefore,
0=1
Yes. That's the central problem: (inf) = (inf) + 1 is correct, but you can't expect to subtract infinity from both sides to get 0 = 1.

But no, that's not the case. There is a 9 at the end, you just will never be able to reach it because there's an infinite amount of 0s in the way.
No.

[Run]

what a horrid thread

[Shadowmoon]

You mean a boring thread. Don't we get enough maths work during a school day?:D

[Paul.Power]

You mean a boring thread. Don't we get enough maths work during a school day?:D
Well I don't, I haven't learnt any proper maths for two years. This (and helping Blinx with his maths homework) helps keep me sharp.

[MtlAngelus]

You mean a boring thread. Don't we get enough maths work during a school day?:D
You're the boring one, maths are fun.

I do basic maths at work, but it gets complex because I have to explain it to our customers as if they were 3 year olds. And I can't use apples or oranges as examples. :(

[Shadowmoon]

Maths is fun, but not for everybody. And when you get home from school and look at your favourite forum you don't want to do mathworks do you? i have never came across pi before. Is it something to do with shapes?

[MtlAngelus]

Maths is fun, but not for everybody. And when you get home from school and look at your favourite forum you don't want to do mathworks do you?
Then you don't click on the thread that has "MATH" written all over it. :rolleyes:

[Run]

Then you don't click on the thread that has "MATH" written all over it. :rolleyes:

yeah, shadowmoon

you don't see me complaining

[Shadowmoon]

Well my eyesight is perfectly fine, and in the title of the thread it says Calculating pi debate, arguement, discussion AND contest. Congratulations Mtlangelus for letting this thread reach its 100th reply!:D
Or do you mean math all over the thread?
And run, i am not complaining, i do like maths, but its a little unnapropiate in a forum in my opinion. The reason you don't complain is because you have a different opinion towards this thread.

[yakuza]

Well my eyesight is perfectly fine


what a horrid thread

The reason you don't complain is because you have a different opinion towards this thread.

I AM CONFUSED.

[Paul.Power]

And when you get home from school and look at your favourite forum you don't want to do mathworks do you?[Sure, why not? It's called "recreational mathematics".

i have never came across pi before. Is it something to do with shapes?Pi is, among other things, the ratio between the circumference (the length around the edge) and the diameter (the length across the middle) of a cicle.

[*Splinter*]

Why are people picking on shadowmoon?

Also, the title is NONSENSE, there is nothing to 'argue', 'debate' or 'discuss' (since they're... the same thing) about calculating pi, it is a finite number known precisely to however many decimal places. As a contest its sort of valid, but more a contest of persistance than deeply-fantastical mathematical knowledge.

[Plasma]

Yes. That's the central problem: (inf) = (inf) + 1 is correct, but you can't expect to subtract infinity from both sides to get 0 = 1.

No.
Right. So that's three conflicting theories of infinity in this thread. And neither of us have any backing for our theories.
In a business, this would be called 'progress'.

[Paul.Power]

Right. So that's three conflicting theories of infinity in this thread. And neither of us have any backing for our theories.
In a business, this would be called 'progress'.

Could you describe the three, so I don't have to read the whole thread again?

[Kelster23]

Maths is fun, but not for everybody. And when you get home from school and look at your favourite forum you don't want to do mathworks do you? i have never came across pi before. Is it something to do with shapes?

Take it as
"Shut up and observe people's godly math skills"
I'm just in here to look at what type of math is out there as you get older. I'm not a math fan either, but I do think it's really neat how people can calculate and say wordsthatdon'tmeanathingtome.
No one said you had to participate... you could just read it and give an occasional thought on the matter like I am.
pi r squared?
I thought pies were round... :p

[Shadowmoon]

Why are people picking on shadowmoon?

Also, the title is NONSENSE, there is nothing to 'argue', 'debate' or 'discuss' (since they're... the same thing) about calculating pi, it is a finite number known precisely to however many decimal places. As a contest its sort of valid, but more a contest of persistance than deeply-fantastical mathematical knowledge.

