Investigating Patterns: Symmetry and Tessellations
Investigating
Patterns
Symmetry
and
Tessellations
ACTIVITY LINKS
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7
8
9
10
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12
13
14
15
16
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18
20
22
23
24
25
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30
These links are coordinated with the chapters and activities
of
"Investigating Patterns: Symmetry and Tessellations"
ACTIVITY
1 (What is Mathematics?)
Title:
What
is Mathematics?
Comment:
Observations on the the nature of mathematics from Pathways to School
Improvement. Includes: "Mathematics should include experiences that
help students to shift their thinking about mathematics and define mathematics
as a study of patterns and relationships."
Title:
Pythagoras:
Music and Space
Comment:
A brief introduction to Pythagoras' observations on the relationship
between music and number. Graphics show music intervals expressed as mathematical
ratios. If you have a plug-in that can play sound (like
Real
Player), you can pluck the strings to hear the notes.
Title:
How to Make Ukrainian Easter
Eggs
Comment:
Tells you everything you need to know about the basics of making pysanky
(Ukrainian Easter Eggs). Click on any design and you'll be taken to the
instructions for it. Challenge students to explain why the egg at the right
from Pysanky Designs
(Advanced Designs) is different from the others. [Click
on the egg for the solution.] Symbols
and Colours can be used to investigate the geometric nature of the
designs. There's even a Colouring
Book for kids.
Title:
Decorate
an Easter Egg
Comment:
Decorate an Easter egg by dragging and dropping the items with your
mouse. When done, print and cut it out for your own decoration. Game uses
Javascript. Also available in Flash
Format (requires Macromedia Flash
Player). A similar applet is found in Pryansky
Easter Egg Game (requires a JAVA-capable browser).
Title:
Donald
in Mathmagic Land
Comment:
Donald Duck discovers the fascinating world of mathematics, including
the pentagon, the golden rectangle, and the spiral. Students see how mathematical
principles influence science, art, music, architecture, and even sports.
Special:
View the entire film in three parts (PART
1, PART
2, PART
3) courtesy of YouTube.
ACTIVITY
2 (Introduction to Symmetry)
Title:
ETA/Cuisenaire:
Products - Plastic Mirrors
Comment:
On-line source of the 2¼" x 3½"
plastic mirrors using in this and subsequent activities of Investigating
Patterns: Symmetry and Tessellations. Mirrors come in sets of four.
They are also available from the author [e-mail address below] in sets
of three (the maximum required for all activities), two of which have been
hinged with cloth tape, for $3 US including shipping.
Title:
Photo
Activity for Symmetry
Comment:
The left side of a human face is close to being
the mirror image of the right side - but not exactly. Includes details
on an activity requiring a digital camera and a simple paint program, such
as Paint
Shop Pro or Ultimate Paint.
An evaluation copy of each program is available for download (30-day and
30-use restrictions apply respectively). Visit Symmetrical
Jill Britton for another example.
Title:
SymFace
Comment:
SymFace is a simple and fun way to see
how your face would look if it was perfectly symmetrical. Just follow the
steps using an appropriate digital picture of yourself. [If necessary,
use Ultimate Paint to crop
and/or resize your picture. Visit Ultimate
Paint Lab for details.] The results can be saved and/or printed. Requires
a JAVA-capable browser.
Title:
The Butterfly Web Site
Comment:
The most complete information on butterfly gardening, farming, ecology,
and education. Includes a link to a Photo
Gallery containing butterfly and moth images. Look for images with
a symmetrical configuration. In most cases, a larger picture is available
by clicking on a small picture.
Title:
Manual of Traffic Signs
Comment:
Contains graphics of the most commonly used traffic signs in the United
States. You can use the site to challenge students to find symmetrical
signs.
Title:
SymmeToy - Symmetric
Art Program
Comment:
Permits downloading of a trial version of SymmeToy, a Windows
program for creating paint patterns, symmetry roses, tessellating art,
and so forth.
TOP
ACTIVITY
3
(Symmetry in the Alphabet)
Title:
On Reflection
Comment:
Details how some clever "secret" coding can be done using a small mirror
and the reflectional symmetry characteristics of many capital letters and
some numbers.
Title:
Inversions
Comment:
The inversions gallery of Puzzlemaster Scott Kim, whom Isaac Asimov
called "The Escher of the Alphabet". An inversion is a word or name
written so that it reads in more than one way. Some inversions read upside
down, some flip in a mirror. Some read as two different words, some read
as the same word both ways. Web page includes a link to Teacher
Resources for Inversions with classroom exercises. Half
Words is an intriguing and challenging warm-up exercise suitable for
printing. The corresponding teacher notes includes Answers.
Don't miss Scott's
Origami
with its animated vertical reflectional symmetry. His Signature
Piece also makes for interesting animations.
Title:
Ambigrams, Logos,
Word Art
Comment:
The generic term for inversions is ambigrams, a word coined by cognitive
scientist Douglas Hofstadter. The webpage of John Langdon, known for his
Angels
& Demons ambigrams. Ambigram
Generator produces ambigrams with rotational symmetry for any word
or phrase you type in.
TOP
ACTIVITY
4 (Symmetry in Flags, First Nations Art, and Quilt Blocks)
Title:
Flags
Comment:
Contains links to images of National Flags, International Maritime
Signal Flags, Motor Racing Flags, and the Semaphore Flag Signaling System.
Additional flag images are available from the World
Flag Database and the Flags
of the World web site. The latter includes links to an on-line Colouring
Book of Flags with images available in three sizes.
Title:
Binary Numbers and the South Korean Flag
Comment:
What do the markings on the flag of the Republic of South Korea have
to do with the binary number system? What do they have to do with the number
7? Can you locate and identify the binary numbers in this Chinese
Zodiac Paper Cut (requires
Adobe
Acrobat Reader)?
Title:
Carving at
Skidegate
Comment:
A photo essay of a symmetrical totem pole being carved at Skidegate,
Haida Gwaii (Queen Charlotte Islands, British Columbia, Canada). The photos
show the carving process from raw log to finished pole.
Title:
Tribal Spirit Gallery
Comment:
Source of northwest coast native art. The clothing is highly
recommended - in particular articles embroidered with Tony
Hunt's Symmetrical Sun.
Title:
Shapes, Lines, Angles & Quilts
Comment:
In this site, quilting is a hands-on application for geometric principles.
Requires the copying of traditional quilt block designs from sources such
as
Quilt
Blocks Galore and Quilt Block Collection
(requires
Adobe
Acrobat Reader). For the best commercial resource, consult Mary Ellen
Hopkin's The
It's Okay If You Sit on My Quilt Book with over 350 color examples
of geometric quilt blocks on a gridded background.
Title:
Quilt Maker
Comment:
Design a quilt block by clicking on the squares. Make a quilt by selecting
REPEAT,
REFLECT
or ROTATE. Includes an index of quilt block patterns. Quilters
(from ProtoZone)
features the same activity in a different configuration. Quilt
Reflect challenges students to complete the symmetrical design of a
quilt while racing against the clock. All require Macromedia
Shockwave
Plug-in.
