GEOMETRIC MODELING

Instructor:

Goal: The primary goal of this class is for you to be able to describe any given shape by a mathematical formula or algorithm.

Topics:

Graphs of functions (1 variable)

Vector-valued functions (2-D)

Multicurves

Vector-valued functions (3-D)

Graphs of functions (2 variables)

Surfaces of revolution

Other Parametric Equations from Cylindrical Coordinates

Parametric Equations from Spherical Coordinates

Parametric Surfaces

Affine Linear Transformations

Possible others: implicit functions, complex functions, basic differential geometry of curves and surfaces, flow lines of vector fields, etc.

Projects

Software: Mathematica is strongly recommended for all projects (but not required). You may obtain a free copy on your machine by emailing

edtech@pitzer.edu, and saying you need it for our class. There is a cloud version as well that will allow you to run it on a tablet, but you may have to purchase a subscription for that (its less than the cost of a textbook). You may use other graphing programs at your own risk (i.e., I may not be able to help you if you run into trouble). One nice alternative that will work for most projects is Grapher, which comes pre-installed on all Macs (hidden in the Utilities folder). There are also various ios/Android apps, such as GoodGrapher. However, only Mathematica may be powerful enough for our more advanced projects.

Hardware: You are required to bring some device capable of graphing the kinds of equations we will be dealing with to class every day. If you do not own such a device, please come talk to me. Graphing calculators will not be sufficient. A smartphone may work, but it will be hard to see more intricate projects on a small screen.

3D Printing: We have been given some money to 3D print a few projects from the Sontag Center (the "Hive"). This will be optional, and very likely require that you are running Mathematica. If enough people are interested, we can have an end-of-semester Mathematical Art show featuring your work at the Hive.

**Exams/Grades:** There will be no exams. Your grade will be
based solely on your performance on projects.