## Sunday, August 28, 2016

### CAMP Day 5

Friday marked our final day of CAMP. Despite the sadness of the end of the Bard Math Circle CAMP quickly approaching, we were able to have an awesome and fun last day that began with our mathematicians working to solve a number of math problems and puzzles. Some of the problems were taken from the AMC, a competition that Bard Math Circle hosts at Bard every year, while others were found by our high school volunteers to let our mathematicians warm up their brains! These bright young students were able to whiz through many of these problems on their own and the more difficult ones they discussed with their peers to try to find a solution.

Our schedule was a little different for our last day. We had gotten far enough in our math class to combine the class with computer science! Side by side, we compared a list of how to create fractals geometrically, mirrored by the code that would be entered into the program in NetLogo to achieve the same transformation of a figure. Together, we learned the specific code that creates a scaling transformation and the code that translates our x-coordinates. Then, we split up in pairs to input this code and try to discover the specific commands that would program the proper translation of the y-coordinates. We all came up with the code that will generate the Sierpinski triangle in NetLogo and then some of us even went on to develop the code that would create other fractals from the Yale Fractal Lab worksheet that we had received in math class the day before. We were able to learn how to turn the rules we discovered the day before into code that would create these fractals!

After lunch we returned to the RKC to finish up what we needed to in art and to take a short break before returning to class. Some students who had been learning the algorithms of the Rubik's cubes over the last few days, picked up a few of the cubes to practice and show their new skills to their friends. Some students even helped others who had not been to any of the Rubik's cube activities to see how to start solving the Rubik's cube.

In art class we finished designing and altering our fractal lamps in order to have them ready to present to our parents and friends at the open house that was happening at the end of the day. After finishing the creation of the lamps we discussed the installation of our art pieces and ventured out into the lobby of the RKC building (as well as some other rooms in the building) to install our art in beautiful and interesting ways. Some of the lamps were placed in a dark room with lights strategically placed within them. While others were attached to strings and then hung over the railings above the lobby. The lamps hung perfectly in front of the windows letting the light shine through them in just the right way to display the beautiful ways in which we had cut and sculpted the paper to make the lamps: finally now illuminated in the way they were meant to be.

After some final preparations of our computer programs and art pieces we were ready for our open house! Parents began to arrive and the students were able to showcase their accomplishments of the week. In one room the computer screens were filled with the wonderful and fascinating results of the code that the students had been writing to create fractals that we had learned about in math class. In the lobby one could see marbled paper and fractal lamps hanging from the second floor in front of the big windows and installed in tactical places to highlight the beauty and individuality of each piece of art. And in one room the lights were turned off to let the lamps really shine! The dark room showcased the amazing shadows that could be created by a light shining through the intricate lamps. After sharing with the parents, the staff was introduced and brief announcements were made before the Bard Math Circle CAMP of 2016 came to a close. Every student in the program this summer was absolutely brilliant and a joy to work with. Thank you to every student mathematician and staff member that made this amazing week the success that it was!

-Meagan (with the help of some amazing math CAMP friends!)

## Friday, August 26, 2016

### CAMP Day 4

Thursday was our fourth day of CAMP and for our morning activity we played an observational game entitled "Find the Chief." We sat in the auditorium in an ellipse, per the students’ request, and learned how to play this exciting game! A detective was picked and then asked to leave the room. While the detective was away we picked a chief who would serve as our leader. When the detective returned, the chief would begin performing a motion of their choice (a common favorite is to clap) and then the rest of the group would follow the chief. The chief’s job is to repeatedly change their motions while trying to make sure the whole group can follow them; the detective’s, to pick out the chief from the rest of the group. One of our student’s observantly pointed out that a great strategy would be to pick fake chiefs, who could watch the real chief, while the rest of the group could watch the fake chiefs to throw the detective off! After this fun game we started our classes of the day.

