ABOUT THE COURSE:
This course will explore how one of our senses -- our sense of sight -- relies on our brain's seemingly hardwired understanding of a fascinating geometric space. What's more, this space -- known as the two dimensional Projective Plane -- is surprisingly different from the familiar Euclidean plane.
By examining some basic questions related to perspective drawing, like why parallel lines appear to converge in our vision, we can identify and analyze the defining properties of this space — properties which are well known to our visual sense, but defy our logical intuition.
As the course progresses, we'll situate perspective drawing in the framework of Projective Geometry, and get familiar with the algebra of homogeneous coordinates, which will allow us to translate our sensory intuition into precise information we can easily communicate. Finally, we'll get to know the topological space known as the real projective plane, as well as the matrix group that governs its transformations.
Being a four-week long elective, this course will nicely complement standard courses on geometry and topology, by giving hands-on experience with several important mathematical objects you’ll meet in those classes. But much of the course will also be interesting for artists, designers, or anyone else looking to understand deeper connections between math and art that humankind has been exploring for thousands of years.
Here you can easily navigate between videos, lectures, and chapters, understand the context of each video, and access interactive exercises that transition from one video to the next.
INTENDED AUDIENCE : Any Interested Learners.
PRE-REQUISITES : None, but some experience with mathematical proofs will be useful. Linear Algebra will be useful in the fourth week, but not essential.