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Originally Posted by NegativeNine
Perhaps Pi is rational and we'rethe irrational ones...
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Originally Posted by flstf
If I'm not mistaken I think pi does exist in Euclidean geometry (as just the ratio between c and d). It becomes irrational when we try to fit it's value into our existing numbering system (by definition within that system). As welshbyte said in an earlier post we could have designed a new numbering system around it and made pi = 1.
Someone let me know if I'm all wet, I think I am way over my head here, LOL.
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Just to clarify for those who don't realise, in this context "rational" does not mean "logical" or "reasonable" but
ratio-nal, as in to do with ratios. In other words an irrational number cannot be expressed as a
ratio of two whole numbers. Take a half: that can be expressed as 1/2. Or 0.66666... can be expressed as 2/3. Pi and other irrationals (e.g. Root 2) cannot be expressed as a ratio of two whole numbers.
Now, it is important to realise that I have made no reference to any particular number system. Numbers have the property of rationality or irationality regardless of the number system that is used to express them.
So if you were to construct a number system with base pi (I have never seen non-whole number bases, but it is not immediately obvious why you could not do so), then you would have created a
number system with an irational base and the symbol '1' would still refer to an irrational number.
Pi is always the same value, and that value is always irrational.