Our fractal lamp shades continued to be individualized as we accumulated our art projects from the week into our final art piece as we pleased. Alexis (one of our superb TAs) even taught us how to cut paper in simple ways resulting in intricate and gorgeous radial fractals! Some of us even added these radial fractals to our lamps!! Other students found more ways to incorporate the marbled paper they had created in the beginning of the week. In addition to working on our lamps we watched a video of a dancer who choreographed dances on sand that would result in geometric patterns drawn in the sand!

In math class we were able to apply our recently obtained knowledge of how we can use geometry to create and draw fractals! We experimented with applying planar transformations—specifically scaling and translating—onto the unit square to begin to make the Sierpinski triangle. We developed a set of rules that would transform the figure between stage 0 and stage 1, and then observed how the figure would change after multiple iterations of the rules we found together. Through this exercise, we were able to better understand how fractals are created using planar transformations. Frances, our lovely math instructor, then gave us a worksheet from the Yale Fractal Lab to work through in order to attempt to look at fractals, that had already gone through multiple iterations of a set of rules, and be able to discover these sets of rules on our own.

Our math class showed us the geometry behind making fractals, which connected fluidly to our computer science class where these brilliant mathematicians learned how to program our computers to make the fractals for us. We programmed commands that essentially perform the equivalent of scaling and translating, but instead of performing these planar transformations on points on a graph written on paper, the transformations were applied to our turtles in the world that we created in NetLogo. The students were able to see the program they created forming these fractals, and be grateful for the computers because they had personal experience with how complex and difficult it can become to compute and create fractals by hand!

Following lunch we held the much anticipated game of capture the flag: Team Team versus Team Mystic!!  Both teams defended their flags admirably, but Team Team was able to capture Team Mystic's flag and return safely to their side without being caught!  The teams then united again to hear about options for their afternoon activities: finishing tessellation art, continuing work on their stunning lamp shades, or learning about the Physics of Chaos Theory from one of our excellent TAs Victoria!

And to end the day we hosted another game of Bard Math Circle CAMP Jeopardy! Today we achieved a new wonderful accomplishment: we were able to have a Jeopardy game that was not only filled with excitement, but also was filled with listening to other teams answer each question. We learned that, instead of planning an answer in case another group misses the questions, it actually is beneficial to listen as other teams guess because then it helps us understand the questions better and also makes it less likely to restate a wrong answer if the questions gets to your team! Another exciting part of this day's Jeopardy was that during the game we all got our CAMP shirts to wear on the last day! So at the end of the fourth day of camp everyone left with more than they had when they came in that morning: a little extra knowledge and a fun shirt!

## Thursday, August 25, 2016

### CAMP Day 3

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)

## Wednesday, August 24, 2016

### CAMP Day 2

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)

## Tuesday, August 23, 2016

### CAMP Day 1

Hello everyone! So Monday marked the first day for the Bard Math Circle CAMP of 2016!! On the very first day of our exciting mathematical journey we jumped quickly into our explorations of fractals!

The day started with a game that involved team work and communication: the catch, we could not use our voices. Everyone received a card from a normal playing deck that we placed on our foreheads without looking at the card and then were instructed to try to line up in order based on card value or the suit of the cards. There was some phenomenal team work happening with this group of students who were able to create nearly perfect lineups in very little time. After that morning activity, we went on to play a few rounds of human knot in which the students stood in groups of even numbers and grasped hands of other group members to form our very own human knots. Then we observed the patterns that occurred while trying to untangle each of the human knots!

In math class we first learned about places in nature where we can find fractal-like compositions: trees, clouds, lungs, and more! Then we transitioned into learning about planar transformations; we learned about scaling, translating, rotating, and reflecting! And we all figured out how to apply those transformations to the Cartesian coordinates of an irregular figure that looked like the silhouette of an abstract tent with a tree behind it.

