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To: Boogieman
The infinite decimals are simply an artifact of performing a mathematical operation in a number system unable to render the result with precision. If we use fractions, they all vanish into thin air :)

I assume you are alluding to CONTINUED fractions? Many irrationals have a simple repetitive continued fraction representation, and even 'e' has a regular pattern, even though it doesn't actually repeat. And of course any finite continued fraction is a simple fraction, and can be represented by a repeating decimal.

40 posted on 04/02/2013 9:57:33 PM PDT by dr_lew

To: dr_lew

“I assume you are alluding to CONTINUED fractions?”

Well, yeah I wasn’t really clear on that point, maybe I should have left it off. What I meant, in terms of Pi, is that it looks irrational written as a decimal, but in fact, the only reason it is a significant number to us is because it’s the decimal approximation of a ratio. That ratio isn’t one between two whole numbers, that might produce a repeating fraction, but between two related geometric quantities.

So, if one theoretically constructed a number system using some geometric base rather than our arithmetic one, Pi would be completely rational, and could be approximated exactly. So, I think it’s all a matter of perspective.

43 posted on 04/02/2013 10:35:59 PM PDT by Boogieman

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