Fall 2017 Projects

Project: Visualizing polytopes in 4 dimensions: the work of Alicia Boole Stott

Faculty supervisor: Olga Lukina

Description: Alicia Boole Stott was an amateur mathematician of the 19-20th century, who lived in Ireland and Britain. She worked on visualizing polytopes in 4 dimensions by building cardboard models of their 3-dimensional sections. In visualizing the 4th dimension, she developed an original approach, very different from the one adopted by the trained mathematicians of the time. She was the first to discover the 45 semi-regular polytopes in the 4th dimension. Later in life, she collaborated with mathematicians Schoute and Coxeter, and was awarded an honorary doctorate from the University of Groningen at the celebration of its 300 year anniversary. The goal of this project is to understand Alicia Boole Stott’s method of building sections of regular and semi-regular polytopes, and to 3D print these models.

Accepting applications from: Undergraduate students

Prerequisites: Calculus I. Math 215 is preferred but not required. Some familiarity with programming, or experience of work in programs as Mathematica or Maple is preferred, but not required.

Reading: Irene Polo-Blanco, Theory and History of Geometric Models, Chapter 5, PhD thesis, University of Groningen, 2007.

Project: Wikipedia Math Illustration Task Force

Faculty supervisor: Jan Verschelde

Description: The goal of this project is to improve the mathematical content of Wikipedia by contributing new or improved illustrations (graphs, diagrams, animations) to articles that would benefit from them—focusing especially on articles about plane curves and algebraic curves. This is a great way to learn about programming techniques and tools for creating mathematical images while also making a valuable contribution to the mathematical community.

(This project was inspired by a Spring 2016 project at the Washington Experimental Mathematics Lab.)

Accepting applications from: Undergraduate students

Prerequisites: Calculus III and MCS 260 or equivalent programming experience. MCS 320 or concurrent registration is helpful but not required.

Project: Visualizing the Fourth Dimension with Virtual Reality

Faculty supervisor: David Dumas

Description: We will create a series of virtual reality (VR) experiences illustrating the geometry of four-dimensional spaces and four-dimensional mathematical objects using the Unity 3D graphics engine and the lab’s Oculus Rift head-mounted VR display. This series of short VR experiences will start with familiar objects and interactions and gradually introduce more complicated aspects of four-dimensional geometry, thus making ideas of higher-dimensional geometry accessible to a broad audience of VR users.

Accepting applications from: Undergraduate students

Prerequisites: Multivariable calculus and linear algebra. 3D graphics programming and VR experience would be helpful, but are not required; please specify any such experience when applying.

More projects to come…