milica mijailović, lazar mijailović, biljana janković, dragan tošić
DESCRIPTION
TESELACIJA RAVNI TROUGLOVIMA, ČETVOROUGLOVIMA (I PETOUGLOVIMA). Milica Mijailović, Lazar Mijailović, Biljana Janković, Dragan Tošić. Profesor: Srđan Vukmirović. Beograd 2010/2011. - PowerPoint PPT PresentationTRANSCRIPT
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Milica Mijailović,
Lazar Mijailović,
Biljana Janković,
Dragan Tošić
Profesor:
Srđan Vukmirović
TESELACIJA RAVNI TROUGLOVIMA, ČETVOROUGLOVIMA (I PETOUGLOVIMA)
Beograd 2010/2011
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Teselacija ravni predstavlja popločavanje ravni oblicima bez preklapanja i šupljina. Opšte poznate su teselacije kvadratom i pravilnim šestouglom.
Postoje pravilne i nepravilne teselacije.
Pravilne su one kod kojih se za teselaciju koristi isključivo jedan oblik, dok se kod nepravilnih vrši korišćenjem dva ili više oblika.
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Teselacija trouglovima
Bilo koji proizvoljni trougao teselira ravan.
To se može uraditi rotacijom trougla oko središnje tačke neke od stranica. U nekim slučajevima formira se paralelogram koji teselira ravan.
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Teselacija trouglom za koordinate: (7,7) (5,15) (1,10);
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Teselacija trouglom za koordinate: (8,10) (15,32) (10,22);
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Teselacija trouglom za koordinate: (1,8) (15,3) (7,9);
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Teselacija trouglom za koordinate: (2,1) (8,5) (10,25);
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Teselacije četvorouglovima
Takođe, svi četvorouglovi mogu teselirati. To se takođe može izvršiti rotacijom tog četvorougla oko središnjih tačaka njegovih stranica i na taj način se formira oblik koji teselira.
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Teselacija četvorouglom za koordinate: (8,5) (10,12) (6,9) (2,3) ;
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Teselacija četvorouglom za koordinate: (8,0) (12,2) (13,5) (5,10);
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Teselacija četvorouglom za koordinate: (5,3) (8,9) (6,2) (1,4);
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Teselacija četvorouglom za koordinate: (1,2) (3,8) (5,7) (9,2);
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Teselacija petouglovima
Postoji 14 različitih teselacija petouglovima:
D + E = 180o
C + E = 180o, a = d
(Velika slova predstavljaju uglove kod tih temena, a mala stranice)
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A = C = D = 120o, a = b, d = c + e
A = C = 90o, a = b, c = d
(Velika slova predstavljaju uglove kod tih temena, a mala stranice)
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C = 2A = 120o, a = b, c = d
C + E = 180o, A = 2C, a = b = e, c = d
(Velika slova predstavljaju uglove kod tih temena, a mala stranice)
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2B + C = 360o, 2D + A = 360, a = b = c = d
2A + B = 360o, 2D + C = 360, a = b = c = d
(Velika slova predstavljaju uglove kod tih temena, a mala stranice)
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2E + B = 360o, 2D + C = 360o, a = b = c = d
E = 90o, A + D = 180o, 2B - D = 180o, 2C + D = 360o, a = e = b + d
(Velika slova predstavljaju uglove kod tih temena, a mala stranice)
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A = 90o, C + E = 180o, 2B + C = 360o, d = e = 2a + c
A = 90o, C + E = 180o, 2B + C = 360o, 2a = c + e = d
(Velika slova predstavljaju uglove kod tih temena, a mala stranice)
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A = C = 90o, 2B = 2E = 360o - D, c = d, 2c = e
D = 90o, 2E + A = 360o, C + A = 180o, B + D + E = 360o, 2e = 2c = a
(Velika slova predstavljaju uglove kod tih temena, a mala stranice)
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Teselacija petouglom za koordinate: (0,0) (9,8) (9,15) (6,20) ;
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Teselacija petouglom za koordinate: (5,6) (10,6) (7,6) (5,5);
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Teselacija petouglom za koordinate: (2,2) (12,2) (6,8) (5,10);
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Teselacija petouglom za koordinate: (8,0) (24,0) (13,5) (10,10);