pi
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Jeremy Falcon wrote:
Given what you and Chris said, I suppose the idea I'm trying to understand then is why is Pi an irrational number? What makes it go on forever?
Because pi <> P/Q ;P Seriously, if you can answer why some of the most important numbers known to man are irrational (e, pi, h_bar, etc) you will be a god among insects. -Sean ---- Shag a Lizard
Sean Cundiff wrote:
Seriously, if you can answer why some of the most important numbers known to man are irrational (e, pi, h_bar, etc) you will be a god among insects.
It's going to drive me crazy if it never "clicks". Time for my medication now! Breathe. Breathe Jeremy! :-D Jeremy Falcon
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Sean Cundiff wrote:
Seriously, if you can answer why some of the most important numbers known to man are irrational (e, pi, h_bar, etc) you will be a god among insects.
It's going to drive me crazy if it never "clicks". Time for my medication now! Breathe. Breathe Jeremy! :-D Jeremy Falcon
Think of it this way: pi = circumference of a circle / diameter of the circle. There is no way to set the circumference to a rational quantity while at the same time keeping the diameter a rational quantity. pi = rational/irrational or irrational/rational. Why such a fundamental thing as a circle exhibits this quantity property is a matter of philosophical debate. -Sean ---- Shag a Lizard -- modified at 22:06 Thursday 16th March, 2006
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Sean Cundiff wrote:
Seriously, if you can answer why some of the most important numbers known to man are irrational (e, pi, h_bar, etc) you will be a god among insects.
It's going to drive me crazy if it never "clicks". Time for my medication now! Breathe. Breathe Jeremy! :-D Jeremy Falcon
When the meds have kicked in take a look at transcendental numbers[^]. Pi's not only irrational, it's also transcendental. cheers, Chris Maunder
CodeProject.com : C++ MVP
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Sean Cundiff wrote:
Seriously, if you can answer why some of the most important numbers known to man are irrational (e, pi, h_bar, etc) you will be a god among insects.
It's going to drive me crazy if it never "clicks". Time for my medication now! Breathe. Breathe Jeremy! :-D Jeremy Falcon
Work the proof for PI you might find that is exactly what you need. http://en.wikipedia.org/wiki/Pi[^]
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Super Lloyd wrote:
Could you explain your exact problem? That would help us give you a good solution!
I did. I asked why is Pi infinite. I understand what you said, but that still doesn't address why it is like that - it just reaffirms it's infinite. I'm trying to really understand Pi outside a textbook definition I reckon. Jeremy Falcon
it's not infinite, it's 3.14159265.... infinite is much bigger than that! ;P do you mean never repeat? 1st I believe you could have never repeating rationale (integer / integer) as well, this is simply an artefact of decimal notation. 2nd: yes PI is very special, it's a not even a real such as SQRT(2). Real number (as opposed to rational and integer) are solutino to polynomes equation (e.g. x^2 = 2) No Polynome with real parammters has PI has its solution. (same for 'e' (i.e. 2.7182818...)) they solve an other class of problem altogether...
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Super Lloyd wrote:
Could you explain your exact problem? That would help us give you a good solution!
I did. I asked why is Pi infinite. I understand what you said, but that still doesn't address why it is like that - it just reaffirms it's infinite. I'm trying to really understand Pi outside a textbook definition I reckon. Jeremy Falcon
BTW, if PI repeated, it could expressed as a rational, hence it can't be!
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Think of it this way: pi = circumference of a circle / diameter of the circle. There is no way to set the circumference to a rational quantity while at the same time keeping the diameter a rational quantity. pi = rational/irrational or irrational/rational. Why such a fundamental thing as a circle exhibits this quantity property is a matter of philosophical debate. -Sean ---- Shag a Lizard -- modified at 22:06 Thursday 16th March, 2006
Sean Cundiff wrote:
Why such a fundamental thing as a circle exhibits this quantity property is a matter of philosophical debate.
You just beat me to my question. Jeremy Falcon
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Work the proof for PI you might find that is exactly what you need. http://en.wikipedia.org/wiki/Pi[^]
A Plain English signature. Code-frog System Architects, Inc.
It still didn't address the why. If it did, I didn't understand it. :) Jeremy Falcon
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When the meds have kicked in take a look at transcendental numbers[^]. Pi's not only irrational, it's also transcendental. cheers, Chris Maunder
CodeProject.com : C++ MVP
Chris Maunder wrote:
Pi's not only irrational, it's also transcendental.
:doh: Back to the books for me. :laugh: Jeremy Falcon
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it's not infinite, it's 3.14159265.... infinite is much bigger than that! ;P do you mean never repeat? 1st I believe you could have never repeating rationale (integer / integer) as well, this is simply an artefact of decimal notation. 2nd: yes PI is very special, it's a not even a real such as SQRT(2). Real number (as opposed to rational and integer) are solutino to polynomes equation (e.g. x^2 = 2) No Polynome with real parammters has PI has its solution. (same for 'e' (i.e. 2.7182818...)) they solve an other class of problem altogether...
Super Lloyd wrote:
do you mean never repeat?
I was under the impression it was infinite, just as 1/3 would also be. Jeremy Falcon
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it's not infinite, it's 3.14159265.... infinite is much bigger than that! ;P do you mean never repeat? 1st I believe you could have never repeating rationale (integer / integer) as well, this is simply an artefact of decimal notation. 2nd: yes PI is very special, it's a not even a real such as SQRT(2). Real number (as opposed to rational and integer) are solutino to polynomes equation (e.g. x^2 = 2) No Polynome with real parammters has PI has its solution. (same for 'e' (i.e. 2.7182818...)) they solve an other class of problem altogether...
