dlnash@ut-ngp.UTEXAS (Donald L. Nash) (10/03/85)
*** REPLACE THIS LINE WITH YOUR MESSAGE ***
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!
Bizarre....
Don Nash
UUCP: ...!{ihnp4,allegra,seismo!ut-sally}!ut-ngp!dlnash
APRA: dlnash@ngp.UTEXAS.EDUpdg@ihdev.UUCP (P. D. Guthrie) (10/06/85)
In article <2452@ut-ngp.UTEXAS> dlnash@ut-ngp.UTEXAS (Donald L. Nash) writes: >*** REPLACE THIS LINE WITH YOUR MESSAGE *** > >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! > >Bizarre.... > > Don Nash > >UUCP: ...!{ihnp4,allegra,seismo!ut-sally}!ut-ngp!dlnash >APRA: dlnash@ngp.UTEXAS.EDU "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!
lp102911@sjuvax.UUCP (palena) (10/07/85)
In article <2452@ut-ngp.UTEXAS> dlnash@ut-ngp.UTEXAS (Donald L. Nash) writes: >*** REPLACE THIS LINE WITH YOUR MESSAGE *** > >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! > >Bizarre.... > > Don Nash > >UUCP: ...!{ihnp4,allegra,seismo!ut-sally}!ut-ngp!dlnash >APRA: dlnash@ngp.UTEXAS.EDU Well GOLLLLLLY!!!! Consider an infinite sum with a limit. What this means is that I can add something together forever without it ever exceding a certain amount. Bizarre....... Larry Palena St. Joseph's Univ. { astrovax | allegra | bpa | burdvax } !sjuvax!lp102911
mcewan@uiucdcs.CS.UIUC.EDU (10/07/85)
>>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." "Are too! Are too! Woof! Woof!"
wtm@bu-cs.UUCP (W. Thomas Meier) (10/07/85)
Peace and tranquility to you all, However, to the person who thought that trying to find the surface area of the 3D graph of 1/x rotated around Y, was something new and wonderfull, I would say, "Welcome to the known universe, and be greated by Gabriel's horn". One-ness fellow babes. Wally T. (Babes) Meier, Ex math person at large present computer person on site, hopefully an engineer in a bit.
gjk@talcott.UUCP (John) (10/07/85)
In article <346@ihdev.UUCP>, pdg@ihdev.UUCP (P. D. Guthrie) writes: > In article <2452@ut-ngp.UTEXAS> dlnash@ut-ngp.UTEXAS (Donald L. Nash) writes: > >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... ... > "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.... This man is giving Byte magazine the credit for a math problem between two and three centuries old. Now that's bizarre! P.S. You'll never guess when the fast fourier transform was invented... -- abcdefghijklmnopqrstuvwxyz ^ ^^
dlnash@ut-ngp.UTEXAS (Donald L. Nash) (10/07/85)
In <346@ihdev.UUCP>, a follow up to my bizarre mathematics posting, pdg@ihdev.UUCP (P. D. Guthrie) writes: > In article <2452@ut-ngp.UTEXAS> dlnash@ut-ngp.UTEXAS (Donald L. Nash) writes: /* My message here.*/ > "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! Ooooooops! Sorrrrry! No plaguerism intended. Yes, I did see that stuff in BYTE, but I also learned it in calculus class before I read it in BYTE. The idea of that funnel having infinite surface area and finite volume is not new. I posted it on the net for the benefit of those people who do not subscribe to BYTE. I was not aware that posting such well known facts (well known in the area of mathematics, anyway) constituted plaguerism. PLEASE, no flames to my mailbox. I apologize if I have insulted or injured anyone. Don Nash UUCP: ...!{ihnp4,allegra,seismo!ut-sally}!ut-ngp!dlnash APRA: dlnash@ngp.UTEXAS.EDU
carl@aoa.UUCP (Carl Witthoft) (10/08/85)
In article <346@ihdev.UUCP> pdg@ihdev.UUCP (55224-P. D. Guthrie) writes: >> >>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. ...and lots more>>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.... > Sorry to look like a serious person, but I saw this in Goodman's Calc. text in 1972, and I think in Johnson&kiokemeister in '70, so this particular "fun" problem in intro calc is almost certainly in the public domain. But then, net.bizarre is rated "S" for sickos only (:==> ) Darwin's Dad (Carl Witthoft) ...!{decvax,linus,ima,ihnp4}!bbncca!aoa!carl @ Adaptive Optics Assoc., 54 Cambridgepark Dr. Cambridge, MA 02140 617-864-0201 " Buffet-Crampon R-13 , VanDoren B-45, and VanDoren Fortes ."
