This PREP workshop was made possible by the NSF grant DUE: 0341481

From Prep08Wiki

Hi, My nickname is Catie which I like better than Catherine, but I was formal when I applied to attend this wonderful Geometry and Art discussion/workshop/math and art gallery! I was a student at Cal Arts in the early 70's and started math 6 years later at age 29 with basic math...It took seven years to get my degree in mathematics. I taught middle school and high school and have always found some ways to put art and math together. I taught for 10 years in a court and community school setting and started work on a masters in teaching math here at Cal State Bakersfield. I just finished. It took me another 7 years. I have been working as a "math specialist" for the court and community students and their teachers here in Kern county. I have the pleasure of bringing math and math/art or art/math into the classrooms here. I may get the opportunity to teach at a local community college and am nervous and excited. What I have seen this week helps me to feel connected with a larger community of math educators who see the importance of this kind of collaboration. I think I find it hard to ask good questions and am soaking all this in like a sponge.

Work with Students

Creating a huge Sirpinski Triangle: Each student's equilateral triangle was 8 inches on each side. This way when you find the midpoints you can have at least 5 iterations on each student's triangle that can be easily measured by students that have difficulty measuring divisions other than 1/2 and 1/4 with inches..(I work with students that may not know how to use or measure with a ruler) It didn't take much time to put the final giant one together. They were all put together with double stick tape on larger triangles made with butcher paper....Be careful what wall you try to put this on...It's heavy and we removed some old paint when it fell off the wall!

The art teacher here at the school where my office is and I are experimenting with plastic straws to make a 3-D sipinski that we can attach student 2-D sirpinski triangles on it in a way that we can see through the empty spaces to see the other triangles.

I have used the Koch Island, and other fractal images...The Cantor Dust idea is great for teaching fractions of thirds and ninths and measurement. Student first make them by hand without measuring and then I ask them what would be easier...centimeters or inches if they want to make one that measures easily if they want to do several iterations.

We make tesselations using tracing paper and create a template that can be placed under a large sheet of tracing paper and then they can make lots of copies trying to keep their work very careful. As you keep tracing the pictures can sometimes become distorted because we don't work on a grid. This makes for some understanding of how accurate you need to be in the beginning and also that art can lead to a problem solving situation that you need to find a creative solution for. So we have had things like empty spaces that were filled with irregularly placed parts of the "puzzle" pieces...or "breakaways".. Similar to Escher's print of the butterflies.

Field Trip images

Triangle, Church Bakersfield, CA

 Poppa O's Pizzeria Wall next to gas station, Bakersfield, CA

Rim Art, (Pacific Tire and Wheel, Bakersfield, CA) More Rims

Here is some of my own humble work.

This was made using the ideas from Greek Geometry Hippocrates of Chios quadrature of lunes. This piece is actually titled "1+1=2" It is not too difficult to show that if this is built on a 2X2 unit square that the area of the first lune is 1/2 and the sum of the seashell shape series of lunes on one side is equivalent to 1 and is a nice example of 1/2 + 1/4 + 1/8+.... = 1 The artwork is a little crude, but the rotation symmetry is nice. There may be some distortion due to the photograph, but the lunes were created with compass and straight edge and they are built on the semicircle.

These are the same type of lunes. The center focus for the work was purposely placed by dividing the rectangular paper so that the golden rectangle was used. Then the lunes were made to the right instead of alternating. I call these "lunar clouds" and will put a few more up if people are interested. I looked everywhere for images like these and thought certainly they had been done before. It seems when people think of lunes they mostly think of "squaring" them. The next one shows a type of spiral...Can anyone say what type of spiral this is?

Here are 3 more showing the "lunar cloud" without anything and the "lunar seashell" with the diagonals connecting the midpoints of the isosceles triangle...I have seen the diagonals connected before, just not their connection to the lunes. Also a "sirpinski" with lunes!