Tessellations from Hawaii

Mrs. Cathi Sanders' geometry students at Punahou High School in Honolulu, Hawaii, used The Geometer's Sketchpad to construct these tessellations.

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"In a Rainbow Sea" by Maxine:

I constructed a tessellation using Geometer's Sketchpad. It looked a bit like a fish, so I decided to use that theme for my project, and worked on it a bit to make it look more "fish-like." I copied the line drawing into SuperPaint, and played around with colors. I wanted to make one fish stand out from all the others, so I made it a rainbow fish! By contrast I made the other fish shades of red. Tessellations are really interesting because all the pieces fit together so perfectly. I like geometry because you can be really creative with it and make unique projects.

I admired Escher's birds in many of his interesting drawings, so I wanted to try a bird in my tessellation. I felt that my bird was very simple compared to his, so I filled it with a rainbow of colors to create a more beautiful graphic. It's amazing to me that starting with a simple geometric shape, you can make such complex patterns. Now that we've explored this, I see these patterns all over the place - in fabrics and in plant forms, too. Nature is very geometric!

"Humuhumunukunukuapuaa" by Beth:

I decided to make fish in this project because they fit together well. (Fish are rather symmetrical creatures.) The fish named humuhumunukunukuapuaa is the Hawaiian state fish, and is often called "the little fish with the big name" (it is a very small fish!). This fits my picture, because although the one fish is small, it is important, and is colored so brightly.

"Popoki" by Kathleen:

I didn't plan what I was going to make for my tessellation. I just moved the points around until I saw something in the figure. It turned out to be a cat, which was sort of cool because all my friends call me Kat. This was an easier and faster way to make tessellations - in other classes we had to draw them out by hand so it wasn't as much fun, and you couldn't change them, either. With Sketchpad, you can change a tessellation and make it be what you want.

"Tapa Design" by Will:

This tessellation was constructed in Geometer's Sketchpad and later transferred into SuperPaint for coloring. Sketchpad is an excellent program for the building of tessellations because you can continually change and experiment with the shape of your original tessellation. My work was inspired by our annual Holoku (Hula) Pageant, which is filled with an abundance of patterns and colors.

 Tapa is a cloth made by ancient Hawaiians from plant fibers. The cloth is decorated with geometric designs using plant dyes. Tapa designs are almost always very geometric, and display a number of symmetries. Here is a sample tapa pattern:

"Hawaiian Petroglyphs" by Lauren:

This design was inspired by the ancient Hawaiian ki'i pohaku (petroglyph). The gray and black shading was used to create a sense of depth, as if carved in lava rock. Using Sketchpad I was able to transform a simple square into a complex spiralled pattern.

 Petroglyphs are Hawaiian rock carvings, somewhat like cave paintings or hieroglyphics. They are pictograms, and the patterns formed are often geometric in nature. Here is an example of some petroglyphs found on the island of Maui: