From: tdb@maths.qmw.ac.uk (Thomas D Bending)
Newsgroups: sci.math
Subject: Re: Pi
Date: 06 Mar 1995 09:46:26 GMT
In article <3jdmka$ja0@grivel.une.edu.au> mnaylor@neumann.une.edu.au (Mark Naylor) writes:
> All I need to know is the following
> Is 22/7 an approximation of pi because thats what I think but a fuckhead
> maths guy whos been to uni a bit longer then me says it IS pi?
First things first: please don't use words like f*ckhead on the net -
a lot of people are offended by them.
22/7 is indeed only an approximation to pi, which is irrational
(indeed transcendental) - you are right and he is wrong. There have
been a number of threads recently about rational apporoximations to
pi, and how to prove it's irrational and transcendental, but to answer
the specific question "Does pi=22/7?" here's an unusual proof:
The value of the definite integral between 0 and 1 of
(x^4)*((1-x)^4)/(1+x^2) is 22/7 - pi. The integrand is clearly
non-negative in this range, and is non-0 at x=1/2, so the value
of the integral is not 0, so pi isn't 22/7.
This is adapted from "Fifty Per Cent Proof" (ed. Selkirk and Willson),
a collection of mathematical humour from the Mathematical Gazette and
elsewhere, which I thoroughly recommend.
Dr Thomas Bending JANET: tdb@uk.ac.qmw.maths
WWW homepage