Title:
QuiltComposer
Comment:
QuiltComposer is shareware that will enable you to design your
own quilts before you make them. Accompanying instructions are simple and
clear.
Title:
Quilt Design Program
Mini-Reviews
Comment:
Contains a brief review of several quilt design programs. Links permit
you to download a demo version of some programs. In the demo version of
PCQuilt
(Windows or MacIntosh), you will be able to try most of the features of
the full version but some of the menu items will be disabled. Quilt-Pro
is the Windows-based program of choice.
TOP
ACTIVITY
5
(More on Reflectional and Rotational Symmetry)
Title:
Upside Down Heads
Comment:
Weird and wonderful, this amazing collection of images
celebrates the unique art form of topsy-turvy faces. Cards can be viewed
upside down or right side up (or is it the other way around?) - either
way, a face appears. Cracker Jack's 2-Face
Stickers has further examples. This upside down ad for Niblets
Corn appeared on the back cover of Life Magazine in 1953.
Title:
The Upside Downs of Gustave Verbeek
Comment:
Gustave Verbeek published a series of upside down comics
in The Sunday New York Herald in the beginning of the 1900's. The
first part of the comic is read normally, then you can turn it upside down
and the story continues! Contains links to five complete comics. In a similar
vein, this ad for Niblets Corn appeared on the
back cover of Life Magazine in 1953.
Title:
Symmetry
Comment:
A Flash movie by Mike Shepperd featuring two geometric
shapes - one with 4th order rotational symmetry and no reflectional symmetry
- the other with 2nd order rotational symmetry and 2 lines of reflectional
symmetry. Requires Macromedia
Flash
Player.
Title:
The Diamond 16 Puzzle
Comment:
Rearrange the rows, columns, and quadrants in a 4 x 4
array of 2-colour tiles to solve this online Javascript puzzle and make
hundreds of symmetric patterns. For a somewhat more user-friendly version
of the puzzle, visit Alexei Vernitski's 16
site.
Title:
Rotational
Symmetry - Hub Caps
Comment:
A good source of objects that have rotational symmetry
happens to be hub caps. Car Wheel Covers
has more details. Alloy
Wheels Photo Gallery features classic designs as do links from Style-Line
Home Page. Students can investigate the designs for reflectional and/or
rotational symmetry.
Title:
Hex
Signs
Comment:
Features details on several symmetrical hex signs with internal links
to quality enlargements thereof. A Hex
Sign Poster is available from folkart.com, where you can learn What
the Hex Signs Mean and How
to Make Your Own Hex Sign.
Title:
The Best Brands of the World
Comment:
Features a collection of over 60,000 corporate logos.
Challenge students to find familiar logos with reflectional and/or rotational
symmetry or to prepare logo exercises. Search by company name. [Downloads
are
EPS files. Open with a high-end graphics program like Photoshop or
Photoshop Elements, specify a large resolution, then adjust to the desired
size. Or insert into a Word document (using the Insert / Picture / From
File Option) provided the Word EPS filter is installed.] Logotypes
has a similar format and usage.
Title:
GoodLogo!com
Comment:
Logo database is searchable by company name and category,
but lacks many major corporations. Cick on thumbnails to access enlargements
(gif
files). Saved graphics can be opened with a simple graphics program
or inserted directly into a Word file (using the Insert / Picture / From
File Option).
Title:
Family Crest
Comment:
There are over 4,500 Ka-Mon or family crests in
Japan. Artistically simpler than their European counterparts, they are
a wonderful cultural source for symmetry investigations. This web page
provides an excellent introduction to the history and structure of the
crests. Japanese
Crests has links to highly stylized, symmetrical crests based on butterflies.
Kamon
features a chart of 259 Japanese family crests.
Title:
Symmetry Around the
World
Comment:
A collection of web pages by students of St Kieran's ManlyVale
(Sydney, Australia) to help children around the world find out about reflectional
symmetry and rotational symmetry. Elegant illustrations include examples
from nature, the human body, masks, reflections in water, architecture,
geometric shapes, hubcaps, kaleidoscopes, capital letters, advertising
logos, and more.
Title:
Symmetry
Artist
Comment:
Mathematics and Art come together! Create your own line
drawing with reflectional and/or rotational symmetry. Applet permits selection
of mirror line orientation, the order of rotation, and the pen width, color
and style. Part of Maths Is Fun
website. Requires a JAVA-capable browser.
TOP
ACTIVITY
6 (Symmetrical Strip Patterns)
Title:
Frieze Patterns
Comment:
Details the seven combinations of symmetries that can be found in a
frieze pattern. Sequential pages include exercises and corresponding answer
key.
Title:
Frieze
Patterns in Cast Iron
Comment:
Contains examples of all seven frieze pattern types in cast iron decorative
work - in the Sidney Lace of Australia - and the rest of the world.
You can find cast iron patterns everywhere!
Title:
Border Liner
Comment:
Make patterns which go on and on forever, repeating the same pattern
in one direction or the other. BorderLiners
(from ProtoZone)
features a similar interactive activity. Sampler
(also from ProtoZone)
allows you design a cross-stitch sampler that stretches out into seven
border patterns. All require Macromedia Shockwave
Plug-in.
Title:
Great
Math Fun With Paper Dolls
Comment:
With strings of paper dolls, you can decorate a party, make the border
of a bulletin board, create a frame for your favourite picture, and of
course, learn some math in the process. Visit How
To Make Paper Chains to access links to templates for making Christmas
chains, dinosaur chains, Halloween chains and wild animal chains.
Title:
Celtic
Knot-Design Bookmark
Comment:
Contains instructions for making a symmetrical Celtic Bookmark. Download
a high-res version suitable for coloring.
Design custom Celtic artwork with the amazing Celtic
Knot Font. Outline style highly recommended.
TOP
ACTIVITY
7 (Introduction to Polygons)
Title:
Connect the Dots
Comment:
Select a numbered dot to begin. Draw a polygon as you click on the
dots sequentially to complete the image. There is an animation on completion.
Seven different examples with a US Air Force theme. Requires Macromedia
Flash
Player.
Title:
Connect the
Dots
Comment:
Draw a polygon as you click on the dots sequentially to complete the
image. There is an interpretation on completion. All examples involve
Chevron
Toy Cars. Depending on the game you wish to play in this website, you
will need a Macromedia Flash
or Macromedia Shockwave
plug-in.
Title:
Lizards
of M. C. Escher SoftPuzzle
Comment:
Through this site you can purchase the Lizards of M. C. Escher SoftPuzzle,
an officially licensed adaptation of Escher's famous reptile.
Title:
Tangrams
Comment:
Tangram is a centuries old Chinese tile game consisting of 7 geometric
shapes. Learn its history, make your own tan set, or try solving one of
the shapes. Includes great downloads and interesting links to explore.
Title:
Tangram
Comment:
To play this on-line tangram game, you must flip, rotate and drag the
seven pieces to exactly reproduce the given image. When you have mastered
the 49 pre-designed patterns, you can make up your own. Enchanted
Mind - Tangram Java Puzzle features a similar applet with 18 patterns.