They are not picking on me Splinter. They disagree with what i have said. We did do circumference once, and Ratio and the diameter. I think we have actually done Pi. Right now i am in year 8, and it hasn't came up yet. But i think i have done it before.

[Kelster23]

Well isn't the formula for getting circumfrence piR^2 or something like that?
They just tell us here to put it as 3.14.

[Plasma]

Could you describe the three, so I don't have to read the whole thread again?
One is that infinity is a maximum limit of numbers, and any more numbers past it aren't counted, and infinity can be subtracted from infinity.
One is that infinity should be treated the same way as algebra, and that any number higher than infinity shouldn't be equal to infinity in the same equation.
And your one is that infinity is a maximum limit of numbers, and any more numbers past it aren't counted, but infinity can be subtracted from infinity.

I think. That's about the gist of what I understood, and put in layman's terms. (I HATE being complicated in any way)

pi r squared?
I thought pies were round... :p
How the hell do you still remember that joke? I told you it sometime last year, I think.

They are not picking on me Splinter. They disagree with what i have said.
*sniff* They grow up so fast!

Right now i am in year 8, and it hasn't came up yet. But i think i have done it before.
Well, I think the first time you come across Pi is when you're asked to find the area of a circle. But it could be before that...

[Kelster23]

How the hell do you still remember that joke? I told you it sometime last year, I think.


I don't know, I think my mom told it to me too. I still remember it because one of my foster cousins was talking about that formula and I asked that.
He sat there with his finger in the air with the funniest expression on his face, completely silent.

[Paul.Power]

One is that infinity is a maximum limit of numbers, and any more numbers past it aren't counted, and infinity can be subtracted from infinity.
One is that infinity should be treated the same way as algebra, and that any number higher than infinity shouldn't be equal to infinity in the same equation.
And your one is that infinity is a maximum limit of numbers, and any more numbers past it aren't counted, but infinity can be subtracted from infinity.

The first and third of those are exactly the same, but you've replaced "and" with "but". Well done.

[Run]

They are not picking on me Splinter. They disagree with what i have said.

no i'm pretty sure i was mocking you

[Plasma]

The first and third of those are exactly the same, but you've replaced "and" with "but". Well done.
Gawd damnit, that third one was supposed to say "infinity can't be subtracted from infinity."

Remember, you didn't see nuthin'...

[Paul.Power]

Gawd damnit, that third one was supposed to say "infinity can't be subtracted from infinity."

Remember, you didn't see nuthin'...

Okay, as far as I can tell, it goes like this:

Infinity + x = Infinity, regardless of what x is.

Therefore

Infinity - Infinity = x.

In other words, you cannot define infinity - infinity because it could literally be anything.

[Melon]

There are different sizes of infinity. The sum of 1 + 2 + 3 + 4 + ...... to an infinite number of places would be larger than the sum of 1 + 1 + 1 + 1 + ... to the same number of places, yet they both sum to infinity.

Infinity isn't a number, and the sooner you stop treating it like one, the sooner you'll stop coming up with these daft non-sensical problems.

[Paul.Power]

There are different sizes of infinity. The sum of 1 + 2 + 3 + 4 + ...... to an infinite number of places would be larger than the sum of 1 + 1 + 1 + 1 + ... to the same number of places, yet they both sum to infinity.

Infinity isn't a number, and the sooner you stop treating it like one, the sooner you'll stop coming up with these daft non-sensical problems.That's the same size infinity, as it happens.

There are a few different sizes of infinity, though. The infinity of real numbers is larger than the infinity of rationals, for example, because the latter is countable, but the former is not.

Yes. This is mathematics: leave your common sense at the door.

[thomasp]

They just tell us here to put it as 3.14.

*Screams*

Do you realise the inaccuracies you're introducing there??? Let's take something like the Boeing 777 aircraft as an example here - an average widebody plane with a maximum fuselage diameter of 6.19m. By using pi as 3.14, as opposed to 3.141592654 (the pi on my calculator - 9dp), you have introduced a potential 31cm^2 error in the cross sectional area of your aircraft. That is quite large and could have serious consequences downstream (yes, it's only a 0.05% error).


