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From: mcewan@uiucdcs.CS.UIUC.EDU
Newsgroups: net.bizarre
Subject: Re: Bizarre mathematics
Message-ID: <161000016@uiucdcs>
Date: Mon, 7-Oct-85 13:34:00 EDT
Article-I.D.: uiucdcs.161000016
Posted: Mon Oct  7 13:34:00 1985
Date-Received: Sat, 12-Oct-85 14:02:29 EDT
References: <2452@ut-ngp.UTEXAS>
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Nf-ID: #R:ut-ngp.UTEXAS:-245200:uiucdcs:161000016:000:1365
Nf-From: uiucdcs.CS.UIUC.EDU!mcewan    Oct  7 12:34:00 1985


>>Here's a bit of bizarre math stuff which may warp your mind.  Imagine
>>if you will, the graph of the function y = 1/x from x=1 to x=infinity.
>>I'm sure that everyone out there is smart enough to draw this picture
>>mentally.  Now rotate this graph about the x-axis.  You get a long,
>>skinny funnel of infinite length.  If you work out the integral which
>>determines the surface area of the funnel, you will find that it also
>>is infinite.  Now comes the bizarre part.  If you work out the integral
>>which determines the volume enclosed by that funnel, you find that it
>>is not infinite, but that it is pi cubic units!  Think of the significance
>>of that:  You can fill the funnel with paint, but you can't paint its
>>surface, because you will never have enough paint!
>
>"Mathematical Recreations: Pi, e and all that" By Robert T. Kurosaka.
>Byte Magazine, September 1985, v10 no.9, P.409
>
>Credit where credit is due....
>
>Come on, NO plaguerism even in net.bizarre!

Believe it or not, this was known before it appeared in Byte. I first heard it
in my high school calculus class over 10 years ago, and I doubt it was a recent
discovery then.

			Scott McEwan
			{ihnp4,pur-ee}!uiucdcs!mcewan

"I know what you are. Nut. Screwball. Flake. Lunatic. Fruitcake.
 Bats in the attic. Psycho. All your dogs aren't barking."

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