pi
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I'm trying to find a good way to explain why pi is infinite (not what it is). And I'm drawing up blanks. Any math gurus care to shed me some light please? Jeremy Falcon
Pi is irrational, like my ex-wife. Fortunately, neither is infinite. Both go on forever, without end, for no good reason, never repeating any sensible pattern. Thank God that Pi can't hold a credit card. "...a photo album is like Life, but flat and stuck to pages." - Shog9
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I'm trying to find a good way to explain why pi is infinite (not what it is). And I'm drawing up blanks. Any math gurus care to shed me some light please? Jeremy Falcon
Let me approach this another way. You are just wondering - why the heck must a simple thing such as the ratio of the circumference to the diameter be so darn complex. For gawds sake it is a ratio ! Assuming you are able to measure both the circumference and diameter to a great precision with an electron microscope thing. Then PI would simply be c/d - right ? So why on earth is Pi so enormously complicated. Why is Pi irrational/ trancedental/ math-mumbojumbo word - when both circumference and diameter are simple, measurable real numbers. The answer to that lies in the fact that there is no such thing as a measurement. We humans cannot measure, we can only count. We can count inches, millimeters, microns, nanometers and call it a measurement, but we are fooling no one. Still, you wonder how did this monstrosity creep up on us. Why cant PI be something simpler like a square root (3). I think the best answer I have heard so far is "yeah, it might be a really simple number in another universe parallel to ours, we might have just got unlucky in our universe". The moment I heard this from a scifi geek buddy - I understood I had hit a culdesac. There was no point trying to get to the root of this without some tools such as a wormhole-stargate.
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Ryan Binns wrote:
i * i = sqrt(-1) * sqrt(-1) i * i = sqrt(-1 * -1)
The property that sqrt(a) * sqrt(b) = sqrt(a * b) only applies to real x >= 0. So you really can't do that.
They dress you up in white satin, And give you your very own pair of wings In August and Everything After
I'm after everything
Aah. Ok. Perhaps you could explain that to every maths lecturer I ever had. 5 years of maths, and they all said the same thing :~
Ryan
"Punctuality is only a virtue for those who aren't smart enough to think of good excuses for being late" John Nichol "Point Of Impact"
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Hang on. If the definition if i is i^2 = -1 then i = +/- sqrt(-1) Nothing wrong with i := sqrt(-1) cheers, Chris Maunder
CodeProject.com : C++ MVP
Chris Maunder wrote:
If the definition if i is i^2 = -1 then i = +/- sqrt(-1)
I thought that was implicit. SQRT(36) is -6 as much as it is 6. Cheers, Vikram.
I don't know and you don't either. Militant Agnostic
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Hang on. If the definition if i is i^2 = -1 then i = +/- sqrt(-1) Nothing wrong with i := sqrt(-1) cheers, Chris Maunder
CodeProject.com : C++ MVP
Chris Maunder wrote:
If the definition if i is i^2 = -1 then i = +/- sqrt(-1)
I thought that was implicit. SQRT(36) is -6 as much as it is 6. Cheers, Vikram.
I don't know and you don't either. Militant Agnostic
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Chris Maunder wrote:
If the definition if i is i^2 = -1 then i = +/- sqrt(-1)
I thought that was implicit. SQRT(36) is -6 as much as it is 6. Cheers, Vikram.
I don't know and you don't either. Militant Agnostic
Right - every square root has two solutions so you can't define a single quantity as the solution to a square root, otherwise you'd be implying sqrt(-1) = -sqrt(-1). And that would cause a few problems ;) cheers, Chris Maunder
CodeProject.com : C++ MVP
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if complex number don't coun't, what's the point of your definition then? :omg: :laugh:
The set of complex numbers is a superset of the set of real numbers. So real numbers are included in the set of complex numbers. Unreal numbers are just the set of all numbers that are not in the reals.
They dress you up in white satin, And give you your very own pair of wings In August and Everything After
I'm after everything
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Right - every square root has two solutions so you can't define a single quantity as the solution to a square root, otherwise you'd be implying sqrt(-1) = -sqrt(-1). And that would cause a few problems ;) cheers, Chris Maunder
CodeProject.com : C++ MVP
Chris Maunder wrote:
every square root has two solutions so you can't define a single quantity as the solution to a square root
Except, of course, SQRT(0). ;P Cheers, Vikram.
I don't know and you don't either. Militant Agnostic
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Aah. Ok. Perhaps you could explain that to every maths lecturer I ever had. 5 years of maths, and they all said the same thing :~
Ryan
"Punctuality is only a virtue for those who aren't smart enough to think of good excuses for being late" John Nichol "Point Of Impact"
That really sucks. Those profs should be dragged out back and shot. (In the mathematical sense, of course. ;P)
They dress you up in white satin, And give you your very own pair of wings In August and Everything After
I'm after everything
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The set of complex numbers is a superset of the set of real numbers. So real numbers are included in the set of complex numbers. Unreal numbers are just the set of all numbers that are not in the reals.
