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> Gabrijelova Horna, paradoks

Puzzler
post Jul 25 2006, 02:23 PM
Post #1





Group: Članovi
Joined: 2-July 06
Member No.: 74
Status: Van MGa
Škola/Razred: MG/IIb (proud of it)



Ne znam koliko je vas čulo za ovo...
Sve u svemu, pitanje je: Šta se desi kada rotiramo grafik funkcije y=1/x za x koje pripada intervalu  [1,{\infty}) oko x ose, kao na slici?

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Telo koje se dobije naziva se Gabrijelova horna (ili Gabrijelov rog). Šta je čudno u vezi sa njom?
Za x ->  {\infty} važi

 lim_{x-> {\infty}}V_{dobijenogtela}={\pi}

 P_{dobijenogtela}={\infty} (?!?)

Dakle, površina je neograničena, a zapremina ograničena! Zar to nije paradoks prve klase? Čekam neko vaše mišljenje... Da li je to uopšte moguće? Da li je to Božja tvorevina laugh.gif laugh.gif laugh.gif ?

P.S. Evo i nekih korisnih linkova...

Gabriel's horn 1
Gabriel's horn 2

This post has been edited by Puzzler: Jul 27 2006, 10:19 AM


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Posts in this topic
Puzzler   Gabrijelova Horna   Jul 25 2006, 02:23 PM
^_NiN0_^   RE: Gabrijelova Horna   Jul 25 2006, 07:26 PM
Puzzler   RE: Gabrijelova Horna   Jul 25 2006, 07:33 PM
Puzzler   RE: Gabrijelova Horna   Jul 25 2006, 08:13 PM
Puzzler   RE: Gabrijelova Horna   Jul 25 2006, 08:57 PM
Puzzler   RE: Gabrijelova Horna   Aug 16 2006, 01:44 PM
ex-paydoman   RE: Gabrijelova Horna   Jul 26 2006, 12:16 AM
^_NiN0_^   RE: Gabrijelova Horna   Jul 26 2006, 12:21 AM
Puzzler   RE: Gabrijelova Horna   Aug 14 2006, 07:48 PM
^_NiN0_^   RE: Gabrijelova Horna   Aug 14 2006, 08:04 PM
Puzzler   RE: Gabrijelova Horna   Aug 14 2006, 09:18 PM
Legenda   RE: Gabrijelova Horna   Aug 15 2006, 09:05 AM
Puzzler   RE: Gabrijelova Horna   Aug 15 2006, 09:04 PM
^_NiN0_^   RE: Gabrijelova Horna   Aug 16 2006, 12:37 AM
Legenda   RE: Gabrijelova Horna   Aug 16 2006, 01:42 PM
^_NiN0_^   RE: Gabrijelova Horna   Aug 16 2006, 02:51 PM
Legenda   RE: Gabrijelova Horna   Aug 16 2006, 05:27 PM
^_NiN0_^   RE: Gabrijelova Horna   Aug 16 2006, 06:33 PM
Legenda   RE: Gabrijelova Horna   Aug 16 2006, 06:45 PM
^_NiN0_^   RE: Gabrijelova Horna   Aug 16 2006, 06:57 PM
Legenda   RE: Gabrijelova Horna   Aug 16 2006, 07:04 PM
^_NiN0_^   RE: Gabrijelova Horna   Aug 16 2006, 07:16 PM
Puzzler   RE: Gabrijelova Horna   Aug 17 2006, 09:40 PM
^_NiN0_^   RE: Gabrijelova Horna   Aug 17 2006, 09:55 PM
Legenda   RE: Gabrijelova Horna   Aug 18 2006, 04:07 PM
^_NiN0_^   RE: Gabrijelova Horna   Aug 18 2006, 07:37 PM
pyost   RE: Gabrijelova Horna   Aug 18 2006, 08:35 PM
^_NiN0_^   RE: Gabrijelova Horna   Aug 18 2006, 09:39 PM
pyost   RE: Gabrijelova Horna   Aug 18 2006, 09:43 PM
^_NiN0_^   RE: Gabrijelova Horna   Aug 18 2006, 09:50 PM
Legenda   RE: Gabrijelova Horna   Aug 19 2006, 11:54 AM
^_NiN0_^   RE: Gabrijelova Horna   Aug 19 2006, 12:08 PM
Legenda   RE: Gabrijelova Horna   Aug 19 2006, 12:09 PM
Puzzler   RE: Gabrijelova Horna   Aug 22 2006, 05:33 PM
^_NiN0_^   RE: Gabrijelova Horna   Aug 22 2006, 06:08 PM
pyost   RE: Gabrijelova Horna   Aug 22 2006, 06:00 PM
Legenda   RE: Gabrijelova Horna   Aug 22 2006, 06:03 PM
Legenda   RE: Gabrijelova Horna   Aug 22 2006, 06:17 PM
^_NiN0_^   RE: Gabrijelova Horna   Aug 22 2006, 08:17 PM
Puzzler   RE: Gabrijelova Horna   Aug 22 2006, 06:30 PM
Legenda   RE: Gabrijelova Horna   Aug 22 2006, 06:34 PM
Legenda   RE: Gabrijelova Horna   Aug 23 2006, 08:42 AM
^_NiN0_^   RE: Gabrijelova Horna   Aug 23 2006, 11:01 AM
Puzzler   RE: Gabrijelova Horna   Aug 23 2006, 10:12 AM
Puzzler   RE: Gabrijelova Horna   Aug 23 2006, 11:10 AM
Legenda   RE: Gabrijelova Horna   Aug 23 2006, 01:02 PM
Eli0t   RE: Gabrijelova Horna   Aug 23 2006, 01:32 PM
^_NiN0_^   RE: Gabrijelova Horna   Aug 23 2006, 03:52 PM
Legenda   RE: Gabrijelova Horna   Aug 23 2006, 06:08 PM
Puzzler   RE: Gabrijelova Horna   Oct 14 2006, 12:34 PM


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