Javalovers
Tangram has over 100 patterns divided into three levels of difficulty.
All require a JAVA-capable browser. For a
Flash version, visit Interactive
Tangram or Tangram
Game. In
A Movie in Flash
Using Tangrams, some 20 tangrams are used to tell a story with on-line
questions. All three require Macromedia
Flash
Player. Windows users can download tangram.zip
(includes an editor that lets you create your own collection of puzzles).
Decompress with WinZip
or freeware ZipCentral.
Tangram
Puzzle contains a link to a printable PDF version (requires Adobe
Acrobat Reader). An inexpensive wooden version is available from Highland
Games. Hungry? Try Puzzokies
- a commercial tangram cookie - or bake your own!
TOP
ACTIVITY
8 (Regular Polygons)
Title:
Naming
Polygons and Polyhedra
Comment:
What do you call an 11-sided polygon? A 14-sided polygon? A 50-sided
polygon. Doctor Math provides Greek prefixes for the first 50 polygons,
among others.
Title:
Welcome to
the Polygon Playground
Comment:
Come play with polygons! You can drag and arrange hundreds of colorful
polygons to create your own online art. The introductory page includes
a little slide show of ideas to get started, including: patterns, symmetrical
designs, and polygon animals. Requires a JAVA-capable browser.
Title:
Plentiful Pentagons
Comment:
The pentagonal shape is one of the primary geometric forms for organic
shapes (living organisms). Many flowers and starfish have pentagonal shapes.
Title:
Snowflakes
Comment:
All snowflakes have a fundamentally hexagonal shape. Generate symmetrical
snowflakes with this project. Set the slider bar to thin line (left) or
thick line (right), then press draw. Requires Microworld's
Web
Player. Or you can Create
Your Own Snowflakes and then execute a 2D or 3D rotation (requires
Macromedia Flash
Player). SnowFlaker
(from ProtoZone)
challenges you to draw the same snowflake twice (requires Macromedia
Shockwave
Plug-in).
Title:
Kids Snow Page
Comment:
Includes links like Snow Science (snow
crystals and how to study them) and Snow Art
(paper snowflakes and a "self-sticking" snowflake). Learn how to
Grow
Your Own Borax Crystal Snowflake. All the snow activities are available
as an Acrobat
Reader document, snowbook.pdf.
Title:
Paper Snowflakes for Children
Comment:
Everyone can make artist quality paper "snowflakes" by following these
easy patterns! Many patterns were adapted from pictures of real ice crystals.
Make Mother's Day, Valentine's Day, Halloween Snowflakes as well as Christmas
snowflakes!
Title:
Wilson Snowflake Bentley
Comment:
Provides a comprehensive resource of everything related to Wilson "Snowflake"
Bentley. Links to Original
Wilson Bentley Images, a collection of 21 of Bentley's snow crystal
photomicrographs. Click on each thumbnail for a closeup view.
Title:
Geometric
Dissections on the Web
Comment:
A geometric dissection is a cutting of one or more figures into pieces
that can be rearranged to form other figures. Features links to animations
of dissections (such as Swing-Hinged
Dissection of Triangle to Square and Dodecagon
to a Hexagon), dissections as puzzles, and more.
TOP
ACTIVITY
9
(Symmetry and Regular Polygons)
Title:
BBC
Education - Revision Bite - Symmetry
Comment:
Interactive animated treatment of reflectional and rotational symmetry,
including symmetry in regular polygons and other polygonal shapes. Includes
classroom exercises.
TOP
ACTIVITY
10
(Symmetry by Paper Folding and Cutting)
Title:
Snowflakes
Comment:
Contains simple instructions for folding and then cutting snowflake-like
designs with two, four, six, and eight repeats. Excellent supporting graphics.
TOP
ACTIVITY
11 (Paper & Scissors Pentagon)
Title:
5-Pointed Star
in One Snip
Comment:
Take a thin piece of paper 8-1/2" x 10" (or an exact proportion thereof),
fold it as indicated and cut yourself a perfect 5-pointed star. Printable
Version requires
Adobe
Acrobat Reader.
Title:
Some Golden Geometry
Comment:
A sequence of linked pages leading from the Golden Rectangle to the
Golden Spiral, the Golden Section, and ultimately to the Golden Triangle.
Original webpage by Rashomon.
TOP
ACTIVITY
12
(Paper & Scissors Hexagon and Beyond)
Title:
Folding and Cutting
a Snowflake
Comment:
Features instructions (require Adobe
Acrobat Reader) for folding and cutting a hexagon. The cutouts in the
edges of the folded paper create a snowflake appearance. Paper
Snowflake Designs has suggestions for artistic cutouts.
Title:
Make-a-Flake
Comment:
Allows you to cut polygonal wedges from a virtual piece of folded paper
with virtual scissors (requires Macromedia Flash
Player). Click on Make Your Own Snowflake to begin. Place the
(red dot on the) scissors on an edge of the triangle, then click the mouse
button. Move the scissors within the triangle, then click again. Continue
until the scissors return to an edge. A polygonal wedge will be removed.
Repeat, using Undo/Redo as required. Once you Preview Flake,
you can Cut Some More or Start Over.
Title:
Paper & Scissors Heptagon
Comment:
Extend your paper folding skills beyond the pentagon and hexagon. Features
instructions for folding a heptagon. Or try an Octagon,
Nonagon,
Decagon
(based on a pentagon),
11-gon or Dodecagon
(based on a hexagon). All require Adobe
Acrobat Reader. The instructions were scanned from Paper and Scissors
Polygons, the first edition of Paper
and Scissors Polygons and More.
Title:
Kirigami
Comment:
Kirigami is the Japanese art of folding and cutting paper. This program
lets you create similar figures on your computer by cutting a polygonal
wedge from a virtual piece of folded paper. You can change the regular
polygon, your wedge, and your paper color. You can then see the figure
that results when the paper is unfolded. Requires a JAVA-capable browser.
Title:
Origami Help for Beginners
Comment:
Origami is the Japanese art of folding paper. A folded model is both
a piece of art and a geometric figure. Learn these simple symbols and directions
and you'll be able to make almost any well-diagrammed model in any book.
Title:
Joseph Wu's Origami Page
Comment:
The home page of origami master Joseph Wu. Contains links to the most
comprehensive collection of origami materials available on the world wide
web. Accessible diagrams include the traditional Origami
Crane (a beautiful presentation with very clear instructions presented
using photographs).
Title:
Paperfolding.com
Comment:
Eric's Andersen's origami site includes Origami
History, Origami &
Math, galleries of insects and dinosaurs, and links to a variety of
origami diagrams on the web.
Title:
Origami Diagrams
on the Web
Comment:
Includes classic folding techniques and origami diagrams for models
(like a simple Jumping
Frog) arranged according to level of difficulty. Jasper's
Origami Menagerie features galleries of origami models and links to
other origami information on the web.
Title:
Pieces 'n Creases
- A Fun Guide to Origami
Comment:
After you visit this web site, you won't able to pick up a square piece
of paper without a little folding. Includes links to History
of Origami and Fun
Activities. Winner of the 1999 Think Quest Junior "Best of Contest".
