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Games
Family Fun Activities
MIRROR YOUR FRIEND GAME
Ages 5 and up, two or more players
Materials needed: one large or one travel set
Teaches reflection symmetry, cooperation
First set up the game by placing any two tiles, edges together, near the center of the board.
Player #1 places a third tile adjacent to one of the tiles on the board so that the three tiles together form a design with reflection (mirror image) symmetry.
Player #1 then selects a fourth tile and adds it to the design making sure that the next player will be able to place a tile that mirrors that move.
Player #2 places a tile that mirrors the last player’s move, and then adds a tile of her own for the next player to mirror.
Continuing in this manner, it is fun to see the cooperative designs that emerge. This is an easy game to play with young children.
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SYMMETRY GROUPS
Ages 7 and up
Materials needed: one large or one travel set
Teaches basic symmetry groups
Symmetry Groups, Activity # 1
Optional: Review the section “Fractiles and Symmetry” printed on the inside cover of the Fractiles-7 package for illustrations and definitions of symmetry groups.
Next, make some simple designs that are examples of each symmetry group.
Give each child at least seven tiles of each color. Have each child use their tiles to create one or more simple designs for one or more of the symmetry groups.
Have a discussion asking the children to think of some everyday objects belonging to each of the symmetry groups. Ask them to name some examples that are man-made and some that are natural forms. Examples might include the human face as reflection symmetry, a daisy as rotational symmetry, or a checkerboard as translation symmetry. Hint – some objects have more than one kind of symmetry.
Symmetry Groups, Activity # 2
Materials needed: Magazines with lots of colored pictures, scissors, paste, scrap book.
Look through the magazines, select and cut out pictures that are examples of the different symmetry groups you have learned about. Use the pictures to begin a symmetry scrapbook with separate pages or chapters for each symmetry group. Explain in your own words why each picture belongs to a particular symmetry group.
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MAKING SMALL CIRCLES
Ages 7 and up
Teaches symmetry, areas, angle combinations
Materials needed: one large or one travel set
Allow at least 15 minutes
Divide the tiles into smaller sets of 21 tiles – 7 of each color. Give each person one of these smaller sets and a Fractiles board or other suitable steel-based playing surface.
Each person works independently to form a circle using all their 21 tiles. It will be easier if you refer to packaging illustrations of 21-piece circles. It will be more challenging if an example is not shown.
Discover your own unique style of tiling the same circular area with your 21 tiles.
Compare the various circles you have made and describe the similarities and differences. If you can, describe what symmetries have emerged? Do any of the circles have translation symmetry? rotation? reflection? or more than one kind of symmetry? no symmetry?
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STAR MAKING
Ages 8 and up
Work individually or as a team
Develops awareness of spatial relationships, and angle combinations.
Materials needed: one large or one travel set
Allow at least 15 minutes
If desired, you can refer to package instructions section “Why the Tiles Fit Together So Many Ways”. This will be more challenging if you do not read the material first.
1. Give each person at least 14 red tiles, 7 yellow tiles, and 7 blue tiles.
2. Make a yellow star, using 7 yellow tiles. A full circle has 360 degrees, so what fraction of 360 degrees is one yellow tile (answer: 1/7th)
3. Next make a star with red tiles (14 red tiles). What fraction of 360 degrees is one red tile’s angle (answer: 1/14th)
4. Use a calculator with as many decimal places as possible to see how many degrees are there in a single red tile. (answer: 360 divided by 14)
5. Again use the calculator to see how many degrees are there in a single red tile. (answer: 360 divided by 14)
6. Calculate all the angles of the tiles (six angles in all) – 1/14 of 360, 2/14 of 360, on up to 6/14. Did you notice anything weird about the numbers you got?
7. Next try to make a star using only blue tiles. Can you make a blue star in the same way as you made a yellow or red star? Why or why not?
8. Now make another star, but this time use more than one kind of tile. This star will look uneven or nonsymmetrical compared to the stars you made using only one color. After you have made this star, try trading some of the tiles in your star for different tiles. For instance, two red tiles can fit in place of one yellow tile. Try other combinations. What does this tell you about the relationships of the angles?
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FOUR PLUS STARS GAME
Ages 7 and up, for 2 or more players
Develops awareness of spatial relationships and angle combinations.
Materials needed: one large or one travel set
Allow 15 minutes or more
Object of the game:
Be the first player to complete a star composed of 4 or more tiles.
A star in this game is made of 4 or more tiles whose corners meet in the middle. Together these tiles close the circle. In other words, their adjacent corners have angles which add up to 360 degrees.
How to Play:
Set up the game by placing one tile near the center of the board.
Players take turns placing one tile at a time on the board.
The tile being placed must have at least one of its edges adjacent to the edge of a tile that is already on the board.
Tiles may not hang over the edge of the board or overlap other tiles.
You are not allowed to make a star with only 3 tiles as this is too easy and the game would end quickly.
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Recommended Reading
Sacred Geometry Design Sourcebook – Bruce Rawles, Elysian Publishing.
A Beginner’s Guide to Constructing the Universe – Michael S. Schneider, Harper Collins Publishers (Recommended reading for beginners).
Connections: The Geometric Bridge between Art and Science – Jay Kappraff, McGraw-Hill.
