## The Gift of Math

Devember 6, 2019

BAMM participated in Columbus Science Pub. The Columbus Science Pub presents a new talk every month. Speakers are invited based on requests from the audience, science topics in the news, and recommendations from the Columbus community. By connecting the Columbus community with expert speakers from across the fields of scientific study who use science in their daily lives, we grow science literacy.

In “The gift of math", Monica Delgado, the Associate Director of Outreach at the Department, talked about the beauty of math. Every Science Pub is unique but math talks are always special. Monica had a table full of gadgets that we were all wondering how she was going to use. She discussed three topics that she learned about when she became a math student and that she still finds amazing and mind blowing. The first topic was the infinity, where Monica showed us infinity is not only really big numbers but very little numbers as well. By the second topic, soap bubbles, we knew what all the stuff on the table was for! When she asked us to suggest a possible shortest path to connect three cities, a young girl from the audience gave a good solution: connect two of the cities with a straight line and then connect the third one with a second line perpendicular to the first one. People are good at solving these problems but bubbles are better. Monica showed how bubbles can also plan the best path for a road trip across the USA. The third topic, Mobius bands, was an audience favorite. Everyone got to make their own bands, identifying their sides and cutting them to figure out the number of edges.

Monica closed her talk suggesting we all follow her example and put up math shows with our families this holidays. “This holiday season, give the gift of math", she said.

Article contributed by Katherine O'Brien

## Origami Holiday Decorations

December 5, 2019

After a hard work's term, members of the Math community took a break before the exam week to make some paper holiday decorations. Reading day is meant to be a day for studying and preparing for the final exams. However, it is also a chance to take a deep breath and relax to be ready for the last stretch of the term.

Many opportunities are provided across campus for students to relax. Here at the Department of Mathematics BAMM offered a holiday origami workshop. Students and staff folded paper Christmas wreaths and stars that were then hanged for decoration on the Department's tree.

## BAMM @ Your School

November 21, 2019

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.

Just 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 paintors 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.

## Inspiring Women of Color to do Math

Novembe 16, 2019

AWOW, Advocates for Women of the World, is a student organization at Ohio State that advocates for international women's rights. One of their goals is to promote access to education for everyone. As such, on November 16 they held an event in which around 30 young girls visited the Columbus Campus. For this, they partnered up with Proyecto Mariposas, a non-profit Columbus based organization that provides an environment of learning, sharing, and support to Latina girls and their mothers.

During the event, AWOW members led the girls on a tour around campus. The visitors also met with Office of Diversity and Inclusion Assistant Vice Provost, Yolanda Zepeda, to talk about the Latinx experience on a college campus.

Buckeye Aha! Math Moments was happy to join their efforts by welcoming the girls in the Mathematics Tower. During their short visit to our Department, they listened to Assistant Professor Liz Vivas' experience. Originally from Peru, Liz is a living example of how women of color can succeed in college and in mathematics. Girls also peaked into a Girls Exploring Math Monthly workshop that was being held that same day and were invited to join for those workshops as well as BAMM's other activities.

The Department of Mathematics is a big one, and it welcomes all people regardless of race and gender. However, certain groups, such as women of color, are still underrepresented. With small actions like this one, BAMM hopes to contribute to create a more diverse environment.

## The Mathematics of Origami

November 18, 2019

Last week, the Department of Mathematics, through the outreach initiative, had a guest for the Recreational Mathematics Seminar. Laura Jimenez is a mathematician and a PhD candidate at the Department of Ecology and Evolutionary Biology at the University of Kansas. In college, she began to develop a passion for origami, and she was able to tie it with mathematics. When she was a master's student, she worked in mathematical outreach and popularization and gave workshops about the mathematics behind origami.

At the Recreational Mathematics Seminar on Friday, November 15, Laura talked about how not only math is used in proving whether something is foldable or not and finding the folding pattern, but also origami can be a powerful tool for solving mathematical problems, such as solving a third-degree equation.

During the talk, the speaker presented the Huzita axioms, the mathematical principles of paper folding. The axioms list the seven operations that can be achieved by folding paper. The first axiom reads "Given two distinct points *p _{1}* and

*p*, there is a unique fold that passes through both of them." The second one goes about placing a point into another; in this case the fold created turns out to be the perpendicular bisector to the segment joining the two points. Later on, Laura showed how one can trisect an acute angle by folding paper, in other words, by following the Huzita axioms.

_{2}The seminar was followed by a workshop where attendants learned how to fold a cube and a 12-pointed star of modular origami. Some would say that this type of origami is the most mathematical one. Modular origami pieces are made up by several sheets of paper. Each sheet is folded in the same manner, creating a unit with flaps and pockets. Then all pieces are put together by inserting flaps into pockets. This type of origami allows us to build geometrical objects such as the platonic solids.

Laura emphasized how origami is a great tool for teaching geometry.

On Saturday, our guest also ran our Girls Exploring Math Monthly workshop. Students explored the properties of buckyballs, polyhedra with regular pentagons and hexagons as faces. They analyzed the number of vertices, edges, and faces of each type, and came up with a relation between them. When building the origami model of a dodecahedron, the girls also looked at its graph representation and found a Hamiltonian path on it. Then, they used it to decide how to assemble the origami modules so that all the edges connected in every vertex had different colors (using modules of three different colors - it's not as easy as you might think!).

The Recreational Math Seminar is gaining presence within the Department's community, showing the most entertaining side of math. Recreational Math is a great way of getting undergraduate students interested in research. We will continue to bring more guests next term.

## Building Real Mathematical Surfaces

November 1, 2019

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.

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, and 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.

## Math at the Market

October 19, 2019

On 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.

This 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.

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 math

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

This 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.

This 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

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 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

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.

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.