Title:
Oriland: Origami Galore
Comment:
Oriland is a children's world made of origami - half game and half
resource. In Oriland Oriversity, you can learn most basic origami points
through Animated
Origami Symbols (requires Macromedia Flash
Player), explore Base
Folds that are the basis for folding many models, then take ten
Practical
Lessons for practicing the folds from the most basic to the complex.
More models (with instructions) can be found in the Origami
Studio.
Title:
Origami - The Fascination
of Folding
Comment:
Fabulous origami web site. Click on any thumbnail for the corresponding
instructions. Be sure to explore Origami Tablecards - a collection
of 31 tablecards folded from a square.
Title:
Tammy Yee's Origami
Page - Easy Paper Folding Crafts for Children
Comment:
Wonderful original artwork combined with origami. If you have access
to a color printer, illustrated squares can be printed so the finished
project is already decorated.
Title:
Origami
for Kids
Comment:
Origami is a fascinating and creative craft for kids, especially if
you can find origami models appropriate to their age. Includes links to
a variety of models suitable for kids.
Title:
Diagrams, Instructions,
and Puzzles
Comment:
PDF instructions for folding 9 origami models from OrigamiUSA.
Options include a cup,
jumping
frog, blow-up
bunny and traditional
crane. Each requires
Adobe
Acrobat Reader to view and print.
Title:
Origami Bird
Comment:
Learn to fold a bird from a piece of paper by following animated visual
instructions. Designed so you can repeat a step over and over if you need
to, or watch the whole bird fold from start to finish. Requires Macromedia
Shockwave
Plug-in.
Title:
Flapping Bird
Comment:
Learn to fold a flapping bird from a single piece of paper. Excellent
graphics. Also available in PDF Format
(requires
Adobe
Acrobat Reader). Animated Origami
Diagrams for Flapping Bird and Crane requires Macromedia Flash
Player.
Title:
Fabric Origami Workshop
Comment:
Features instructions, photos, and 50 detailed diagrams to make origami
boxes and other items by folding fabric instead of paper. Diagrams require
Adobe
Acrobat Reader.
Title:
Robert Neale's Magic Pinwheel
Comment:
A uniquely wonderful modular design. Despite the fact that the design
of the modules is extremely simple, the octagonal wreath can be compressed
(in stages) until it becomes a pinwheel. In both these forms, and at each
stage in between, the design remains stable. Requires
Adobe
Acrobat Reader. UFO has
similar directions.
Title:
Tea Bag Folding
Comment:
Tea Bag Folding (also known as Miniature Kaleidoscopic Origami) is
used to create symmetrical designs and medallions.
Includes links to instructions, printable tiles, and commercial sources.
Be sure to access the Tea Bag Medallions (Using
Tea Bag Wrappers) by Gizella Hagedus.
TOP
ACTIVITY
13 (Angle Relations in Triangles and Quadrilaterals)
Title:
Angle Relations in Triangles and Quadrilaterals
Comment:
How do I know that every triangle has three angles that add up to 180°
and that all quadrilaterals have four angles that add up to 360°? Well,
try this!
Title:
Triangle
Geometry: Triangles
Comment:
Two applets that demonstrate using animation that the sum of the measures
of the interior angles of a triangle is 180 degrees. Before you start the
second applet, get a piece paper and a pair of scissors so that you can
try to perform the demonstration for yourself. Requires a JAVA-capable
browser.
Title:
The
Sum of Three Angles of a Triangle
Comment:
Move the triangle by dragging the red point. What do you find? Requires
a JAVA-capable browser. For a Flash movie (by Mike Shepperd) with
a non-interactive mode, visit Triangle
(requires Macromedia
Flash
Player).
Title:
Paper Folding
Comment:
All of the constructions of Plane Euclidean Geometry that can be performed
by straightedge and compass can also be performed by folding and creasing
paper. Details how to illustrate that the three interior angles of a triangle
is 180 degrees by making just three specific folds to a triangle cut from
a sheet of paper.
TOP
ACTIVITY
14 (Angle Measures in Regular Polygons)
Title:
Interior Angles
Comment:
Details two more methods for finding a formula for the measure of each
interior angle of a regular polygon. Both results are equivalent to the
formula deduced in the book activity, namely: 180 - 360/n. Web site is
part of
Cool Math.com.
Title:
BBC
Education - Revision Bite - Polygons
Comment:
Considers regular and irregular polygons, angle properties of polygons,
and calculating the interior and exterior angles of regular polygons. Includes
classroom exercises.
TOP
ACTIVITY
15
(The Regular Tessellations)
Title:
Totally
Tessellated
Comment:
A superbly well-done site on tessellations. Winner in the ThinkQuest'98
competition. Features over 100 dynamic pages with quality illustrations,
photographs, and links. Main topics: History of Tessellations, Essentials,
Mosaics/Tilings, Escher, and Beyond.
Background
Information has links to polygons and angles, symmetry and transformations,
regular polygons, plus links to a simple introduction to tessellations
and to the effect of color usage on tessellated designs. Regular
Tessellations contains links to real examples.
Title:
Tessellation.org
Comment:
Includes information on all aspects of tessellations, from their history
and development to complete galleries of examples by M. C. Escher,
the master of the art. Also included are extensive workshops showing how
to design and produce your own artistic tessellations.
Title:
Investigating
Tessellations Using Activity Pattern Blocks
Comment:
Features activities for investigating tessellations with pattern blocks
as well as student tessellation samples. Contains links to a Patterns Program
by Jacobo Bulaevsky (including How
to Use the Pattern Blocks Program and a direct link to the Pattern
Blocks Applet) in which you can experiment on-line with the shapes
(provided you have a JAVA-capable browser).
Title:
Virtual
Manipulatives: Pattern Blocks
Comment:
Features an interactive pattern blocks applet which uses six common
geometric shapes to build patterns. Includes icons for student activities,
teacher information, and assistance. Produced by the National
Library of Virtual Mathematics for Interactive Mathematics. Requires
a JAVA-capable browser.
Title:
LinoTiler
Comment:
Decorate square tiles on a flat floor in a symmetrical configuration.
Then create repeating wallpaper patterns from identical square tiles using
wallOVERS
(also from ProtoZone).
Both interactive activities require Macromedia
Shockwave
Plug-in.
Title:
Fractiles, Inc.
Comment:
The versatile and elegant geometry of Fractiles allows you to create
aesthetically pleasing designs with repeating and non-repeating patterns.
And unlike pattern blocks, these MAGNETIC tiles stay put, an especially
helpful feature for students with fine motor skill problems.
Title:
Tessellations
Comment:
Tessellations is the company that combines art, math, and fun.
They make Puzzellations, Colorful Connectables and Perpetual Patterns puzzles,
plus a variety of other products inspired in part by the Dutch graphic
artist M. C. Escher, but also by mathematicians such as Roger Penrose and
Benoit Mandelbrot.
Title:
Tilings and Designs
Comment:
Commercial source of several sets of shapely tiles that lend themselves
to unlimited design making, like mosaic inlays and imaginative scenes and
figures.