And in computer science we figured out some code that would have the computer draw this same abstract shape for us! The program used to do this is NetLogo, and we learned how to manipulate what are called turtles to move around the screen for us and draw different shapes. To do this we learned a bit about the different ways to control turtles in NetLogo and even figured out how to create our own commands! Some students were able to finish the task early and then went on to explore the different turtle properties and how to manipulate them using local variables.

Also on this very exciting first day, our mathematicians took some time to be artists as well! We learned how to make vibrant and beautiful fractal prints using a technique called marbling. Paper marbling is an ancient tradition and skill where pigment floats on water and the transfer of the surface information onto paper is both unexpected and mirrors the fractal patterns that naturally occur in water.

To end our day on the beautiful Bard campus, we all came back together in the auditorium of the RKC building for a fun game of C.A.M.P. Jeopardy. This was a little different from your normal jeopardy game show with the normal monetary prizes replaced by the ever more sought after space stickers and Bard math pencils! There was also a little more running around than normal Jeopardy done by our whole staff: high school volunteers, teaching assistants, coordinators, teachers and all could be seen rushing to each group to check their work as our student mathematicians worked at lightning speed to solve each conundrum presented to them. And after a long day of math our day came to an end as everyone returned home to reflect on all of the awesome math and fun that we experienced throughout that eventful first day!

-Meagan (with some help from other Math CAMP friends)

## Saturday, May 7, 2016

### CAMP is now waitlisted

We've experienced strong interest in our 2016 CAMP program, and have moved the registration into waiting list mode.

* We are still processing current applications, and expect to make a first round of invitations very soon.

* If you are interested in attending CAMP, please do complete the application form to be placed on the waiting list. We will make additional invitations as space becomes available.

Bard Math Circle

### MAY We Expect You at these Upcoming Events?

You May wish to take note of some of these cool upcoming math events, especially since this is the last month of our mathematical school year!

# May Library Programs

We have two library programs this month.

## Tivoli Free Library

On Friday, May 6th, please join us at the Tivoli Free Library on 86 Broadway, Tivoli, NY 12583. We will play games, solve puzzles, and tackle interesting problems from 4:00 until 5:30 pm.

## Kingston Library

On Saturday, May 14th, we welcome one and all to the Kingston Library, 55 Franklin Street, Kingston, NY 12401. The Children's Department is undergoing renovation, so we will meet upstairs in the Story Hour Room. Join us at 1:00 until 3:00 pm for some enriching problem solving and fun, math-themed crafts! OR, come by early to participate in the 6th annual Chalk Walk from 12:30pm-2:00pm. Bring your creativity! The chalk is provided.

All library programs are run on a drop-in basis, and registration is not required. We do ask students to sign in each time, and to provide their name, grade, and school. This is done electronically for Kingston, so please sign in using this link at least once this year.

# C.A.M.P. Summer 2016

The 2016 CAMP Application is live; Apply for CAMP 2016 here!

The Bard Math Circle is pleased to announce the CAMP (Creative and Analytical Math Program), set for August 22–26, 2016. This advanced week-long math enrichment program is intended for motivated middle school students currently in grades 5–8.

Dates: Monday, August 22 to Friday, August 26
Time: 9:00 AM to 3:30 PM each day
Location: Bard College, Annandale-on-Hudson, NY
Cost: \$225. Need-based financial aid is available.
Lunch: Lunch will be provided in Kline Commons, the Bard College cafeteria.

For more information about CAMP, please visit bardmathcircle.org. This website contains the latest information about the program, as well as archival blog posts and information from last summer.

# Purple Comet! Results

We would like to extend thanks to all who participated in the Purple Comet! math contest at Bard this year! Our two teams ranked 9th and 20th place in New York State; check out our website soon for more detailed results. Great job, everyone! We invite you all to participate again next year, whether you competed this year or not.

Let's end this year with a bang! We are excited to see you all at these final events to close out a great year.

Bard Math Circle
bardmathcircle.org
bardmathcircle@gmail.com