Los encantos de esta ciencia sublime, las matemáticas, sólo se le revelan a aquellos que tienen el valor de profundizar en ella. Carl Friedrich Gauss

domingo, 14 de febrero de 2010

MOSAICO O TESELADO

¿Qué es un teselado?
Es un patrón repetitivo de figuras geométricas, por ejemplo polígonos, que encajan y cubren el plano sin superponerse y sin dejar huecos.

¿Qué es teselar?
Es embaldosar una superficie con figuras regulares o irregulares. Al teselar un plano, entre las figuras, no quedan espacios y tampoco se superponen.

Los cubrimientos realizados con baldosas, cerámicos, pastelones, azulejos, tejas en pisos, muros y techos son las más comunes teselaciones que se encuentran en la realidad.

  • Observa el siguiente teselado, ¿puedes descubrir el patrón que se repite?
Los teselados regulares se logran a partir de la repetición y traslado de polígonos regulares.

¿Cuáles polígonos se pueden usar para hacer teselados regulares?

Para descubrirlo realiza las siguientes actividades:

  • Recorta varios triángulos equiláteros iguales.
  • De la misma manera, recorta( con la ayuda de un molde) cuadrados, pentágonos, hexágonos y octógonos. Recuerda que todos deben ser polígonos regulares.
  • Utiliza hojas blancas. Pega en una de ellas los triángulos tratando de cubrir todo el plano.
  • Repite la misma operación para los cuadrados, pentágonos regulares, hexágonos y octógonos.
  • Ahora responde: ¿Cuáles son los polígonos que se pueden usar para hacer teselados regulares?
  • Mide ahora los ángulos interiores de los distintos polígonos regulares y suma la medida de los ángulos interiores de los mismos.
  • ¿Qué condición debe existir en cuanto a la suma de los ángulos en un vértice común para poder tener un teselado?
Recuerda que para formar un teselado no pueden quedar espacios en blanco entre las figuras ni se pueden superponer




  • De acuerdo a la información de la tabla, ¿qué polígonos regulares se pueden usar para hacer teselados? ¿Y por qué no se pueden usar otros?
Como habrás visto, una teselación regular es un patrón que se consigue repitiendo un polígono regular (para que sea regular los lados y los ángulos tienen que ser iguales). Sólo existen tres teselaciones regulares:
Los teselados semi-regulares están hechos con dos o más polígonos regulares. ¡El patrón debe ser el mismo en todos los vértices!
Observa algunas de ellas:


Los teselados demi-regulares están formados usando los tres teselados regulares y los 8 teselados semi-regulares. Existen 14 teselados demi-regulares. Algunos de ellos son:
Los teselados irregulares están construidos a partir de polígonos regulares e irregulares que al igual que todas las teselaciones cubren toda la superficie sin sobreponerse y sin dejar espacios vacíos. La distribución de los polígonos en los distintos vértices es cíclica.
Observa estos dos ejemplos:
Manos a la obra:
Ahora, realiza tus propias teselaciones
  • Utiliza uno de los polígonos regulares con los que se puede teselar el plano, por ejemplo, un cuadrado.
  • Recorta una sección del cuadrado, a lo largo de una curva que no tenga autointersercciones.
  • Pega el segmento recortado del lado opuesto al que fue cortado.
  • Repite este proceso cuantas veces quieras.
  • Utiliza esta figura como molde para copiarla en una hoja, después trasládala sobre la hoja sin que haya traslapes.
  • Decora tus figuras.

115 comentarios:

  1. He dejado algo para ti en esta entrada de mi blog.

    Un saludo

    http://creaconlaura.blogspot.com/2010/02/kreative-blogger.html

    ResponderEliminar
  2. Anónimo13:47

    que lindo megusto muxo

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  3. Anónimo18:26

    hola soy v.a. busco un teselado cuadrdo me dicen donde encontrarlo porfis

    ResponderEliminar
  4. Anónimo15:19

    que padre pagina

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  5. ZTHEYZI16:04

    ola
    mi
    nombre
    es ZTHEYZI
    y es un
    pagina
    algo
    interesante
    pero un
    comentario
    suban mas
    informacion
    como las
    caracteristicas
    etc
    BUEN TRABAJO

    ResponderEliminar
    Respuestas
    1. Anónimo15:17

      Amo tu comentario.
      Pero cuidado con la ortografía ;)
      Se ve más presentable, además a mi me chocan los errores.
      Gracias.
      Anónimo

      Eliminar
    2. Anónimo10:20

      hola me gusta el minecraft y busco novia

      Eliminar
  6. Anónimo12:40

    muy bueno,me sirvio arto xd,para hacer este trabajo...