TOP
ACTIVITY
16 (From Crackers to Honeycomb to Soap Bubbles and Beyond)
Title:
Bees,
Microscopy & Mathematics
Comment:
The comb of the honeybee is organized into regular hexagonal cells,
showing a repeating, symmetrical mathematical pattern. Such a pattern could
be equally well achieved by cells based on the equilateral triangle or
square. So why the hexagon?
Title:
Bees-Online
Comment:
An educational web site about honey bees and beekeeping. You can download
Fun
Bee Software and
Bee
Games, such beekeeping jig saw puzzles, beekeeping crosswords, the
only free e-book on the Internet about honey bees, and a honey bee screensaver.
The hands-on game in BeeBopper
asks you to bop bees right out of their hive and leave as few as you can.
The latter requires Macromedia Shockwave
Plug-in.
Title:
Polar Smash
Comment:
Another game based on a tessellation of regular hexagons - designed
as a Christmas promo. Either one or two players - jump up and down on the
ice to send your opponent swimming. Requires Macromedia
Shockwave
Plug-in
Title:
Carbon
Nanostructures
Comment:
Graphite is formed from carbon atoms arranged in a honeycomb pattern.
Discover why this form of carbon is used in pencils. Learn about the strongest
fibers known (tubes of graphite or carbon nanotubes) and their applications.
Title:
Soap Bubbles
Comment:
This site from the Exploratorium in San Francisco has information on
the shape of bubbles and investigates what happens when bubble meets bubble.
Contains formulae for long-life bubble solutions, links to other sites
on bubbles (like Create
Giant Bubbles), as well as a "bubbliography".
Title:
Interlocking Pavers
& Molds
Comment:
Features tessellated, interlocking concrete pavers and molds. Like
Escher's reptile, the tessellating shapes are modified hexagons.
Special:
Click on the photo above to view the tessellation of salamanders in
greater detail.
Title:
Shmuzzle Puzzle
Comment:
A standard jigsaw puzzle is comprised of pieces of many different shapes
that fit together only one way. A Shmuzzle Puzzle is comprised of
Escher-like pieces of only one shape that fit together many ways - but
only one right way! Be sure to try CyberShmuzzling
(requires Macromedia
Flash
Player).
TOP
ACTIVITY
17 (A Regular Tessellation Prism Kaleidoscope)
Title:
Escher: Lizard/Fish/Bat
Comment:
A large color rendition of Escher's lizard/fish/bat tessellation. Suitable
for a color transparency.
Title:
You
Can Create a Kaleidoscope
Comment:
Features simple instructions on how to assemble a basic kaleidoscope
mirror system. Finger
Tips Kaleidoscope features similar directions. Silver Mirricard
makes an excellent mirror. Make an inexpensive Kaleidoscope
from a Potato Chip Can (requires
Adobe
Acrobat Reader).
Title:
Duck
Into Kaleidoscope
Comment:
This simple devise will create hundreds of images of whatever you place
inside it. Make
Multiple Images of Yourself! The basic kaleidoscope is a triangle,
but mirror tiles can deformed into other shapes and angles as well. Mirror,
Mirror contains more details.
Title:
Kaleidoscope Collector
- How Kaleidoscopes Work
Comment:
Features graphics showing the basis of and the dramatically different
images produced by the three mirror, two mirror, twin mirror, and four
mirror scope.
Title:
Kaleidoscope
Show
Comment:
Multi-plex theatre offering kaleidoscope shows. Images load as they
are playing. Once the ANN-imation has finished loading, the fun begins
(provided your browser supports looped animations). Kaleiodo-Headaches
is simply phenomenal!
Title:
Symmetrizer
Comment:
Press play, then move your mouse around to see this on-line kaleidoscope
in action. Allows change of repeating character and superposition of grid.How?
features an animated explanation. Requires Macromedia
Flash
Player.
Title:
Kaleidoscope
Painter
Comment:
Paint your own kaleidoscope canvas! Just drag the mouse slowly around
the canvas and let the computer show your artistic talents. Requires a
JAVA-capable browser. The author's FLAKaleidoscope
(requires Macromedia
Flash
Player) allows you watch colorful and hypnotic patterns emerge from
a selection of simple drawings.
Title:
Kaleidodraw
Comment:
This interactive kaleidoscope from the Long Island Children's Museum
allows you to select the symmetry of a circular canvas, change pen points,
and change color. KaleidoDraw
(from ProtoZone)
features a similar interactive activity. Both require Macromedia Shockwave
Plug-in.
Title:
Build Yer Own
Comment:
Click and drag the shapes provided into the circle. When the blue light
passes over them, they show up like a kaleidoscope image. Another
Virtual Kaleidoscope features a similar interactive activity. Both
require Macromedia
Flash
Player.
Title:
KaleidoMania! Interactive
Symmetry
Comment:
KaleidoMania! is a unique, new tool for dynamically creating
symmetric designs. The CD-ROM software and activities will make your students
eager to explore the mathematics of symmetry.
TOP
ACTIVITY
18 (Tessellating with Irregular Polygons)
Title:
Triangle
Comment:
Every triangle tiles the plane (tessellates) as this Flash movie
by Mike Shepperd will demonstrate. So does every Quadrilateral.
Both demos require Macromedia
Flash
Player.
Title:
Perplexing Pentagons
Comment:
The regular pentagon does not tile the plane, however there are tessellating
pentagons. Fourteen types have been discovered. Are all the types now known?
The problem remains unsolved.
Title:
Pentagons
That Tile The Plane
Comment:
The problem here is to find a single tile shape with five sides which
can tile an infinite floor without leaving holes. Discusses various solutions
to the problem.
Title:
Tessellating
Alphabet
Comment:
Each letter of this tessellating alphabet fits together with copies
of itself to tile the plane. Click a letter to see how it tiles. Some letters
tile in more than one way.
TOP
ACTIVITY
20 (The Semiregular Tessellations)
Title:
Totally
Tessellated: Semiregular Tessellations
Comment:
You can view color renditions and real examples of the semiregular
tessellations in this page of the Totally Tessellated web site.
Templates
allows you to print renditions of each tessellation suitable for coloring
activities.
Title:
Virtual
Manipulatives: Tessellations
Comment:
Features an interactive applet which uses five regular polygons to
build tessellations. Includes icons for student activities, teacher information,
and assistance. Produced by the National
Library of Virtual Mathematics for Interactive Mathematics. Requires
a JAVA-capable browser.
TOP
ACTIVITY
22 (Demiregular Tessellations)
Title:
Totally
Tessellated: Demiregular Tessellations
Comment:
You can view color examples of more demiregular tessellations in this
page of the Totally Tessellated web site. Templates
allows you to print renditions of each tessellation suitable for coloring
activities.
TOP
ACTIVITY
23 (Islamic Tessellations)
Title:
Historical
and Geographical Connections
Comment:
Contains historical and geographical links for tessellations and tilings
in the Moorish architecture of Spain, Chinese and Japanese Designs (with
JAVA applets by Dr. William Chow), Islamic Art and Architecture, and Persian
Architecture.
