1. Surf
the web and find a text related to your teaching career. Please fulfill these
requirements:
a. an
academic text.
b. a valid authentic source
Science Museum Math Exhibit
geometry.pre-college, geometry.college,
Fri, 17 Jun 1994
Geometry
Center staff collaborated with the Science Museum of Minnesota to produce a
museum exhibit on triangle tilings. Starting with a module for Geomview written
by Charlie Gunn, staff members Tamara Munzner and Stuart Levy, with assistance
from Olaf Holt, worked with exhibit developers at the museum to make software
and explanations which are accessible and interesting to the general public.
This is an especially difficult task at a museum; the average length of stay at
the exhibit is only about five minutes. Despite this, the Geometry Center and
museum collaborators managed to create an exhibit which contains sophisticated
concepts such as tilings of the sphere and the relationship between tilings and
the Platonic and Archimedean solids. Here is a brief description of the
exhibit.
The sum of the angles of a
planar triangle is always 180 degrees. Repeated reflection across the edges of
a 30, 60, 90 degree triangle gives a tiling of the plane, since each angle is
an integral fraction of 180 degrees. Figure 1 shows the exhibit's visualization of these ideas.Figure 1
What about a triangle whose angles add up
to more than 180 degrees? Such triangles exist on the sphere. Whenever the
angles of such a spherical triangle are integral fractions of 180 degrees,
repeated reflections across the edges give a tiling of the sphere. The exhibit
shows this for triangles with the first two angles always 30 and 60 degrees,
and the third angle selected as 45, 36, or 60 degrees. See figure 2.
A
spherical triangle which tiles and a point of the triangle, called the bending
point, uniquely determine an associated polyhedron as follows. Repeated
reflection through the edges of the triangle gives a tiling of the sphere, each
tile of which contains a reflected version of the bending point. These bending
point reflections are the vertices of the associated polyhedron. The edges are
chords joining each bending point and its mirror images. The faces are planes
spanning the edges. Associated to the spherical triangle which tiles the
sphere, there is a flattened triangle which tiles the polyhedron. The bending
point is the only point of the flattened triangle which is still on the sphere.
See figure 3. Also compare the spherical tiling with marked bending point in
figure 2 with the associated polyhedron in figure 4.
Tilings
of the sphere and polyhedra visually demonstrate the idea of a symmetry group.
Each choice of angles for the base triangle selects a different symmetry group.
Reflections across the edges of the base triangle are the generators of the
group. In the language of group theory, the vertices are images of the bending
point under the action of the group. The choices of group and bending point
completely determine the polyhedron.
The
exhibit software allows the viewer to move the bending point to see how the
resulting polyhedron changes. For particular choices of bending point, the
resulting polyhedra are Platonic and Archimedean solids. See figure 4. The
software allows viewers to see the relationship between these polyhedra more
easily than would a set of models. Using the mouse, viewers can watch the
polyhedron change as they drag the bend point. Thus they can begin to
understand the idea of duality of Platonic solids, as well as the idea of
truncation to form Archimedean solids.
The
triangle tiling exhibit is currently on view at the Science Museum of
Minnesota. In addition to the software, the exhibit contains books and posters
explaining the software, toys for constructing Platonic and Archimedean solids,
and other gadgets useful for understanding the ideas of tilings of the sphere.
For example, the exhibit includes a set of mirrored triangular tubes, each of
which contains a spherical or flattened triangle. The mirrored walls make it
appear as though inside each tube there is a sphere or a polyhedron. This gives
a physical demonstration that repeated reflections of some spherical triangles
tile the sphere, and repeated reflections of certain flattened triangles result
in the Platonic and Archimedean solids.
The
triangle tiling exhibit is successful with museum visitors; around 2500 people
use it each week. In addition, the exhibit has been accepted for display at the
annual meeting of the computer graphics organization SIGGRAPH. It will be part
of graphics display called The Edge. (For more about SIGGRAPH, see Evelyn
Sander, "SIGGRAPH Meeting," geometry.college, 17 August, 1993.)
This
article is based on an interview with Tamara Munzner and a visit to the Science
Museum of Minnesota. If you are interested in trying the software, which only
works on an SGI, it can be downloaded from the Geometry Center's downloadable software libary. The software is also available by anonymous
ftp from "geom.math.uiuc.edu" as tritile.tar.Z. The exhibit can easily be duplicated at other
science museums. If interested, contact Munzner (munzner@geom.umn.edu).
Macintosh
Version of Science Museum Software
geometry.announcements, Feb 13, 1995.
As of February,
1995, this software is also available on the Macintosh. Here are the details:
Jeff
Weeks has written a Macintosh version of the science museum math exhibit. The
program is called KaleidoTile, and is available from the Geometry Center's downloadable software library, or via anonymous ftp from "ftp://geom.math.uiuc.edu/pub/software/KaleidoTile".
