Download - caleidociclo - sigpibid.ufpr.br
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O termo caleidociclo vem de
kalós (belo) + eidos (forma) +kyklos (ciclo)
Ou seja, podemos pensar que um caleidociclo seja uma bela forma cíclica.
Ele é constituído por uma cadeia de tetraedros, como se fosse um anel que podemos girar infinitas vezes, geralmente são construídos em papel.
Quando giramos o caleidociclo de dentro para fora ou de fora para dentro, a cada giro forma-se uma figura diferente.
Os caleidociclos são utilizados tanto na arte como também no ensino.
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Wallace Walker, durante o trabalho num projeto
para formas estruturais de papel, inventou uma
construção, nomeando-a de IsoAxis, que
consistia em um anel tridimensional capaz de
girar em torno de si mesmo, completando ciclos.
Nomeação - Doris Schattschneider, anos mais
tarde e após muito estudo.
1991 – “Problema de Escher”
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As suas obras são
repletas de coisas
subjetivas e o mais
interessante em suas
obras é a ilusão de
ótica, que nos dá a
impressão de
dimensões jamais
imaginadas na
realidade.
Veja mais em:
http://webeduc.mec.gov.br/portaldoprofessor/matematica/condigital2/midias/experimentos/Geometria_e_arte/
historico.html
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Ascending and Descending (sobe e desce), litografia de 1960.
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Circle Limit IV (Figura limitada por um círculo IV), 1960
xilogravura impressa em preto e ocre, a partir de 2 matrizes.
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Na busca de resolver o problema da
representação de uma superfície
pavimentada infinita, sem deformar as
figuras, Schattschneider e Walker pensaram
em recobrir os caleidociclos com as simetrias
de Escher
https://www.youtube.com/watch?v=-Wu1w1T03hw
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Os mais conhecidos são:
Caleidociclo hexagonal (caleidociclo de Escher);
Caleidociclo quadrado;
https://www.youtube.com/watch?v=eex-QV4HKGM
Caleidociclo contorcido.
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Geometria Plana
Posição relativa entre retas
• Retas concorrentes;
• Retas perpendiculares;
Polígonos
Simetria
Congruência e semelhança
Geometria Espacial
Poliedros
Relação de Euler
Área e Volume
(...)
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4 8L
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Linhas Diagonais: dobra em vale
- Ao dobrar dessa forma, não é possível ver o
traçado do molde. Usar um régua para auxiliar
Linhas verticais : dobra em montanha
- Ao dobrar dessa forma, visualizamos todo o
traçado do molde
Essa nomenclatura das dobras (vale e
montanha) é usada nos origamis.
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4 4
4 4
2
2 2
2
2 2
2 2
3 3
3 3
3 3
3 3
1 1
1 1
1 1
1 1
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Caleidociclo – Ciclo da Água
https://www.youtube.com/watch?v=C-11khHsItU
Caleidociclo – As 4 estações
Caleidociclo – Ciclo da Vida
https://www.youtube.com/watch?v=zuq8S56U-_c
Mini histórias
Caleidociclos de fotos
http://www.manualdomundo.com.br/2014/06/como-
fazer-caleidociclo/
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http://www.manualdomundo.com.br/2014/06/como-fazer-caleidociclo/
http://webeduc.mec.gov.br/portaldoprofessor/matematica/condigital2/midias/experimentos/Geometria_e_arte/episodios/ep_13.html
http://engenhariadepapel.blogspot.com.br/2013/07/caleidociclo-ciclo-da-chuva.html
http://www.mentesabsorventes.com/wp-content/uploads/2013/08/kaleidocycle_sistemasolar.jpg.pdf
http://engenhariadepapel.blogspot.com.br/2011/06/formas-geometricas-de-escher-monte-as.html
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Histótia do Caleidociclo
http://webeduc.mec.gov.br/portaldoprofessor/matematic
a/condigital2/midias/experimentos/Geometria_e_arte/ind
ex.html
http://www.pibid.ufpr.br/pibid_new/uploads/matematica
2011/arquivo/362/Caleidociclos.pdf
Plano de Aula
http://www.pibid.ufpr.br/pibid_new/uploads/Interdiscipli
nar2009/arquivo/574/PLANO-DE-AULA-PIBID-
CALEIDOCICLOS.pdf
Calendário de caleidociclo
http://mat.absolutamente.net/recursos/util/calendario/201
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