Title:
Symmetric Patterns at the Alhambra
Comment:
Features symmetric patterns at the Alhambra with accompanying math
problems. Includes a link to the Four
Types of Symmetry in the Plane with connections to a number of tessellation
pages.
Title:
Symmetry & Pattern:
The Art of Oriental Carpets
Comment:
A joint effort between The Textile Museum and The Math Forum. Link
to Rug Gallery
includes images of carpets with a variety of geometrical patterns and symmetrical
designs.
Educational
Resources contains suggestions for the classroom.
Title:
Magic Carpet
Comment:
Weave symmetries into an instant rug by drawing in a rectangular panel.
Interactive software (from ProtoZone)
requires Macromedia
Shockwave
Plug-in.
Title:
Some
Arabic Tiles
Comment:
Features colorful tessellating Arabic tiles with links to an outline
version of each. Download the tiles and use the paint bucket tool to make
your own color schemes.
Title:
Geometrical Patterns
Comment:
Download seamless decorated tessellating tiles for your web page background
or simply view the full background on a whole page. You can even change
the background color. Options include Moorish (Islamic), Japanese, Celtic,
and Medieval.
Title:
Taprats
Comment:
Taprats is an applet for generating symmetric Islamic-style
star patterns. Includes a detailed on-line user's manual and a library
of built-in tilings that can be used to construct many famous Islamic designs.
Requires a JAVA-capable browser.
Title:
Islamic
Art and Geometric Design
Comment:
Presenting beautiful Islamic works from the collection of The Metropolitan
Museum of Art along with a series of pattern-making activities involving
straightedge and compass, these materials are designed for use in the classroom
and may be readily adapted by teachers to create exciting lessons in art,
culture, math, and geometry.
TOP
ACTIVITY
24 (The Art of M. C. Escher)
Title:
M. C. Escher: The Official
Website
Comment:
Home page of the M.C. Escher Foundation and Cordon Art B.V.,
worldwide and exclusive representative of the works and writings of the
artist. Includes a link to a shop of Escher merchandise. Take a Virtual
Ride through three of his most famous works - Belvedere,
Waterfall
or
Ascending and
Descending (require Real
Player). Read his biography and quotes, or download a FREE Escher
Interactive Puzzle (self extracting Winzip file).
Title:
Escher
in het Paleis (Escher in the Palace)
Comment:
A permanent Escher exhibition in the center of The Hague. Famous prints
are showcased, complemented by changing displays of selected personal documents.
The exhibition includes a Virtual Reality display which enables
visitors to embark on a voyage of discovery through and within Escher's
work.
Title:
Escher
on Display
Comment:
Escher's work can be seen in several other locations in the Netherlands.
They are listed here in chronological order, with accompanying photographs.
A
large print of Escher's Metamorphosis III
used to be displayed in the Kerkplein post office in The Hague. It has
been moved
to Lounge 4 of Amsterdam's Schiphol airport (beyond passport control).
Special:
Escher in The Hague (Jill Britton's
Odyssey)
Title:
M.
C. Escher Mindscapes
Comment:
A wide variety of Escher resources from the National Gallery of Canada.
Content is divided into five sections: Escher's
Life, Escher's
Themes,
Escher's
Techniques, Escher's
Gallery (40 works from the NGC collection), and Reference.
Includes an excerpt from the 1969 film (Adventures in Perception)
featuring M.C. Escher at work, two excerpts from a video interview with
the artist, plus video and sound interviews with his eldest son George.
Video clips require QuickTime
Player.
Title:
NGA
- M. C. Escher - Life and Work
Comment:
A tour of four virtual rooms at the National Gallery of Art in Washington
DC devoted to the art of M. C. Escher. For each graphic, a larger picture
with accompanying commentary is available by clicking on a small picture.
The gallery has 426
Works by Escher with over 80 images available on-line.
Title:
M. C. Escher
Comment:
A Flash experience brought to you by Renee Perry. Requires Macromedia
Flash
Player. Includes four sections: bio, interpretation, visual analysis,
and a gallery of the artist's work. The interpretation section features
a QuickTime movie
of Escher's Reptiles. Nothing short of terrific!
Title:
M. C. Escher
Biography Page
Comment:
Comprehensive biography condensed from the book M. C. Escher - His
Life and Complete Graphic Work (Bruno Ernst © 1981). Includes
additional material from original essays by Escher, supporting graphics,
and links to supporting graphics.
Title:
The Mathematical
Art of M. C. Escher
Comment:
An excellent introduction to the mathematics in Escher's art. Divided
into areas: tessellations, polyhedra, the shape of space, the logic of
space, and self-reference.
Title:
The Shrine of Escher
Comment:
Contains links to an Escher biography and an annotated art gallery
with details on eight Escher prints - including
Moebius Strip II,
Belvedere,
Waterfall,
and Day and Night.
Title:
The Oldest Escher Collection on
the Web
Comment:
Contains links to high resolution copies of 100 of Escher's most famous
prints. On the web since 1993. Assembled by David Kirk McAllister.
Title:
Jill Britton's Escher Gallery
Comment:
Features links to high resolution Escher Graphics - including Drawing
Hands, Moebius Strip II,
Reptiles,
Day
and Night, and (my personal favourite) Sky
and Water.
Title:
Escher
Boxes
Comment:
Click on the selected image for an enlarged version, then download
and print in color on card stock. Score along the indented markings applying
minimal pressure. Cut out the net along the punch-out markings, then fold
as indicated to assemble the box.
Title:
3Quarks
- Applets - Metamorphose
Comment:
Presents Escher's Metamorphosis II as a panorama picture. Use
the scroller to move the picture. To move it with a mouse, click on the
panorama. Includes a link to Background
information. Requires a JAVA-capable browser.
Title:
M. C. Escher: Metamorphose III Panorama
Comment:
Presents Escher's Metamorphosis III as a continuous band. Use
your mouse to pan the image. Requires Macromedia
Shockwave
Plug-in. Visit Metamorphose III for a
graphic version suitable for downloading.
Title:
Snakes
Comment:
Contains links to both a short computer animated movie and stills based
on Escher's last graphic work Snakes. Movie
requires
QuickTime Player.
Title:
The Mathematics
in the Art of M. C. Escher
Comment:
Contains a link to the public lecture (requires TheMathematics in the Art of M. C. EscherComment: Contains a link to the public lecture (requires Real
Player) by the late H. S. M. Coxeter that touches on various mathematical
aspects of M. C. Escher's art, its centre-piece an examination of Escher's
circular woodcuts. That's a very nervous Jill Britton at the very end
(46:16) asking the question "Do you regard Escher as a mathematician?"
... and requesting Coxeter's autograph in the process.
Title:
Adventures
in Perception
Comment:
Offers an on-line resource to Adventures in Perception, a film
which details M. C. Escher's life and work, features an interview with
the artist, and shows him carving a woodblock for and printing his last
work Snakes. Appropriate for middle school students and above. The
site allows access to a short free clip from the film (requires
Real
Player). A VHS video version is available for purchase.
Special:
View the entire film in three parts (PART
1, PART
2, PART
3) courtesy of YouTube.
