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101 uses for tessellations and symmetry:

1. Pattern for quilts.
2. Pattern for manhole covers.
3. Pattern for shoe bottom.
4. Pattern for tire treads.
5. Parking lot design.
6. Geodesic dome structures.
7. Batik fabric design.
8. Pattern for needle point.
9. Design stained glass windows.
10. Reduce scrap and conserve material.
11. Cubical layout in an office.
12. Stackable furniture and storage units.
13. Design furniture cut from a sheet of plywood.
14. Interlocking ceramic tiles and concrete paving blocks.
15. Design backgrounds and wallpapers for webpages.
16. Design wallpaper for interior decoration.
17. The eye is attracted to order and finds beauty in repetition.
18. Latticework and fretwork are used in architecture and furniture.
19. Lattice windows provide a view and improve air circulation.
20. Jali screens allow soft filtered light to enter a room.
21. Design color pattern for necktie and t-shirt.
22. In fabric printing, this technique allows pattern to repeat

seamlessly.
23. It is a high school level exercise for math students.
24. Design masks for photolithography and microchips.
25. Regular plane division is useful in crystallography.
26. X-ray image of a DNA crystal showed the double helix structure.
27. Interlocking wood joints are beautiful and strong.
28. Symmetry is used in product design, modular design and

packaging.
29. Use symmetry to break a product into modules.
30. Nesting and packing are organization tools.
31. Symmetry is seen in biological system because of efficiency

and balance.
32. Symmetry helps us to see by deduction.
33. Symmetry simplifies computation and reduces the size of

a program.
34. Make doodling a productive mental exercise.
35. The periodic table helps to predict chemical and

physical properties.
36. Polyhedrons help to design new temari balls.
37. Reciprocity principal is used to explain behavior and

expectations.
38. Study mathematical qualities of design and art.
39. Design jig-saw puzzles that are more difficult to assemble

because every piece has the same silhouette and will fit.
40. Duality principle ties together two "entities" by a transformation.

A CUBE and an OCTAHEDRON form a dual in that the faces of

a cube transform into the corners of an octahedron.
41. Duality principle works in a "temporal reflection transformation"

in Dynamic Programming methods.
42. Decorate Easter eggs (Pysanka).
43. Design geodesic truss for playground.
44. Use art to soften the fear of mathematics.
45. 5 year old kids can understand tessellation, you cannot really

teach geometry until 13 or 14 years old.
46. Symmetry is a good topic to teach group and set theory.
47. Tessellation shows design ideas for efficient packaging.
48. Symmetrical creatures are simpler on the DNA.

This avoids mistakes.

The genes for a flounder or halibut is much more complex.
49. Tile the surface of the space shuttle or pysanka with a

standardized universal tile, lower cost and simplify maintenance.
50. Let computer geeks draw something impressively complex.
51. Design quilt pattern for paper towels, napkins and toilet paper.
52. Security paper use fine textures to deter counterfeit or alteration.
53. Inside of airmail envelopes are textured to block unauthorized

veiwing.
54. Display of data structure with tessellation makes it easy to find

problems and defects in the data.
55. Perfect subject for multi-cultural mathematics teaching.
56. Rich source of archaeology and history of ornaments and crafts.
57. Color and symmetry are useful tools to learn and think about

group theory and set theory.
58. Design cookie cutters and cookies.
59. Design cereal, alphabet soup and potato chips.
60. Design interlocking bricks and concrete blocks for retaining walls.
61. Interlocking slope paving (ground cover) to prevent soil erosion.
62. Decoration for hot air balloons.
63. Propellers and wheels need symmetry for rotation balance.

Symmetry is required for rotary devices.
64. Area filling and hatching for graphic art and section drawings.
65. Symmetry is useful to the understanding of Relativity and space-time.
66. Design lumina and lamp shade.

* Periodic Drawings with JAVA programs *
* Mathematical Basis of Interlocking Shapes *

Math/ART definitions