Super Lloyd wrote:
PI is very special, it's a not even a real such as SQRT(2).
What do you mean? :wtf: Of course PI is a real number! The definition of a real number is that it's square should be nonnegative. And PI * PI is nonnegative. Cheers, Vikram.
I don't know and you don't either. Militant Agnostic
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Super Lloyd wrote:
PI is very special, it's a not even a real such as SQRT(2).
What do you mean? :wtf: Of course PI is a real number! The definition of a real number is that it's square should be nonnegative. And PI * PI is nonnegative. Cheers, Vikram.
I don't know and you don't either. Militant Agnostic
As Chris Munder said, it's a Transcendental number[^], much more uncommon than mere real number.
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It still didn't address the why. If it did, I didn't understand it. :) Jeremy Falcon
Gosh you got me. I remember doing this in school and I remember using it with integrals and the special number e. Your question doesn't seem to have a conclusive answer from mathematics other than, "Most mathematicians agree that PI is infinite, irrational and transcendental and would be very surprised to learn it wasn't." I remember one form of something we did was that prove pi isn't infinite. So we tried picking a ratio of integers to prove that but the ratio went on forever and a proof was used to demonstrate that. I don't remember the specifics but anyway... Get yourself a couple hundred crays and work it out. I guess they have PI to trillions of non repeating decimals so you'd need a few crays for sure...:omg:
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Sean Cundiff wrote:
All irrational numbers have the property that they are infinitely long, otherwise it would be possible to write them as P/Q and thus be a rational number.
Ok that makes sense. Given what you and Chris said, I suppose the idea I'm trying to understand then is why is Pi an irrational number? What makes it go on forever? And yeah, I'm trying to improve my math skills, so bear with me. :-O Jeremy Falcon
Jeremy Falcon wrote:
What makes it go on forever?
It's a number that is computed by an infinite series of smaller and smaller parts. For example, look at this.[^] Besides a lot of complicated equations, there's this very simple one: pi/4 = 1 - 1/3 + 1/5 - 1/7 ... You can see how the series is infinite, but smaller and smaller. So that's what makes it go on forever, and the resulting number is irrational, as discussed in the previous posts. Marc Pensieve Functional Entanglement vs. Code Entanglement Static Classes Make For Rigid Architectures
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It still didn't address the why. If it did, I didn't understand it. :) Jeremy Falcon
Change the question around. Instead of asking "why can't Pi be expressed as P/Q", ask yourself "Why should any random real number (ie not an integer, not a complex number) be lucky enough to be expressable as P/Q" To have a number be able to be expressed, exactly, as a ratio of two other numbers is pretty remarkable. cheers, Chris Maunder
CodeProject.com : C++ MVP
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Super Lloyd wrote:
do you mean never repeat?
I was under the impression it was infinite, just as 1/3 would also be. Jeremy Falcon
Ha.. but in that case it could be expressed as simple rational such as: big number divided by big power of ten. And why that couldn't be I hear you ask? 1st it would be funny that 10 would be a relevant number for a circle but why not.... Anyway, while I do not know the reason for that myself I could argue that this guy Ferdinand von Lindeman[^] proved PI was transcendental (no solution of any polynome with ration parameter), hence it obviously never repeat
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Super Lloyd wrote:
PI is very special, it's a not even a real such as SQRT(2).
What do you mean? :wtf: Of course PI is a real number! The definition of a real number is that it's square should be nonnegative. And PI * PI is nonnegative. Cheers, Vikram.
I don't know and you don't either. Militant Agnostic
Any number squared would be non-negative...:~
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Jeremy Falcon wrote:
What makes it go on forever?
It's a number that is computed by an infinite series of smaller and smaller parts. For example, look at this.[^] Besides a lot of complicated equations, there's this very simple one: pi/4 = 1 - 1/3 + 1/5 - 1/7 ... You can see how the series is infinite, but smaller and smaller. So that's what makes it go on forever, and the resulting number is irrational, as discussed in the previous posts. Marc Pensieve Functional Entanglement vs. Code Entanglement Static Classes Make For Rigid Architectures
Marc Clifton wrote:
So that's what makes it go on forever
Actually not quite. Infinite series can easily add up to a rational number, or even an integer. 1/2 + 1/4 + 1/8 + ... = 1 cheers, Chris Maunder
CodeProject.com : C++ MVP
-- modified at 22:38 Thursday 16th March, 2006
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Marc Clifton wrote:
So that's what makes it go on forever
Actually not quite. Infinite series can easily add up to a rational number, or even an integer. 1/2 + 1/4 + 1/8 + ... = 1 cheers, Chris Maunder
CodeProject.com : C++ MVP
-- modified at 22:38 Thursday 16th March, 2006
Chris Maunder wrote:
Infinite series can easily add up to a rational number, or even an integer.
Ah, good point. I better stick to programming. :) Marc Pensieve Functional Entanglement vs. Code Entanglement Static Classes Make For Rigid Architectures
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Jeremy Falcon wrote:
What makes it go on forever?
It's a number that is computed by an infinite series of smaller and smaller parts. For example, look at this.[^] Besides a lot of complicated equations, there's this very simple one: pi/4 = 1 - 1/3 + 1/5 - 1/7 ... You can see how the series is infinite, but smaller and smaller. So that's what makes it go on forever, and the resulting number is irrational, as discussed in the previous posts. Marc Pensieve Functional Entanglement vs. Code Entanglement Static Classes Make For Rigid Architectures
Marc Clifton wrote:
You can see how the series is infinite, but smaller and smaller.
I got all of that stuff. But it doesn't explain why the series exist in the first place. Fortunately, I think I got enough info from the fine folks at CP to help me set out a course to improve my understanding on it. I'm just not there yet. :) Jeremy Falcon