Title:
The
Life and Works of M. C. Escher
Comment:
Featuring a rare interview with Escher himself, this new video takes
an in-depth look at the world-renowned graphic artist and his ever-popular
work. Traces his career path and personal life, revealing the people and
places that inspired him to achieve greatness. Far too cerebral for the
middle school student, but an essential resource for the mathematics educator.
Approximately 60 minutes. YouTube's Escher
Interview features a brief excerpt from the film.
Title:
The Fantastic
World of M. C. Escher
Comment:
Through first-person accounts by his friends and mathematicians, computer
animated recreations of his work, and a look at his sources of inspiration
in Italy and Spain, The Fantastic World of M.C. Escher is an engaging
exploration that will enrich the understanding and appreciation of Escher
and his art. Approximately 50 minutes.
Title:
Escher,
Van Gogh and Seurat: Art at Play
Comment:
Canadian animation wizardry brings the work of Escher, Van Gogh and
Seurat) to life in this playful series of three video films for all ages.
M.C.
Escher: Sky and Water 1 is a 3-minute exercise for your brain, capturing
the essence of motion in the Dutch master's print. Inspiring, informative,
and fun!
Special:
View the entire Sky
and Water 1 courtesy of YouTube.
Title:
Masters of Deception: Escher,
Dalí & the Artists of Optical Illusion
Comment:
Augments and enhances the material in the new book Masters
of Deception by presenting those works and interviews that could not
be presented in book form. The Escher
page and its internal links to actual Escher video clips are particularly
recommended. Clips require Real
Player or Quicktime
Player.
Title:
Escher Interactive
Comment:
Escher Interactive is an educational and entertaining CD-ROM
for Windows. Exploiting animation, video, sound commentary and interactive
manipulation of images, it features nine modules, each revealing a separate
facet of Escher's work.
Title:
M.
C. Escher's Legacy
Comment:
The proceedings of the International Escher Congress held in Rome,
Italy in July 1998 (the centenary of Escher's birth). This book contains
40 articles, richly illustrated with original art works in addition
to well-known and little-known works by Escher. A CD-ROM complements the
articles, containing color illustrations of work by contemporary artists,
movies, animations, and other demonstrations. New softcover edition.
Title:
Visions
of Symmetry
Comment:
New edition of Doris Schattschneider's definitive book on Escher's
tessellations. Features an illustrated epilogue that reveals new information
about Escher's inspiration and shows how his ideas of symmetry have influenced
mathematicians, computer scientists, and contemporary artists.
Title:
World of Escher
Comment:
On-line store offering high quality Escher products (T-shirts, computer
accessories, ties, posters, puzzles, books). T-shirts
has 17 options. Art Gallery
features several Escher graphics. Contest
has galleries of quality Escher-like art (in-store contest entries and/or
winners).
Title:
Westside Impressions
Comment:
Manufacturer (with on-line store) of a wide range of officially licensed
Escher clothing, including T-shirts, long sleeve shirts, and the new women's
Tees.
Title:
Instructional Images
Comment:
On-line store offering high quality visual tools for math, science,
and social studies educators. Contains links to Escher
and World
Mathematics posters.
TOP
ACTIVITIES
25 & 26 (Tessellating Template)
Title:
Square Template and Dot Paper Masters
Comment:
Make a tessellating template by sliding cutouts between opposite sides
of a cardboard square, then draw the tessellation by tracing around the
template with its residual corners aligned to the markings on dot paper.
Contains printing masters for a sheet of nine 2-inch cardboard squares
and a letter-size sheet of 2-inch dot paper (requires
Adobe
Acrobat Reader). Visit Escher in the Classroom
for more details.
TOP
ACTIVITY
27 (A Pop-Up Sponge Jigsaw Puzzle)
Title:
Pop-Up
Sponge
Comment:
Pop-Up (compressed sponge) starts out wafer thin and rigid. Cut out
a shape, submerge it in water, then watch it expand! Used in the tessellating
jigsaw puzzle activity of Investigating Patterns:
Symmetry and Tessellations. Perfect for tessellating sponge printing
as well. The creators of the Ellison® LetterMachine (TM) offer pop-up
sponge in 8 1/2" x 12" sheets and includes 6 sheets of one color (blue,
lemon, natural, mint, raspberry, white). Also available in Assorted
12 Pack (2 of each color) and Assorted
48 Pack (8 of each color).
Title:
Lumocolor
Permanent Markers
Comment:
On-line source of Staedtler permanent medium black Lumocolor markers
(S3179). Used in the tessellating jigsaw puzzle activity of Investigating
Patterns: Symmetry and Tessellations.
TOP
ACTIVITY
28 (Mirroring the Craft of M. C. Escher)
Title:
Clear
Plastic Stamp Mounts
Comment:
These clear plastic stamp mounts from Ellison measure 3½" by
3½" and include a set of 12. Ellison's
Self-Adhesive
Rubber comes in 8½" x 11" sheets and includes 6 sheets per pack.
Also available in an economical 48
Pack. Suggestion: Fix a 3½" square of Avery
Window Decals or Inkworks
Clear Window Decal Inkjet Film to the plate of a mount before positioning
the self-adhesive tessellating rubber region. Both see-through material
and rubber can be easily removed when all is done. Used in the tessellating
stamp activity of Investigating Patterns: Symmetry
and Tessellations.
Title:
Acryl-Pull
Handle
Comment:
Make your own transparent plastic stamp mounts. Attach large (½"
x 3½") clear plexiglass handles to 4-inch clear plexiglass squares
(1/8" to 3/16" thickness). Click here
for more information on fabrication (requires
Adobe
Acrobat Reader).
Title:
Carter's
Felt Ink Pad Size #3 (4¼ x 7½)
Comment:
On-line source of the extra large stamp pads used in the tessellating
stamp activity of Investigating Patterns: Symmetry
and Tessellations. Ink with SANFORD Roll-On Stamp Pad Inker, available
in black (SAN58701),
red (SAN58702)
and blue (SAN58703)
inks in a 2-oz bottle.
Title:
Escher in the Classroom
Comment:
A condensation of Jill Britton's article for the proceedings of the
International Escher Congress held in Rome, Italy in July 1998 (the centenary
of M. C. Escher's birth). The book of the proceedings (M.C. Escher's
Legacy: A Centennial Celebration) is available from Springer-Verlag.
Title:
What
Is a Print?
Comment:
Includes links to interactive demonstrations on the principal printmaking
techniques - woodcut, etching, lithography, and screenprint. Escher was
a master of both the woodcut and the lithograph. Requires Macromedia
Flash
Player.
Title:
Patterning
Comment:
Contains exercises to give children a new understanding about how commonly
used patterns and designs based on nets are produced. Includes use of vegetable
stamps. Handwork
contains links to related pedagogical web pages on crafts.
TOP
ACTIVITY
29 (Exploring Tessellating Art)
Title:
Staedtler
Mars All-Purpose Translucent Vellum
Comment:
On-line source of Staedtler 100% rag vellum (translucent bond) in 8-1/2"
x 11" sheets. Used in the Escher-based activities of Investigating
Patterns: Symmetry and Tessellations. Sheets feed easily into a laser
printer.
