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
This train of thought may also help explain why. The equation for a circle centered about (0, 0) is: R^2 = X^2 + Y^2. I have forgotten how to do it, due to extreme 'un-practice', but I recall that determining the length of an arc requires integrating this in some manner. Search for 'Line Integral' in Google. Therefore, 'C' from 'C = Pi * D' is a rather complicated thing that requires square roots and a whole lot more in order to determine it precisely. It is a lot more complicated than 'sqrt(2)', and as the square root of 2 is a non-repeating number (at least in my memory), pi will be even more convoluted.
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1 / 3 is infinite too ! Any number that cannot be write an integer / 10 ^ some power is infinite. what are you trying to understand? It's also irrational, as pointed out. Could you explain your exact problem? That would help us give you a good solution! ;P
No, 1/3 is not infinite, of course. But written in decimal form instead of fractional form gives an irrational number, namely 1,33333333... -- The Blog: Bits and Pieces
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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 (P/Q != Pi with P&Q integer) - Pi has infinite number of decimal, but no sequence in its decimal has been found so far (unlike 1/3 = 0.33333...) . . . & the best you can do to understand Pi is to watch Pi, a great movie by Darren Aronofsky.
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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, Pi is an irrational number, which means that it cannot be expressed exactly in decimal, nor indeed using any other rational base. It will always have an infinite number of digits following the point. This is because an irrational cannot be expressed as a fraction. There are a number of proofs that Pi is irrational, for example, here: http://pi314.at/math/irrational.html[^]. (I must admit, I don't understand the equations myself - it is a long time since I studied this stuff.) As to *why* Pi is irrational: Mathematics is just wierd like that. Perhaps only God knows. BTW: Sorry to be picky, but Pi is *not* infinite. It is irrational. "Infinity is the state of being greater than any finite (real) number however large." (Wikipaedia). So presumably an "Infinite Number" is a number which is greater than any real number. One of the few things I have learned about mathematics is that it is important to be picky about little differences like this.
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It's not infinite. It's irrational[^]. It can be cranky too if you're not careful. cheers, Chris Maunder
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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
I think that we can say that it is infinte because we can conceptualize us having an infinte amount of time to work it out, just as we can conceptualize us having an infinite amount of time to count. I think that your question "Why is it infinte" has more to do with the nature of infinty than the nature of pi.
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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:
1st I believe you could have never repeating rationale (integer / integer) as well, this is simply an artefact of decimal notation.
I think you cannot have a never repeating rational number. As you do the long division, at each step you either end up with zero as a remainder (and terminate the sequence) or some other finite positive number. After some number of steps you must have a zero remainder or repeat a previous remainder, at which point you now have a repeating sequence. Robert