On Wednesday we began the journey of our third day of the Bard Math Circle CAMP of 2016 by experimenting with tooth picks to try to solve the many matchstick puzzles that one of our fantastic TA's, Alexis, brought in for us to think over. Some of us in pairs, and some individually, impressively worked through the sheet of puzzles solving many if not all of the matchstick problems!

We started our math class by learning more about planar transformations! We split up into groups of two or three to experiment and see if any pairs of planar transformations are commutative (meaning the resulting figure after both planar transformations were applied was not affected by the order in which the transformations occurred). Each group drew their findings on the board and presented their conclusions. After that, some students started drawing the Sierpinski triangle by beginning with an equilateral triangle as Stage 0, and then repeatedly "cutting" out a fourth of the previous stage’s triangles after each iteration. We then recorded the area and perimeter of our shape at each stage to observe what was happening to the triangle!

In art class our Sierpinski triangles, that we had made the day before, became three dimensional one of a kind sculptures! We noticed that the paper caught the light in really beautiful ways and so we began to design unique lamp shades using our marbled paper and the texture of the Sierpinski triangle. So in order to add our own individual personalities to these fractal lamp shades everyone took their own steps to alter their designs: making constellational cut outs, layering, cutting out more shapes, attaching geometric solids, and more. And some of us simply spent time as designers, imagining and working through different ideas on our own as well as with our classmates.

We learned about and started practicing our pair-programming techniques in computer science, where one of the students served as the driver and the other a navigator. This way we get to share ideas and come up with creative solutions together; when more of these brilliant computer scientist/artist/mathematicians are working together, the more amazing the solutions can become. Then we did a fun exercise where each person in the class said a line of code as we tried to write a program together. Additionally, we learned about creating functions in the code tab to make each button have only one function controlling it. This makes it easier to edit our program!

After a rousing game of blob tag, following lunch, these mathematicians split into three groups: some of us went to play a game entitled Staying Rational in the Infinite Hotel, some went to continue to explore the mysteries of the Rubik’s cube, and others went to learn about tessellations and create some beautiful and fascinating tessellation artwork.

We finished our day as we normally do with a rousing game of Bard Math Circle CAMP Jeopardy. Today the game was very similar to the day before, but we added the excitement of prizes! Origami paper was handed out as a prize that the students could use to create the intricate origami designs that we have learned during camp. Everyone went home happy: with a smile, some origami paper, and some new knowledge about math!

-Meagan (as normal with help from other lovely Math CAMP friends)

(Photo of Sierpinski's triangle courtesy of zeuscat.com)