Unreasonable pi

[psjm]

What word, meaning 'not reasonable or logical', is also applied to any number, such as pi, which cannot be expressed as an exact fraction?

[mike1222]

Irrational

[Peter Pedant]

psjm, you now owe it to us on answer bank to go to a book and read the standard very easy proof that the square root of two is irrational. It will do you good.

[psjm]

Peter Pedant - get a life!

[JohnPPotts]

Actually, pi is not just irrational, it's a transcendent number (meaning that it cannot be expressed as the answer to any polynomial with non-infinite terms). By contrast root 2 (1.414.....) is irrational (it's a non-terminating, non-recurring decimal) but is not transcendent as it can be given as the solution to the equation x squared = 2. Hope that clears everything up!

[Peter Pedant]

Agreed, a proof that pi is irrational which reduces to why one can't square a circle, or why sinx is irrational, I dont regard as elementary.

and while psjm is getting a life, she could easily get her brain around the irrationality of root 2.

a proof that pi is transcendental, that is that it is not a root of a polynomial was only completely in the late nineteenth century and cannot be called elementary in anyway.