Building Real Mathematical Surfaces

November 1, 2019

The sphere is cut with planes that intersect in a single pointThis 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.

Maria's paper sliced forms

Math at the Market

October 19, 2019

Children assembling a Tangram puzzleOn October 19 OSU joined Celebration of Mind for the first time ever. Celebration of Mind is a yearly event in which people all around the world gets together to share their love for puzzles, games, math, and magic. It is also a commemoration of Martin Gardner's legacy on his birthday (October 21).

But, who was Martin Gardner? He was an American popular science writer and pioneer of the field of Recreational Mathematics. For many years, he wrote a column, "Mathematical Games", in Scientific American. He's column brought mathematics to a big audience and captivated their minds. His monthly puzzle special compelled readers to try solving them, or else they had to wait a full month to know the answer. Gardner is an inspiration for us and many people who works on popularization of mathematics.

A young couple trying to solve the snake cube puzzleThis year, the Department of Mathematics, through the outreach initiative, participated in this great Celebration. Erika Roldan, the Director of Outreach, had an idea: what if we could bring math to the streets and put it side by side with what people nurtures from? So we went to Clintonville Farmer 's Market and "sold" math between apples and tamales, for free! What a better way of celebrating Gardner than bringing math to all people and mix it up with everyday life, like he did?

Our booth in the Market featured games and puzzles Gardner wrote about. We also had posters with challenges and puzzles to go.

At first, people looked at us with suspicion. More than one was probably wondering what was their worst nightmare doing at their favorite market. We offered pi and pentomino shaped organic cookies for those who solved a puzzle, and a few decided to give a try. Little by little more people approached our table. Some stopped, continued shopping and then came back. Once a puzzle was solved, people gained confidence and wanted to try another. Children were seriously engaged playing with math and their parents almost have to drag them away to continue with the shopping.

Then came the bubbles. You can always capture and audience when showing the amazing shapes soap film takes when sticking to the skeleton of a Platonic Solid. By the time the Market was about to end, people were asking if we were going to be there every Saturday.Erika showing a cubic bubble inside the skeleton of a cube

The purpose of the outreach initiative from the Department of Mathematics is to reach the general public of all ages and backgrounds. Events like this fulfill that purpose. When our events take place at a school, a science fair, or even here at OSU, attendees have to be interested enough to make the effort of coming. At the Market, we gave math to people who was not looking for it or even expecting it. We will continue to organize more of these activities to keep up with our mission.

A special thank you to the volunteers who were at the booth sharing their love for math: Maritza Sirvent, Yiwei Ren, KT Goldstein, and Rachel Skipper for baking cookies.

Girls doing mathGirls engaged in playing SET

October 12, 2019

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 naturaly 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 untraditional environment, and seeks to attract women to pursue careers in math.

BAMM @ The STEAM Factory

October 11, 2019

Student trying to arrange the pentominoes on a chess boardThis Friday, Buckeye Aha! Math Moments joined STEAM Factory's Franklinton Friday for its October edition. Franklinton Friday is a monthly event in which 400 West Rich hosts a free art crawl, opening its doors to all public. STEAM Factory offers mini lectures on diverse research and outreach topics, as well as craft and activity tables to explore STEAM themes.

BAMM had a math games and puzzles table. General public and fellow STEAM members had fun solving the soma cube and playing Halloween SET, among other activities. A young attendee was trying to arrange the 12 pentominoes and a 2x2 square on a chess board. He couldn't solve the puzzle that day, but said he hoped to would keep trying on the following Franklinton Friday.

Monica presenting a mini lecture about vampires and mathThis Franklinton Friday was Fear-hundred, a Halloween themed edition. Representing BAMM, Monica Delgado gave a mini lecture titled "How long would we go extinct if Dracula was real?", in which she talked about some math models for vampire and zombie outbreaks. She presented a simple exponential model and concluded that, if no other factors were taken into account, vampires would very rapidly overcome humankind. She remarked that wouldn't be very smart from vampires, as "after humankind is wiped out, vampires are doomed too, with no more blood to drink for survival".

She concluded explaining how these models are suitable for educational purposes, and how they can be adapted for more realistic scenarios. "This also shows how flexible math modeling can be and how it can respond to a wide variety of biological challenges", she finished saying.

This was the first of many future collaborations between BAMM and the STEAM Factory.

Ciencias 2019

September 26, 2019

People at CIENCIAS 2019 playing mathematical games

BAMM attended Ciencias 2019. The event, organized by the Society for the Advancement of Chicanos/Hispanics and Native Americans in Science (SACNAS), is OSU's Annual Diversity in STEM Networking Event.

We had the opportunity to connect with underrepresented minority STEM students and professionals at Ohio State. The attendees enjoyed math by engaging in solving puzzles on our table.

Cole, an Earth Sciences graduate student, said he experienced the "aha!" moment when he figured out a way of solving a puzzle. The puzzle consists of 4 knights on a 3 by 3 chessboard, two black knights on the corners of one side of the board, and two white ones on the corners of the opposing side. The goal is to move the pieces until the black ones are where the white ones were in the begining, and viceversa. Of course the pieces can only be moved following chess rules: the knight moves tracing an "L", to a square that is two squares away horizontally and one square vertically, or two squares vertically and one square horizontally.

Cole has almost given up when he saw it. He said "All pieces move in the same way, so we can circle them around until we reach 4 knights on a 3 by 3 chessboard.the desired configuration". And he did it! Then his friend came and solved the puzzle in a different way. He then experienced a second "aha!" moment.

Other attendees solved the tangram and the soma cube. We loved sharing our passion for math with OSU students, faculty, and staff from different departments.

BAMM strives to be an inclusive program. Some of our activites target specific underrepresented minorities and most of them offer bilingual support (English/Spanish).

Anamorphic Art - Mathematics behind the Illusions

September 23, 2019

Distorted image of the Earth shows corrected when reflected on a cylindrical mirror.

This past 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.