Welcome back! This Tuesday we started the day by getting excited about math through some competitive and fast-paced games of Set. Set is a game that uses cards that have four varying characteristics: the shape shown, the number of times that shape is pictured, the shading of the shape, and the color of the shape. The students attempted to discover sets of three cards for which each characteristic on the cards was either all the same or all different. These mathematicians caught onto the game so quickly that many soon had to start reusing cards from sets they had already discovered to keep the game going!
In math class we learned about scaling (by fractions) figures that were placed at the origin of a graph. We found out that after many iterations of this process we would only be able to perceive a tiny dot because the figure would become so minuscule. But if we magnified the picture we would be able to see that every figure is geometrically similar, meaning all of the angles remain the same and the lengths of the sides are proportional to the original shape though the area of the figures were changing. Because of this geometric similarity, you would not be able to tell which iteration of the scale you were looking at unless given additional information. This started to help us to understand the self-similarity of fractals!
In computer science we got to learn about local variables and creating functions in NetLogo. We explored producing geometric shapes using agent-based programming. Through what we learned we were able to create shapes within other shapes. We also learned about modifying different attributes of the turtles to create and experiment with individual effects. This was a fun way to customize our programs to our own original personalities and tastes!
For art class our mathematician/computer scientist/artists created our own fractal-like art projects! We created a three dimensional paper version of a famous fractal known as the Sierpinski Triangle. Students cut, folded, inverted, and repeated, to ‘infinity’!!!! We could clearly see that if we kept going with our cuts, that eventually the cuts would become too small for our scissors to cut and our eyes to see. This related to our math class because if you zoomed in on any of the triangles you would not be able to tell which part of the triangle you had magnified; similar to the affect that occurs after many iterations of scaling a figure by fractions.
In addition to our everyday classes, after some lunch and time outside, we split up for a few fun activities: a portion of us went to play cards and boardgames while other students ventured out to try to explore and learn the algorithms of a Rubik’s cube in order to solve the puzzle that has stumped many for years. A few of our mathematicians who were more experienced with Rubik’s cubes even helped out some of the novices of the group.
At the end of the day we came back for another fun-filled round of Bard Math Circle CAMP Jeopardy. Today our Jeopardy was a little different than on our first day. The Jeopardy game was projected in the auditorium with organized categories containing five levels of questions each assigned a different point value based on difficulty. In four separate groups the students put their genius minds together to try to claim the title of Jeopardy Champions of Day 2 of the Bard Math Circle CAMP! In the end every student won as we were able to go home with a better understanding of art and math and computer science!
-Meagan (again with the help of some other Math CAMP friends)