    ResponderEliminar
  7. criticar es muy facil, hacer es dificil
    felicitaciones por tu exposicion me gusta y la programare con mis estudiantes

    ResponderEliminar
  8. Anónimo4:50

    esta re cheto el testelado

    ResponderEliminar
  9. aqui les vailo yo4:55

    me aburre el teselado

    ResponderEliminar
  10. papanatas5:01

    den señal de vida

    ResponderEliminar
  11. genaro perez ferro5:06

    canvie de idea me gustan los testelados

    ResponderEliminar
  12. delgadillo5:19

    hola chicos estudiosos como yo

    ResponderEliminar
  13. Anónimo10:12

    Hola Beatriz, soy docente de matemática y me desempeño como gestora de contenidos para el portal Cubaeduca y me ha interesado mucho tu trabajo sobre teselados.
    Necesito por favor que me contactes por matematica@rimed.cu
    Gracias de antemano

    ResponderEliminar
    Respuestas
    1. Anónimo11:11

      OOO, repadree!
      Me encantó que te gustara, ai ai ai!!!
      Bueno buey, ya contactaremos y practicaremos!!
      Chaoo!

      Eliminar
  14. Anónimo7:57

    no tienen algo masssssssss que hacerrr jajaja na de eso esta superrr padre esa pag.

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    Respuestas
    1. Anónimo11:08

      A que si compadre!!!
      Esta super!
      Bueno, recuerdos a la familia bueyy!!
      Adióos!
      AI AI AI! ESTA REPADREE...MADRE MIA!

      Eliminar
  15. Anónimo9:44

    ocupo un teselado jamas antes visto me pueden ayudar o dar una idea porfas

    ResponderEliminar
  16. Anónimo9:41

    bien :)
    deberían de poner mas yo opino pero es un buen trabajo

    ResponderEliminar
  17. Anónimo17:42

    holaa quisiera saber porque en algunas figuras se puede hacer un teselado y en otras no?

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  18. Se dice que la pieza es teselante cuando es posible acoplarlas entre sí sin huecos ni fisuras hasta recubrir por completo el plano; la configuración que en tal caso se obtiene recibe el nombre teselación.

    ResponderEliminar
  19. Anónimo11:52

    es un trabajo muy bien hecho y muestra un lado divertido de las matematicas ¡Felicidades! aunque faltaron algunos aspectos que cubrir con respecto al tema

    ResponderEliminar
  20. Anónimo18:37

    esta super xida la informacion para nosotros los estudiantes que la nesesitamos

    ResponderEliminar
  21. Anónimo14:31

    me gusto bastante

    ResponderEliminar
  22. Anónimo14:34

    amo a ander aguilar corona

    ResponderEliminar
  23. Anónimo14:34

    :) bien hexo

    ResponderEliminar
  24. Anónimo7:55

    Muy bueno, gracias por compartir conocimiento.
    Rubén

    ResponderEliminar
  25. Anónimo10:01

    mejor digan si se puede usar un poligono irregular como superficie de una teselacion porfis lo necesito ahora ....

