Not only is pi irrational, it is transcendental which means it is not
the solution of any algebraic equation of the form <some polynomial> = 0
where the coefficients of the polynomial terms are rational numbers
(integers or fractions). This is a stronger statement than saying pi is
irrational which is just saying it can't be expressed (exactly) as a
fraction.
Pi is a specific well-defined number and you can't redefine it to be
something else (such as some rational number) any more than you can
redefine the number four to be the square root of seventeen. Pierre is
correct.
For what it is worth there are vastly more transcendental numbers than
algebraic numbers - it is just that they don't crop up so often in our
mathematics.
Brij Bhushan Vij wrote:
You are talking nonsense. The value of pi is irrational.
No brick batting & I do not mean to hurt!
What makes you conclude.....The value of pi is irrational.?
Brij Bhushan Vij <[EMAIL PROTECTED]>
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From: Pierre Abbat <[EMAIL PROTECTED]>
Reply-To: [EMAIL PROTECTED]
To: "U.S. Metric Association" <[email protected]>
Subject: [USMA:34900] Re: common fractions fail for some numbers
Date: Sun, 16 Oct 2005 02:33:05 -0400
On Sunday 16 October 2005 01:42, Brij Bhushan Vij wrote:
> The question I raised is NOT which value for Pi is more accurate &
why? BUT
> that *is there a value for Pi that satisfy the relation: a circle
has 2 Pi
> radians - without defining either Pi or radian*? If there is a
deviation to
> value for Pi, with WHAT are we attempting to compare, to kaow how
musch is
> this OFF; AND from what standard!
> I claim my value for Pi that defines *both the value for Pi and
Radian and
> FIXES their values*. Thus, Pi =100000/31831 (exact); and fixes
radian at
> 57*.2958 =57* 17/44".88 - a value fixed by International Society of
> Mathematics.
You are talking nonsense. The value of pi is irrational. It can be
defined as
the ratio of circumference to diameter, the smallest positive number
whose
sine is 0, or the sum of any of various infinite series, and these
are all
the same number. 100000/31831 and 355/113 are not values of pi, they are
approximations to pi.
phma