Title:
The
Mathematics Behind the Art of M. C. Escher
Comment:
A student project for Mathematics in Art and Architecture, a
course offered by Helmer Aslaksen at the National University of Singapore.
Flash Player 6 is required to view the excellent animations.
Title:
Doggy
Mosaic
Comment:
Try to pave an area with the figures of the dogs shown without any
gaps or overlaps. Move the dogs by dragging them. Rotate the dogs by double
clicking on them. Requires Internet Explorer 4.0 or higher, with JavaScript
enabled.
Netscape users beware!
Title:
The
Seventeen Wallpaper Tilings
Comment:
Some of the most fascinating tilings are the so-called wallpaper tilings.
There are exactly seventeen of them. Click on the various icons to see
an animation of the corresponding tiling being built. Each is labeled with
the name used by the International Union of Crystallography since 1952.
Title:
Seventeen
Kinds of Wallpaper Patterns
Comment:
Features examples of the seventeen kinds of wallpaper patterns in Japanese
culture. Includes Japanese nomenclature for the names of the patterns.
Title:
Tessellation Database
Comment:
View the artwork of a myriad of talented tessellation artists. Permits
the searching of tessellations by subject matter. The Virtual
Museum will require a VRML plug-in like
Cortona
VRML Client for your web browser.
Title:
Crompton Tessellations
Comment:
Features tessellations and other works by Andrew Crompton. Contains
a link to his poster of the 17
Wallpaper Groups (available from Instructional
Images).
People
Doing Tessellations has samples and links to other work around the
world.
Title:
Escher Patterns
Comment:
Features tessellations by Japanese artist Yoshiaki Araki - including
his classic tessellating elephant Maozou. Click on the icons to
view the tessellations.
Title:
Tessellation
World of Makoto Nakamura
Comment:
Includes a link to tessellation Animation
and interactive Jigsaw
Puzzles. Imaginative and highly recommended. Requires a JAVA-capable
browser.
Title:
Escher
Tilings
Comment:
A collection of Escher-like tilings by Belgian artist Jos Leys. Many
ultilize hyperbolic ("circle limit") geometry. Click on each graphic for
an enlarged view.
Title:
Tessellations &
Punography
Comment:
Features artistic and thematic tessellations with accompanying verse.
Enjoy "Quantum Leap", a tessellanimation movie with Ozzie the kangaroo,
as the extensive graphics load.
Title:
David Bailey's World of Tessellations
Comment:
Features links to the artistic tessellations of David Bailey, each
generally accompanied by explanatory text, whereby the various "intricacies"
behind the tessellation are discussed.
Title:
Hop's
Escher Tessellation Tiles
Comment:
Imaginative Escher-like artwork by Hollister (Hop) David. Hop's
Gallery includes tessellations, geometric paintings, and various geometric
designs.
David Hop's Magic
Mirror Image Coloring Book is a unique collection of 30 tessellations
of realistic figures ranging from bug-eyed frogs and flying pigs.
Title:
Parcelles
d'Infini - Promenade au Jardin d'Escher
Comment:
Site devoted to book by Alain Nicholas on creating Escher-like art.
The book text is in French, however it is mainly comprised of pictures.
Title:
Escher
Tile Gallery
Comment:
Contains 17 Escher tiles each of which forms a repeating pattern of
interlocking figures when placed side to side and vertex to vertex. Terrific!
Title:
Tessellated Polyhedra
Comment:
Build a durable model of each of the five regular polyhedra (Platonic
solids) from a card stock net fitted with tabs. Each has been decorated
with a tessellation of animals in full color.
Title:
Artlandia
SymmetryWorks
Comment:
Artlandia SymmetryWorks is an Adobe
Illustrator plug-in that lets you create the highest-quality professional
ornaments, designs, and art, and interactively explore symmetry and wallpaper
tilings.
Title:
M. C. Escher Font
Set
Comment:
This font set is based on the lettering styles and artwork of M. C.
Escher with both a formal lettering and a handwritten-style type. Rounding
out the set is a collection of extras drawn from and inspired by Escher's
work. Available for Win or Mac.
TOP
ACTIVITY
30 (Explorations with TesselMania!)
Title:
General Instructions for TesselMania!
Comment:
Includes a link allowing you to Download
the full Windows version of the TesselMania! program as well as
installation instructions specific to older and recent operating systems.
Decompress the program file with WinZip
or freeware
ZipCentral. Visit
Creating
a Quilt Block with TesselMania! for an interesting application of this
software.
Special:
Watch TesselMania's Tile Magic generate
the tessellating bunny of our background using vertex rotation on a parent
square.
Title:
TesselMania! Escher Simulations
Comment:
Permits downloading of a compressed file containing 20 TesselMania!
Escher
simulations (for use with the Windows version of TesselMania! only).
Title:
Tessellation
Exploration
Comment:
With Tessellation Exploration, transformational geometry concepts
are reinforced as students create 2-dimensional tessellations, then watch
them slide, turn, flip, and glide on the screen. Software on Mac/Win CD-ROM
plus a comprehensive teacher's guide with lesson plans and reproducible
masters of student activity sheets. Web page includes a link to a Tutorial
Movie (requires
QuickTime
Player). Visit Creating a Quilt Block with
Tessellation Exploration for an interesting application of this new
software. Download a compressed file containing 20 Tessellation
Exploration Escher Simulations (for use with the Windows version only).
Decompress with WinZip
or freeware ZipCentral.
Special:
Click on the graphic for an enlarged view.
Title:
Tess
Comment:
With Tess, you can quickly create attractive symmetric planar
illustrations. While you draw, Tess will automatically maintain
the symmetry group you have chosen; 11 rosette, all 7 frieze, and all 17
wallpaper groups are included. Visit Downloads
to access a fully-functional evaluation version of the Mac/Win software.
Title:
Tessellate
Comment:
Allows you to generate a new tessellating shape starting from a rectangle,
triangle or hexagon. Select Tessellate to see the complete pattern.
You can choose several different colors to enhance the pattern, and can
observe the different effects that colors have on tessellations. Requires
a JAVA-capable browser.
Title:
Tessellations
- Step by Step with "Paintbrush" or "Paint"
Comment:
Contains instructions for creating tessellating art (involving translation
- slides) using the Paintbrush or Paint software found on
all Windows microcomputers.
Title:
Tessellation Demo
Comment:
Jim McNeill's animated "how to" website for creating translation tessellations.
Brief - but excellent! Includes a link to a book, video and posters.
TOP
These links are coordinated with the chapters and activities
of
"Investigating Patterns: Symmetry and Tessellations"
Jill Britton (Grades 5-8)
Available from BiggerBooks.com
Read the Review in Mathematics Teaching
in Middle School
Requires Adobe
Adrobat Reader
More Books and Web Pages by
Jill Britton
Fun
with Patterns
links
links
All M. C. Escher works (c)
Cordon Art B.V. - Baarn - the Netherlands.
Used by permission. All rights reserved.
Jill Britton
Home Page
20-November-2008
Copyright Jill Britton
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