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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?

user posted image

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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Puzzler
post Oct 14 2006, 12:34 PM
Post #2





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



Ova tema je odavno umrla...
Ali da je malo oživim biggrin.gif
Znate li da po nekim teorijama crne rupe imaju oblik Gabrijelove horne? blink.gif

This post has been edited by Puzzler: Oct 14 2006, 12:35 PM


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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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