Instructor: Dr. Evelyn Sander
Course: This course was offered as Math 493 Spring 2015. It will be offered again as a capstone course in Fall 2019.
This course gives you an opportunity to learn about geometric visualization and its uses within 3D printing.
The course will consist of a series of projects concentrating on the understanding of different types of mathematics through 3D visualization. The idea is to learn to understand and present math both in words and in terms of visualizations. There will be some lectures, and some reading assigned to the whole class, but for the most part the class will work on a series of assigned projects.
The mathematical content of the course consists of an overview of a number of diverse subjects. Thus the reading materials will consist of research papers and small portions of textbooks rather than a single assigned textbook. Software used consists of Mathematica and various free software specially designed for 3D printing. In some cases, students will also use Matlab for creating data and a free software for visualizing it.
Projects will each be in a different general category of mathematics, as follows:
- regular and irregular tilings in two and three dimensions: wallpaper patterns, Penrose tilings, quasicrystals
- polyhedra and their properties: five Platonic solids, duality, truncation
- surfaces and hypersurfaces: quartic surfaces, complex surfaces, isosurfaces, Hopf vibration
- fractals and dynamical systems: Mandelbrot and Julia sets, attractors, chaos, invariant manifolds
- differential equations: isosurfaces of solutions with complex pattern formation
For more information, contact Dr. Sander (esander@gmu.edu).