math-art

BAMM @ Your School

BAMM @ Your School is one of the outreach projects at the Department of Mathematics. Through this program, we take fun, engaging, and deep mathematics workshops to schools in the Columbus Metropolitan area.

Notebook showing 4 by 4 and 5 by 5 configurations with their Mondrian numbersJust on November 21st, we had the opportunity to visit a fourth grade group at Daniel Wright Elementary School. Erika Roldan led a workshop on Mondrian numbers. Students worked in pairs and received an envelope containing red, yellow, blue, and white rectangles of all possible integer dimensions between 1 and 5. “Today you are going to become painters with these pieces”, said Erika.

Their first task was to classify the pieces according to their shape, in other words they had to make groups of congruent rectangles. Then they were asked to find all possible ways of building a 3 by 3 square using non-congruent pieces. When finished, they went on to do the same for a 4 by 4 and a 5 by 5 square.

Their last task was to compute the Mondrian number for all the possible configurations they had found. The Mondrian number of one of these such configurations is the difference between the maximum and the minimum areas of its pieces. To be able to do these, students registered their configurations on their notebooks. Some students made a lot of progress in the task, but even those who weren’t as fast practiced their geometrical skills and had a fun math class.

BAMM @ Your School is free and its only subject to time availability. Volunteers are very much welcomed and appreciated. Contact us, if you would like to visit a school with us.

Building Real Mathematical Surfaces

This week, Buckeye Aha! Math Moments had a series of events around the work of a special guest. Maria Garcia Monera, from the University of Valencia (Spain), is interested in Topology and Geometry and in designing and building paper models of surfaces.Graduate student assembling a paper model of an ellipsoid.

Even from last week we started preparing for Maria’s visit. We built some of her models and displayed them in the Mathematics Tower lobby for everybody to see. Then on Monday, Maria gave the Recreational Mathematics Seminar. She explained that he technique she uses is based on the work of Felix Klein, Alexander Von Brill, and John Sharp. In an era before computers, where one could render the surfaces on a screen, the motivation for creating these models was aiding students in the visualization of the mathematical objects. The idea behind is finding plane curves contained on surfaces that can be cut in paper and used to reproduce the model.

The seminar was well attended by postdocs, graduate and undergraduate students, and lecturers, becoming the most popular Recreational Mathematics Seminar so far.

On Tuesday, Maria gave a workshop at the Columbus Public Library (Northside Branch) were some children built an orange paper sphere and decorated it as a pumpkin. Then on Wednesday, during Teas, those who attended the seminar (and a few others) put in practice what they had learned, building paper surfaces such as paraboloids, water drops, ellipsoids, andMetro School class crafting some surface paper models hearts.

Finally, on Thursday Maria worked with a 6th and 7th grade math class at Metro Middle School. She talked about surfaces of revolution and then the children worked in teams to craft spherical pumpkins and hearts.

Recreational Mathematics is about fun and entertainment, but that doesn’t mean there aren’t serious mathematics involved. As the Mathematical Association of America writes “Recreational mathematics is inspired by deep ideas that are hidden in puzzles, games, and other forms of play”. With Maria’s visit, the Department’s community had fun and obtained a tool for helping students visualize surfaces. Hopefully, some were so inspired that they will design their own paper model.

Girls Doing Math

The second session of Girls Exploring Math Monthly took place this last Saturday. This time the attendees explored latin and magic squares. They worked by themselves, challenged each other and naturally ended up working together to solve the problems.

A Latin square is an n by n grid filled with n different colors, each occurring exactly once in each row and exactly once in each column. When counting the number of different 3 by 3 Latin squares, Ella, a 7th grade student, said “If I fix the red, then there are only two possible ways of arranging the other two colors. Since there are 6 different configurations for the red, then there are 12 distinct colorings.”

During lunch, they had fun playing SET. They were competing against each other, but when the group of cards on play was a particularly difficult one, they joined forces. They came up with classification strategies that could help them better tackle the problem.

This event is part of a long term project that includes monthly workshops and a summer camp. The project Girls Exploring Math invites young women to experience mathematics through engaging activities in an nontraditional environment, and seeks to attract women to pursue careers in math.

Anamorphic Art – Mathematics behind the Illusions

On Saturday the Department of Mathematics received a group of female high school students to learn about using math to create anamorphic art. The workshop was taught by Anna Davis, Ph.D., from Ohio Dominican University.Drawing of a cube appears like floating thanks to an anamorphic effect.

The word anamorphosis refers to a distorted projection or drawing which appears normal when viewed from a particular point or with a suitable mirror or lens. Anamorphosis has become increasingly popular in art, especially in street art.

Led by Prof. Davis, students drew anamorphic projections aided by a laser and further explored them using GeoGebra. They also wrote functions to create an anamorphic version of a “normal” drawing. Finally, they had time to create their own anamorphic art.

This event is part of a long term project that includes monthly workshops and a summer camp. The project Girls Exploring Math invites young women to experience mathematics through engaging activities in an untraditional environment, and seeks to attract women to pursue careers in math.