![[HOME]](file:///C:/DOCUME~1/NOEMIG~1/CONFIG~1/Temp/msohtmlclip1/01/clip_image001.gif){kind=small}
The Geometry Center Home PageCreated: June 17 1994 --- Last modified: Jun 18 1996
Reference
bibliography:
http://www.geom.uiuc.edu/docs/forum/museum/
[18 de junio del 2013]
2- Create: - two questions to answer using skimming.
- two questions
to answer using scanning.
- two questions to answer using reading
in detail.
To answer using skimming:
1- ¿Cuál es el tema
principal del artículo?
2- ¿Quiénes colaboran
con el Museo de Ciencias de Minnesota para producir piezas de mosaicos triangulares?
To answer using scanning:
1- ¿Cuál es el valor de
la suma de los ángulos de un triángulo plano?
2- ¿Cuál es el promedio
de visitantes que recibe el museo cada semana?
To answer using reading
in detail:
1- ¿Cuáles son las tres
ternas de valores para ángulos de triángulos esféricos que se enuncian en el
documento?
2- ¿Cómo puede un
espectador obtener un sólido Platónico o de Arquímedes utilizando el software
mencionado en el artículo?
SKIMMING:
1- ¿Cuál es el tema
principal del artículo?
El tema principal es la descripción de la
exposición de mosaicos de la esfera y su relación con los sólidos
Platónicos
y de Arquímedes.
2- ¿Quiénes colaboran
con el Museo de Ciencias de Minnesota para producir piezas de mosaicos
triangulares?
Personal del Centro de Geometría de la
Universidad de Minnesota.
SCANNING:
1- ¿Cuál es el valor de
la suma de los ángulos de un triángulo plano?
El valor de la suma de los ángulos de un
triángulo plano es de 1800.
2- ¿Cuál es el promedio
de visitantes que recibe el museo cada semana?
Alrededor de 2500 personas lo visitan
cada semana.
READING IN DETAIL:
1-
¿Cuáles son las tres ternas de valores para ángulos de
triángulos esféricos que se enuncian en el documento que se utilizan para
construir un mosaico de la esfera?
Las ternas de valores de ángulos de
triángulos esféricos mencionadas son:
-
300,
600, 450;
-
300,
600, 360 y
-
300,
600, 600.
2-
¿Cómo puede un espectador obtener un sólido Platónico o
de Arquímedes utilizando el software mencionado en el artículo?
El
software disponible en la exposición del
museo permite al espectador mover el
punto de inflexión para ver
cómo
cambia el poliedro resultante. Para
las opciones particulares de punto de inflexión, los poliedros
resultantes
son platónicos y sólidos de Arquímedes. (Ver figura 4)
4-To summarize your reading of the text:
a. Prepare a suitable graphic organizer.
b. Find a non-linguistic text to illustrate the content of the passage.
c. Find a non-linguistic or linguistic text to complement the content of
the chosen text.
a- Prepare a suitable graphic organizer.
|
QUIEN:
Personal del Centro de Geometría de la
Universidad
|
|
QUE:
Colabora con el Museo de Ciencias para producir piezas de mosaicos
triangulares de la esfera y exponer su relación con los sólidos Platónicos y de Arquímedes.
|
|
DONDE:
En Minnesota, Estados Unidos.
|
|
POR QUE:
Son conceptos matemáticos difíciles los que
se involucran la creación de dichos
mosaicos de la esfera y su relación con los sólidos Platónicos y de Arquímedes.
|
|
COMO:
A través de un software se pueden
establecer los ángulos de base de triángulos esféricos de modo que a través
de puntos de inflexión particulares y con reflexiones respecto de los lados
del triangulo se obtienen estos poliedros tan particulares de una forma
sencilla y con explicaciones accesibles e interesantes para todo el público
en general.
|
a- Find a non-linguistic text to illustrate the content
of the passage.
c- Find a non-linguistic or linguistic text to complement
the content of the chosen text.
http://es.touristlink.com/Estados-Unidos/museo-de-la-ciencia-de-minnesota[19 de junio del 2013]
Un Museo de la Matemática
es una colección de piezas reunida con el fin de mostrar a la Matemática como
una componente de la cultura humana, proporcionando un acercamiento no formal
al conocimiento matemático y contribuyendo a su desmitificación como algo
reservado a unas cuantas personas, representa una alternativa de divulgación científica.
Tiene la importante labor de acercar a los niños, jóvenes y adultos a la
matemática a través de medios físicos constituidos por piezas que permiten ser
manipulados para ilustrar o comprobar conceptos y resultados matemáticos. Las exhibiciones
que allí se realizan ofrecen experiencias enriquecedoras e interesantes que
animan a niños y adultos a adquirir un conocimiento profundo de los conceptos matemáticos,
hacen que la práctica de las destrezas matemáticas sea sorprendentemente
memorable y placentera, ayudan a identificar el éxito obtenido con las matemáticas
como algo aplicable y gratificante para sí mismos.
Reference Bibliography:
Adapted from: http://www.geom.uiuc.edu/docs/forum/museum/
de junio[18 de junio del 2013]
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