pdg@ihdev.UUCP (P. D. Guthrie) (10/08/85)
In article <2463@ut-ngp.UTEXAS> dlnash@ut-ngp.UTEXAS (Donald L. Nash) writes: >In <346@ihdev.UUCP>, a follow up to my bizarre mathematics posting, >pdg@ihdev.UUCP (P. D. Guthrie) writes: > >> In article <2452@ut-ngp.UTEXAS> dlnash@ut-ngp.UTEXAS (Donald L. Nash) writes: > > /* My message here.*/ > >> "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! > >Ooooooops! Sorrrrry! No plaguerism intended. Yes, I did see that stuff in >BYTE, but I also learned it in calculus class before I read it in BYTE. The >idea of that funnel having infinite surface area and finite volume is not >new. I posted it on the net for the benefit of those people who do not >subscribe to BYTE. I was not aware that posting such well known facts >(well known in the area of mathematics, anyway) constituted plaguerism. >PLEASE, no flames to my mailbox. I apologize if I have insulted or injured >anyone. > > Don Nash > >UUCP: ...!{ihnp4,allegra,seismo!ut-sally}!ut-ngp!dlnash >APRA: dlnash@ngp.UTEXAS.EDU It's me that owes the apology. On closer examination of Byte, the words were different, and Donald Nash is quite correct, does not constitute anything near plaguerism. Sorry, it won't happen again, and I will keep my future postings to this group as bizarre as possible. Paul Guthrie. P.s. Please send all flames to net.flame as I don't read it! :-)
andrews@ubc-cs.UUCP (Jamie Andrews) (10/09/85)
-- >>> Come on, NO plaguerism even in net.bizarre! ^^^^^^^^^^ >>Ooooooops! Sorrrrry! No plaguerism intended. Yes, I did see that stuff in ^^^^^^^^^^ >>(well known in the area of mathematics, anyway) constituted plaguerism. ^^^^^^^^^^ >anything near plaguerism. Sorry, it won't happen again, and I will keep ^^^^^^^^^^ -- a) it's "plagiarism" (after 3 messages i couldn't stand it anymore) ^^^^^^^^^^ b) since the graph never touches the x-axis, all the paint would leak out the end of the funnel anyway c) how do you cook wombats? i hear death wombats are especially tasty --Jamie. "'If you are a wise man it certainly is your field,' said Maria. 'They said a wise man should be able to catch the wind in a net.'" -R.Davies
lp102911@sjuvax.UUCP (palena) (10/10/85)
In article <315@aoa.UUCP> carl@aoa.UUCP (Carl Witthoft) writes: >In article <346@ihdev.UUCP> pdg@ihdev.UUCP (55224-P. D. Guthrie) writes: >>> >>>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. >...and lots more>>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.... >> >Sorry to look like a serious person, but I saw this in Goodman's Calc. text >in 1972, and I think in Johnson&kiokemeister in '70, so this particular >"fun" problem in intro calc is almost certainly in the public domain. >But then, net.bizarre is rated "S" for sickos only (:==> ) Actually the question of where this first appeared is easily solved.The first person to carry out the two integrals and find out that the first one doesn't exist and the second one does should be given credit.So if that person is reading this net (and I'd be willing to bet s/he is) please inform us so you can receive your "GOD MATH CAN BE WEIRD" award. Larry Palena { astrovax | allegra | bpa | burdvax } !sjuvax!lp102911