pi
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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...:~
A Plain English signature. Code-frog System Architects, Inc.
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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
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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
I'm getting the impression I need to hit the books again. :-D Jeremy Falcon
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Any number squared would be non-negative...:~
A Plain English signature. Code-frog System Architects, Inc.
Only 'real' numbers. There is a whole branch of mathematics that deals with SQRT(-1) these are called 'imaginary' numbers.
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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
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I haven't had anywhere near enough to drink. Can we start with something a little easier, like "what is the length of a piece of string"? :-O
Now taking suggestions for the next release of CPhog...
:) Simple, that would be 4. Next please. Jeremy Falcon
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Any number squared would be non-negative...:~
A Plain English signature. Code-frog System Architects, Inc.
Those imaginary numbers (not real) are the i you see sometimes. It's sqrt(-1). Sometimes you can see numbers writen as
a + b_**i**_, which have a real and an imaginary part. You can read more about them here[^] -- LuisR
Luis Alonso Ramos Intelectix - Chihuahua, Mexico Not much here: My CP Blog!
The amount of sleep the average person needs is five more minutes. -- Vikram A Punathambekar, Aug. 11, 2005
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Any number squared would be non-negative...:~
A Plain English signature. Code-frog System Architects, Inc.
code-frog wrote:
Any number squared would be non-negative
Not imaginary numbers, like i. By definition, i * i = -1. Cheers, Vikram.
I don't know and you don't either. Militant Agnostic
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As Chris Munder said, it's a Transcendental number[^], much more uncommon than mere real number.
Super Lloyd wrote:
As Chris Munder said, it's a Transcendental number[^], much more uncommon than mere real number.
Erm, I never disagreed with that. You said PI is not real, and I only said it is. Cheers, Vikram.
I don't know and you don't either. Militant Agnostic
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It still didn't address the why. If it did, I didn't understand it. :) Jeremy Falcon
Jeremy Falcon wrote:
It still didn't address the why.
It simply is. Go in peace. Be. Cheers, Vikram.
I don't know and you don't either. Militant Agnostic
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code-frog wrote:
Any number squared would be non-negative
Not imaginary numbers, like i. By definition, i * i = -1. Cheers, Vikram.
I don't know and you don't either. Militant Agnostic
Vikram A Punathambekar wrote:
By definition, i * i = -1
Thankyou! Someone who gets the definition correct! :-D I see most people say that i = sqrt(-1), which is NOT correct - it implies that i2 = 1
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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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
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"
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Vikram A Punathambekar wrote:
By definition, i * i = -1
Thankyou! Someone who gets the definition correct! :-D I see most people say that i = sqrt(-1), which is NOT correct - it implies that i2 = 1
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"
Ryan Binns wrote:
I see most people say that i = sqrt(-1), which is NOT correct - it implies that i2 = 1
Uh, how? If you say
i = SQRT(-1)
squaring both sides will give you
i * i = -1
How does i = sqrt(-1) imply i2 = 1 ? Cheers, Vikram.
I don't know and you don't either. Militant Agnostic
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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
I always thought it was 22/7 atleast that was what my math teacher told me!! :doh: If you need a hammer get C and shut up. If you need a nail gun get C++ and shut up. If you don't need *those* things (and good design should tell you) then by all means get a factory, factory, factory. --code-frog@codeproject
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Super Lloyd wrote:
As Chris Munder said, it's a Transcendental number[^], much more uncommon than mere real number.
Erm, I never disagreed with that. You said PI is not real, and I only said it is. Cheers, Vikram.
I don't know and you don't either. Militant Agnostic
it's a pure definition problem then? I think the issue here is the same as vegetable and fruit. Some people would say tomatoes is a fruit, some people would say it is not. And then they each refer to their own definition. Doens't matter too much. Anyway I will stick to my definition which means that PI is part of super set of the real (hence it is not a real number). And that Math teacher don't bother make the difference explicit until you are in advanced math studies....