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> Gabrijelova Horna, paradoks

Puzzler
post Jul 25 2006, 02:23 PM
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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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post Jul 25 2006, 07:26 PM
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Grrrr....geometrija...ali ipak ponesto znam o tome. Ne bas o Gabrijelovoj horni, vec o necemu drugom.


'vako... kada jednakostranicni trougao delite na cetiri jednaka dela do beskonacnosti i uzmete jedan deo, i tako dalje dobijate figuru beskonacnog obima a konacne povrsine... biggrin.gif biggrin.gif

A interesantna je ova horna wink.gif


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Puzzler
post Jul 25 2006, 07:33 PM
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Aha... Misliš na fraktalnu geometriju tj. geometriju samosličnosti? Odlično!!! smile.gif smile.gif smile.gif

Trougao Sierpinskog

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This post has been edited by Puzzler: Jul 25 2006, 07:36 PM


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Puzzler
post Jul 25 2006, 08:13 PM
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P.S. Zeznuo sam se sa prevodom... Ipak je "Gabrijelov ROG" a ne "Gabrijelova HORNA"! Ipak, to je pomalo glupo, jer je rečeno da je ime dobila po INSTRUMENTU (videti linkove), a kol'ko se ja sećam Muzičke, instrument se zove HORNA! smile.gif smile.gif smile.gif


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Puzzler
post Jul 25 2006, 08:57 PM
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Ha, ha ...
Evo još nečega za razmišljanje...

Bojlova samopuneća boca

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Šta mislite, da li je ovo moguće? Meni se čini da jeste... Sistem spojenih sudova i tako to... Ali dobro, ja sam "očajan" fizičar laugh.gif laugh.gif laugh.gif


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ex-paydoman
post Jul 26 2006, 12:16 AM
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alo bre!!! raspust je!!!
a owa samopunetja chasha je nemogutja, bar ne owa na crtezzu!


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post Jul 26 2006, 12:21 AM
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Naravno da je raspust, ali za ucenike MG-a nema odmora laugh.gif laugh.gif laugh.gif (ovo je bila sala mellow.gif )

Ipak sto se tice case mislim da je moguce zbog svih silnih potisaka, kretanja fluida(ili kako vec)....
btw pitajte Sibija on zna biggrin.gif


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Puzzler
post Aug 14 2006, 07:48 PM
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Da, ipak je ova samopuneća čaša nemoguća smile.gif


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post Aug 14 2006, 08:04 PM
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Lepo ... nego jel bi mogao da objasnis zasto, da bi i ostali clanovi razumeli smile.gif


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Puzzler
post Aug 14 2006, 09:18 PM
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Iz jednostavnog razloga što bi trebalo da se nivoi vode u oba dela suda izjednače, kao na ovoj slici... Nacrtano je na brzinu, nemojte mi uzeti za zlo biggrin.gif

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Legenda
post Aug 15 2006, 09:05 AM
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Tako je Puzzleru. wink.gif
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Puzzler
post Aug 15 2006, 09:04 PM
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Znači, ipak nisam tako "očajan" fizičar biggrin.gif


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post Aug 16 2006, 12:37 AM
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Ko je to rekao ?


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post Aug 16 2006, 01:42 PM
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Ovaj Puzzler...pametan covek,skoro k'o ja. biggrin.gif
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Puzzler
post Aug 16 2006, 01:44 PM
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QUOTE(Puzzler @ Jul 25 2006, 09:57 PM)
Ha, ha ...
Evo još nečega za razmišljanje...

Bojlova samopuneća boca

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Šta mislite, da li je ovo moguće? Meni se čini da jeste... Sistem spojenih sudova i tako to... Ali dobro, ja sam "očajan" fizičar  laugh.gif  laugh.gif  laugh.gif
*



Jel' ti sad jasno, Ljubo? wink.gif


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post Aug 16 2006, 02:51 PM
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Grrrr... pa i ja sam kazem sebi mnoge stvare, koje nisu tacne


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post Aug 16 2006, 05:27 PM
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To svakako. laugh.gif
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post Aug 16 2006, 06:33 PM
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Znate vi iz mog odeljenja vrlo dobro, tj. odlicno! smile.gif


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post Aug 16 2006, 06:45 PM
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Da kao npr. "Stefan Nemanja je postavljen na kolac,a na glavu mu bese postavljen kamen" laugh.gif
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post Aug 16 2006, 06:57 PM
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Ja to rekao ??? Sta ti pada na pamet rolleyes.gif rolleyes.gif rolleyes.gif


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