They dress you up in white satin, And give you your very own pair of wings In August and Everything After
I'm after everything
hu.... ??? for the remark my remark was related the Vikram definition of real number. Vikram definition: number whose square value is not negative.
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Chris Maunder wrote:
every square root has two solutions so you can't define a single quantity as the solution to a square root
Except, of course, SQRT(0). ;P Cheers, Vikram.
I don't know and you don't either. Militant Agnostic
There's always one... :rolleyes: cheers, Chris Maunder
CodeProject.com : C++ MVP
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I thought you could still have an infinite irrational number though. Or, is that not the case? Jeremy Falcon
That's one of these things one can't be certain of. I think. What's to say that pi doesn't plane out on zero decimals halfway to infinity? :)
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I'm trying to find a good way to explain why pi is infinite (not what it is). And I'm drawing up blanks. Any math gurus care to shed me some light please? Jeremy Falcon
Isn't Pi a coëfficiënt for the circle? I'm thinking that it keeps on going because a real circle doesn't exist, it's always a rounding of some polygone. The more decimals you have, the closer you get to the real circle and because a real circle doesn't exist, you can keep on going. But that's just a theory :-). There are other rational numbers you know: e, root of 2, ... :-D No hurries, no worries. -- modified at 2:25 Friday 17th March, 2006
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That really sucks. Those profs should be dragged out back and shot. (In the mathematical sense, of course. ;P)
They dress you up in white satin, And give you your very own pair of wings In August and Everything After
I'm after everything
David Stone wrote:
Those profs should be dragged out back and shot. (In the mathematical sense, of course. ;P)
Of course. We should mathematically prove that the shot will kill them before firing it ;)
Ryan
"Punctuality is only a virtue for those who aren't smart enough to think of good excuses for being late" John Nichol "Point Of Impact"
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Chris Maunder wrote:
every square root has two solutions so you can't define a single quantity as the solution to a square root
Except, of course, SQRT(0). ;P Cheers, Vikram.
I don't know and you don't either. Militant Agnostic
Vikram A Punathambekar wrote:
Except, of course, SQRT(0).
You mean you can't have -0 ? :rolleyes: The Intel 387 maths coprocessor could. It differentiated between +0 and -0 :~
Ryan
"Punctuality is only a virtue for those who aren't smart enough to think of good excuses for being late" John Nichol "Point Of Impact"
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You're getting confused here because math people don't like to hear that a number is infinite. The term you're looking for is infinitely repeating. :)
They dress you up in white satin, And give you your very own pair of wings In August and Everything After
I'm after everything
:-D Thanks for the tip. Jeremy Falcon
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I think most people above didn't approach their explanation as follows: Pi is an "infinitely long" number due to its transcendental nature. I will explain why I put that in quotes. That is, there is no closed algebraic function whose solution yields exactly pi nor are there two whole numbers whose ratio expresses pi exactly. Consequently, we must use an approximation to pi. The precision of the approximation is limited to the computing power and time you want to spend on calculating pi. That is why the approximation to pi is infinitely long.
Ok, that makes perfect sense. Thanks. Jeremy Falcon
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Jeremy Falcon wrote:
I'm trying to find a good way to explain why pi is infinite (not what it is).
Because. :)
Ryan
"Punctuality is only a virtue for those who aren't smart enough to think of good excuses for being late" John Nichol "Point Of Impact"
Why not? :) I was asked by someone btw, and I didn't have an answer. Jeremy Falcon
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Pi is irrational, like my ex-wife. Fortunately, neither is infinite. Both go on forever, without end, for no good reason, never repeating any sensible pattern. Thank God that Pi can't hold a credit card. "...a photo album is like Life, but flat and stuck to pages." - Shog9
Roger Wright wrote:
Thank God that Pi can't hold a credit card.
:-D Jeremy Falcon
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Let me approach this another way. You are just wondering - why the heck must a simple thing such as the ratio of the circumference to the diameter be so darn complex. For gawds sake it is a ratio ! Assuming you are able to measure both the circumference and diameter to a great precision with an electron microscope thing. Then PI would simply be c/d - right ? So why on earth is Pi so enormously complicated. Why is Pi irrational/ trancedental/ math-mumbojumbo word - when both circumference and diameter are simple, measurable real numbers. The answer to that lies in the fact that there is no such thing as a measurement. We humans cannot measure, we can only count. We can count inches, millimeters, microns, nanometers and call it a measurement, but we are fooling no one. Still, you wonder how did this monstrosity creep up on us. Why cant PI be something simpler like a square root (3). I think the best answer I have heard so far is "yeah, it might be a really simple number in another universe parallel to ours, we might have just got unlucky in our universe". The moment I heard this from a scifi geek buddy - I understood I had hit a culdesac. There was no point trying to get to the root of this without some tools such as a wormhole-stargate.
Vivek Rajan wrote:
Assuming you are able to measure both the circumference and diameter to a great precision with an electron microscope thing. Then PI would simply be c/d - right ? So why on earth is Pi so enormously complicated. Why is Pi irrational/ trancedental/ math-mumbojumbo word - when both circumference and diameter are simple, measurable real numbers.
Bingo. Jeremy Falcon