STAC Students Win Award at Math Research Conference

Apr 07, 2016

STAC Students Win Award at Math Research Conference

Dr. Meghan De Witt, Assistant Professor of Mathematics at St. Thomas Aquinas College, recently took three students, Lindsey Heiberger '17 (Garnerville, NY), Heather Palmer '16 (Chester, NY), and Daniel Viaud '17 (Bloomfield, NJ) to Los Angeles, CA, to participate in a mathematical research conference as the culmination of their year long research project. Each student gave a 20 minute presentation on their work and then participated in a poster session at a concurrently run Mathematical Association of America conference where they won an award for having an excellent poster.  

The goal of the project was to study the symmetric group of various dimensional cubes.  Symmetries of an object are the result of picking an object up, turning it around in various ways, and being able to place it back down so that it occupies the exact same space as it did originally.  For instance, a cube has 24 different arrangements that you can experience with a die--6 different numbers can be on top, and once that number is selected 4 different numbers can be on the side facing forward.  We not only found the symmetric groups of lines, squares, and cubes, but also of the tesseract (4D) and penteract (5D) which we 3D printed models of using STAC's Innovation Center. 

 

Lindsey, Daniel and Heather pictured with their dimensional cubes.

Dr. Meghan De Witt, Assistant Professor of Mathematics at St. Thomas Aquinas College, recently took three students, Lindsey Heiberger '17 (Garnerville, NY), Heather Palmer '16 (Chester, NY), and Daniel Viaud '17 (Bloomfield, NJ) to Los Angeles, CA, to participate in a mathematical research conference as the culmination of their year long research project. Each student gave a 20 minute presentation on their work and then participated in a poster session at a concurrently run Mathematical Association of America conference where they won an award for having an excellent poster.  

The goal of the project was to study the symmetric group of various dimensional cubes.  Symmetries of an object are the result of picking an object up, turning it around in various ways, and being able to place it back down so that it occupies the exact same space as it did originally.  For instance, a cube has 24 different arrangements that you can experience with a die--6 different numbers can be on top, and once that number is selected 4 different numbers can be on the side facing forward.  We not only found the symmetric groups of lines, squares, and cubes, but also of the tesseract (4D) and penteract (5D) which we 3D printed models of using STAC's Innovation Center. 

 


In this process the students discovered and proved several useful formulas and also redefined how symmetric groups are understood for higher-dimensional objects after they found a significant misunderstanding that has been perpetuated in mathematics for several hundred years.  They also discovered how knowing the symmetric group of a lower dimensional object (such as the square) allows you to create the symmetric group of any higher dimensional cube.