# Is there a rational way to conceptualize an irrational number?

This is a request for help, not an attempt to challenge anything.

Since $\pi$ is irrational, this tells me that it's impossible to express the distance around a circle in terms of the distance accross.

That boggles my mind, but maybe it should not.

I think crazy thoughts like: "this means that a the path of a circle around a unit lenth line segment has a non existant length".

Is there a way to accept that the number is irrational and not break from reason?

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Knowing what rational and irrational actually mean would be a good start. The irrationality of $\pi$ certainly does not mean that it's impossible to express the circumference of a circle in terms of the diameter. –  Chris Eagle Feb 22 '12 at 17:15
apologies.. maybe i have to delete this –  Aaron Anodide Feb 22 '12 at 17:16
Why it tells you that it is impossible to express it? You can express it using $\pi$. You can't say that is is a nonexistant length it is just a length that is not a fraction. Like the length of the diagonal of the unit square. Nothing special. –  savick01 Feb 22 '12 at 17:17
@PradipMishra We do not call numbers without decimal representation irrational. ($1/3=0.33333\ldots$ is rational but has no representation) We call numbers irrational if they are not rational, so they are not a ratio $a/b$ of some integers $a,b$. –  savick01 Feb 22 '12 at 17:24
It's of interest to note that the modern connotation of "irrational" arose from the consternation expressed by those who first realized $\sqrt 2$ is not a ratio (of integers), at least according to some sources... –  David Mitra Feb 22 '12 at 17:41

That $\pi$ is irrational does not mean that it's impossible to express the distance around a circle in terms of the distance across. It only means it can't be expressed as a ratio of integers.

BTW here you can read some proofs that $\pi$ is irrational.

It is quite easy to prove that $\sqrt{2}$ is irrational. It's even easier to prove that $\log_2 3$ is irrational. But it's hard to prove $\pi$ is irrational.

Here is a related question that may be of interest, where you will read about how to prove some numbers are irrational.

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