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Fractals and Polytopes

Promoting community appreciation for the beauty of mathematics, on December 13, 2018, a team of university faculty, high school faculty, university students, and high school students worked together to create beautiful, and meaningful, 3-dimensional mathematical models.

Tabatha Rainwater, a math teacher at Austin East Magnet School, organized the event called, “AE/UT MATH DAY” at which University of Tennessee Department of Mathematics faculty and students visited the school, bearing glad tidings of mathematics.

Dr. Heather Booth, with the help of Dr. John Griffis, first gave a lecture about fractals and then led the Austin East students in the creation of Sierpinski fractals. While these fractals teach students about non-integer dimensions and self-similarity, they also serve as fantastic Christmas tree decor for the school hallways.

Dr. Jeneva Clark, then led a mini-lesson about polytopes, followed by an announcement that a polyhedron now bears the name “The Austin East Roadrunner,” a name accepted by Discretization in Geometry and Dynamics, supported by the German Mathematical Society, to honor the school’s 50th anniversary. The students and faculty then created individual models of The Austin East Roadrunner.

“We are all familiar with a cube, or maybe a tetrahedron, but there are others out there that don’t have names. There are so many different polytopes that mathematicians can’t name them all or make models for them. We are helping by adopting this particular 13-faced polytope and giving it a name. Not to mention, it makes a great ornament for our fractal Christmas tree,” Dr. Clark told the group.

Mrs. Rainwater believed the positive interaction of learning engaging math with UT Math Department faculty would enhance her students’ success in college. “Many students do not regularly interact with college faculty, and because Dr. Booth and Dr. Clark teach fun math in their Mathematical Reasoning class, I eagerly welcomed UT Math faculty, who show the true meaning of a volunteer’s spirit. They find ways for students to engage in math that are meaningful to their lives,” said Mrs. Rainwater.

“I’m very happy the students of Austin East Magnet High School were given this opportunity to build a Sierpinski Fractal and ‘The Austin East Roadrunner’ Polytope. It’s not in the high school standards to create a polytope or build a fractal, but I’m thrilled to introduce high school students to new and engaging math.” said Mrs. Rainwater.

“I didn’t know college math was going to be so fun. I wasn’t expecting the professors to be nice either. I’m glad I participated in this event. I’m looking forward to taking math in college.” -Leshundra Selmon, senior at Austin East Magnet High School

“This was my favorite experience of the semester. I enjoyed going to a school that I have never been to and meeting a class of high school students. Seeing these students get excited about the activity, want to participate, and make the tree as big as possible, was very refreshing to see and hear. This particular activity made me very excited for my future in education. Students were engaging in mathematics topics without even realizing it; it was great to see.”

-Francesca Grill, undergraduate mathematics major, with an emphasis in mathematics education, at the University of Tennessee.