And who says engineers are never accurate :p



Yes, I'm bored :p

[Paul.Power]

Well isn't the formula for getting circumfrence piR^2 or something like that?That's the area.

c = πd = 2πr

A = πr² = πd²/4

Also, funnily enough, A = cd/4 - no need for π

[quakerworm]

Technically, every number is made up of two "numbers" - a real part and an imaginary part.

So 3 is actually 3 + 0i, and SQRT(-9) is 0 ± 3i. And then there's the weird ones which have both real and imaginary parts which I can't think of off the top of my head.
false. every complex number is made up of real and imaginary part. a ring of complex numbers is an entirely different ring than ring of real numbers. otherwise, i can drive this to absurd by claiming that by 'number' he actually meant rank 3 tensors.
Except that that's a diverging series, not a converging one. So you can't really conclude anything from it.
but i did not use an assumption on divergence/convergence. i took a sum 9*10^n from n=0 to inf, and summed it. i got -1. that shows that the series converges. now, if you can prove that it diverges, that would demonstrate a contradiction, saying that one of these proofs is wrong. but it still doesn't point out where the computation fails, and why it doesn't fail for 0.999...

[hdhdhd]

Still, pi isn't a terminating decimal, so you could find a pattern after the first hundred or so decimal places, thus rendering it possible to find a lot of decimal places in it.

[quakerworm]

no, that's the point. there is no pattern. if there was a periodic pattern, pi would be rational, and it isn't.

edit: take as a simple example some pattern that repeats as 0.123451234512345(12345). then, by laws of geometric progression, it is equal to 0.12345 * sum 0.000001^n for n = 0 to inf. the sum can be evaluated giving you 1/(1-0.000001) = 100000/99999. performing the above multiplication gives us: 0.12345(12345)=12345/99999, which is rational. and this can be done for any periodic decimal, no matter the length or structure. if there is a period, it is rational.

[*Splinter*]

There are a few different sizes of infinity, though. The infinity of real numbers is larger than the infinity of rationals, for example, because the latter is countable, but the former is not.

Surely there are an infinite number of sizes of infinity? Since 1/0 is only half of 2/0, even they both = inf.

[Melon]

Surely there are an infinite number of sizes of infinity? Since 1/0 is only half of 2/0, even they both = inf.

WRONG WRONG WRONG WRONG WRONG

x/0 does not equal infinity. Never has done, never will.

[AndrewTaylor]

Surely there are an infinite number of sizes of infinity? Since 1/0 is only half of 2/0, even they both = inf.

Also, for any given infinity, doubling it does not affect its size. Nor does adding things to it.

[Paul.Power]

WRONG WRONG WRONG WRONG WRONG

x/0 does not equal infinity. Never has done, never will.Well, there are systems where it does (the Riemann Sphere (http://en.wikipedia.org/wiki/Riemann_sphere), for example). But not in the set of "real" numbers.

[Kelster23]

*Screams*

Do you realise the inaccuracies you're introducing there??? Let's take something like the Boeing 777 aircraft as an example here - an average widebody plane with a maximum fuselage diameter of 6.19m. By using pi as 3.14, as opposed to 3.141592654 (the pi on my calculator - 9dp), you have introduced a potential 31cm^2 error in the cross sectional area of your aircraft. That is quite large and could have serious consequences downstream (yes, it's only a 0.05% error).


And who says engineers are never accurate :p



Yes, I'm bored :p

Told you my teacher in grade 8 and 9 was an idiot.

[*Splinter*]

WRONG WRONG WRONG WRONG WRONG

x/0 does not equal infinity. Never has done, never will.

Care to elaborate? 1/x tends to inf. as x tends to 0, so why not?

[Melon]

as x tends to 0
This is true. But we're talking about x = 0 in this case. What does tan (pi/2) look like? It's an assymptote, it's undefined, and so is 1 / 0.

[AndrewTaylor]

Care to elaborate? 1/x tends to inf. as x tends to 0, so why not?

Only from above. From below it tends to -infinity.

[quakerworm]

not only that, but even if the limit did exist the value is undefined. lim x->0 of 1/x^2 = +inf. but 1/x^2 |x=0 is undefined.