    ResponderEliminar
  26. Anónimo14:03

    esta información es muy buena me gusto y me ayudo a pasar mi tarea

    ResponderEliminar
  27. fernanda rival13:05

    Hola Bety, nosé si me recordarás, soy Fernanda Rival. Ex alumna tuya...
    Me dedico a diseñar y tallar calabazas para mate y me gusta mucho el teselado, así que trato de plasmarlo a la misma. Entré a la pág. y me encuentro con la sorpresa de tu foto...con las matemáticas...
    Una honor y alegría ésta suerte de encontrarte.!!
    Mandaré fotos para que veas el trabajo.
    Saludos y cariños a los tuyos.
    Desde el Bolsón.
    Fer

    ResponderEliminar
  28. Hola Fernanda, qué alegría al leer este comentario. Cómo no te voy a recordar!!!
    Cómo verás ahora torturo gente con la Matemática a través del blog.
    Espero tus fotos.
    Cariños
    Bety

    ResponderEliminar
  29. Anónimo16:15

    no tienen mas informacion sobre las caracteristica ????

    ResponderEliminar
  30. Anónimo18:11

    Este comentario ha sido eliminado por un administrador del blog.

    ResponderEliminar
  31. Anónimo12:09

    Este comentario ha sido eliminado por un administrador del blog.

    ResponderEliminar
  32. Anónimo20:45

    pq no0 ponen en que se utilizan los teselado0z
    pd:bna pagiina !!!

    ResponderEliminar
  33. Anónimo20:48

    alguien m puede ayuUdar sthoii buskndo0 en qe se utilizan los teselados ????

    ResponderEliminar
  34. Anónimo17:02

    q padre esta esta pagina, me gusto muchoooooooooooooooooo

    ResponderEliminar
  35. super chida la pagina

    ResponderEliminar
  36. Anónimo12:05

    muy bien
    pero no todos
    decian co0mo0 hacerlo...
    jejejej

    ResponderEliminar
  37. Anónimo16:36

    Gracias este blog me ha servido de mucho

    ResponderEliminar
  38. Anónimo14:44

    Excelente trabajo yo hice el del pez

    ResponderEliminar
  39. Pase por tu Blog y me gusto, estoy viento tema de los teselados con 2o secundaria,Bye

    ResponderEliminar
  40. Anónimo17:24

    donde esta el significado de mosaico porfisssss

    ResponderEliminar
  41. Anónimo14:27

    y el mosaico que

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  42. Felicidades Maestra Bety.... Excelente blog... Reciba un saludos desde Tixtla, Guerrero, México... creo que falto referencia bibliográfica.... Felicidades

    ResponderEliminar
  43. Felicidades Maestra Bety.... Excelente blog... Reciba un saludos desde Tixtla, Guerrero, México... creo que falto referencia bibliográfica.... Felicidades

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  44. Este comentario ha sido eliminado por un administrador del blog.

    ResponderEliminar
  45. Genial
    Es un buen material, muchas gracias por compartirlo

    ResponderEliminar
  46. Anónimo20:30

    Este comentario ha sido eliminado por un administrador del blog.

    ResponderEliminar
    Respuestas
    1. Anónimo9:44

      Fueron muy responsables ;-) ;-D

      Eliminar
  47. Anónimo15:53

    Hola solo quería decirte que esta bueno tu blog pero una pregunta se puede hacer un teselado de hexágono, octógono, eneagonos, decagonos con sólo una figura. Me refiero a que sólo con esas? ?? ?

    ResponderEliminar
  48. Anónimo9:39

    Muchas gracias me salvaron de un apuro :D:-) :-) :-) :-) :-) :-)

    ResponderEliminar
    Respuestas
    1. Anónimo9:41

      De nada niñ@ o joven chic@

      Eliminar
  49. Buenas noches, una pagina muy buena, pero sigo sin encontrar mi solución

    ResponderEliminar
  50. Anónimo8:39

    x favor necesito un informe para exponer de teselaciones con problemas faciles para expocicion . si pueden mandarmelo en face se los agradeceia alejandro alarcon

    ResponderEliminar
  51. Anónimo20:54

    puto juan carlos

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  52. Anónimo17:40

    Con cuáles figuras no se puede hacer una teselación

    ResponderEliminar
  53. Anónimo7:46

    muy buena informacion

    ResponderEliminar
  54. me gusta ver comentarios bien escritos, detesto escritura cambiada por modismos, eso solo de debe hacer con personas de tu mismo ambito

    ResponderEliminar
  55. Anónimo16:38

    hola XD

    ResponderEliminar
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