Dissections: Plane and Fancy – Greg Frederickson, Cambridge University Press.
Flatland: A Romance of Many Directions – Edwin A. Abbott, Dover Publications (Recommended reading for beginners).
The Fractal Nature of Geometry – Benoit Mandelbrot, W.H. Friedman, Publisher.
Patterns in Space – Col. Robert S. Beard, Creative Publications (our tiles are disclosed in his book).
Projective Ornament – Claud Bragdon, Dover Publications.
Symmetry, A Unifying Concept – Istvan and Magdolna Hargittai, Shelter Publications.
(IMAGE) full mandeala no.2
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Favorite Quotes
To see the World in a grain of Sand
And Heaven in a wild Flower
Hold Infinity in the palm of your hand
And Eternity in an hour.
William Blake
He looked at his own Soul with a Telescope.
What seemed all irregular,
he saw and shewed to be beautiful Constellations:
and he added to the Consciousness hidden worlds within worlds.
Coleridge, Notebooks
Indra’s Jewelled Net is a metaphor for the summation of Buddhist thought. Each of us is a jewel in Indra’s Net, which replicates the whole and is the whole. At each intersection in Indra’s Net is a light reflecting jewel and each jewel contains another Net, ad infinitum. The jewel at each intersection exists only as a reflection of all the others and hence it has no self-nature. Yet it also exists as a separate entity to sustain the others. Each and all exist in their mutuality.
Ken Jones, The Social Face of Buddhism
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“The ocean is a large drop; a drop is a small ocean.”
Ralph Waldo Emerson
Full quote “Give me an understanding of today’s world and you may have the worlds of the past and the future. Show me where God is hidden…as always…in nature. What is near explains what is far. A drop of water is a small ocean. Each of us is a part of all of nature.”
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What’s So Special About 7?
Using angles based on the number 7, these unique MAGNETIC tiles allow you to easily make your own aesthetically pleasing designs with repeating and non-repeating patterns. Use FRACTILES-7 to create starbursts, spirals, butterflies, beautiful mandalas of infinite complexity, bouquets of flowers, swarms of fireflies, spaceships, illusions of 3D space, and lots more.
Seven days of the week, seven colors of the rainbow, seven seas ….. seven dwarves, seven notes of the musical scale, seven year itch …… Seventh Heaven, seven metals of ancient alchemy, seven planets of ancient astronomy, seven classes of crystals ….. seven chakras, Seven Aztec Caves of Initiation, Magnificent Seven, Seven Samurai ….. Seven Voyages of Sinbad, Seventh Seal, Seven Mysteries of Life ….. Seven Ages of Man, Seven Wonders of the World.
Fractiles Heptagon Holes No. 1 Heptagon Holes No. 1
Seven has an abiding significance in cultures everywhere.
The Seven Muses: History, Poetry, Comedy, Tragedy, Music, Dance and Astronomy.
The Seven Medieval Arts: Grammar, Rhetoric, Logic, Music, Arithmetic, Geometry, and Astronomy – which are also called the Seven Liberal Arts because they are intended to liberate us from a mundane life.
The Bible has thousands of references to seven: Wisdom hath builded her house, she hath hewn out her Seven pillars.
-Proverbs 9:1
All the World’s a stage and all the men and women merely players; They have their exits and their entrances; And one man in his time plays many parts, His acts being the seven ages.
-William Shakespeare
In Native American Culture: In our every deliberation we must consider the impact of our decisions on the next seven generations.
– from the Great Law of the Iroquois Confederacy.
One, two, three, four, five, six, seven; All good children go to heaven.
-Children’s rhyme
In many societies every seventh year is a “Year of Release”. It is the statute of limitations for various crimes and debts, slaves are set free after seven years, planted fields are allowed to rest, etc.
In Greek Mythology, seven is the symbol of the Virgin. It is not possible to construct a perfect heptagon or to divide the circle into seven equal portions using only simple geometer’s tools. Hence, seven is indivisible, unconquerable, and virginal.
Nature delights in the number seven.
-Philo Judaeus, Alexandrian philosopher
(IMAGE) Fractiles Heptagon Holes No. 4 Heptagon Holes No. 4
Most of the information contained here about the number seven is from “A Beginner’s Guide to Constructing the Universe” by Michael S. Schneider. This is a beautifully illustrated and spiritually insightful book about the numbers one through ten.
Seventh Circuit Labyrinth
This is the classical or seventh circuit labyrinth. Seven circuits refers the seven paths that lead to the center or goal. This is an ancient design and is found in most cultures. It is sometimes dated back more than 4000 years. Also known as the Cretan Labyrinth it is associated with the myth of Theseus and the Minotaur. This design was found on Cretan coins.
Labyrinths have most likely always been used in a spiritual manner. They can create a heightened awareness of the human condition and aid psychological and spiritual growth. To build a labyrinth is to create a sacred space. To walk a labyrinth is to imbue it with power and meaning. The more a labyrinth is used the more powerful it becomes as a symbol of transformation.
The classical labyrinth has an association with Christianity. A cross is the starting point used to construct this labyrinth. The cross at the center can become the focus for meditation and the experience of the labyrinth. The classical labyrinth design is found in many churches in Europe.
