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