This class is intended for freshmen and sophomores.
This course satisfies the math requirement in the College of Arts and Science.
This course does not serve as a prerequisite for pre-calculus and calculus.
Students who need to take (pre-)calculus to satisfy requirements in their
major, should note that this course can not be used to satisfy that requirement,
nor can they skip college algebra if they have not taken that course yet!
During the semester we explore mathematics as it is used in art. Geometry has long been an inspiration for many artists. M.C. Escher is one of the main artists we focus on, but definitely not the only one!
Escher spent a lot of time exploring the so called regular divisions of the plane. Examples of this work can be found at may places on the internet.
In this class we explore Escher's work. We analyse his "divisions of the plane". One of the assignments this year was to create your own tessellation. Here are some examples of students work:
"Mummies" "The Dwarf and the Princess"
More examples can be found on another page.
We also study border patterns and wallpaper patterns. You are all familiar
with borders which can be used to decorate your wall. Often wallpaper comes
with a choice of borders which can be used to decorate the top of the wall.
These borders have distinct mathematical patterns which are determined by
looking for certain types of symmetry. Examples of Borderpatterns
can be found on a webpage maintained by John Wolfe ( Oklahoma State University).
Similarly Wallpaper
Groups (a webpage by David E. Joyce, Clark University) fall into 17
distict types, depending on what sort of symmetry is exhibited by the pattern.
We also cover the following topics:
Spherical Geometry
What changes to the rules governing geometry if start to desccribe a sphere,
instead of a flat plane? What do triangles look like? Can we draw squares
and rectangles on a sphere? (The answer in no!)
Here's a tessellation of a sphere. How would you go about doing that?
Hyperbolic Geometry
Are there other geometries besides Flat (=Euclidean) and Sperical Geometry?
The answer to this is yes. Escher is one of the few artists who has ever
attempted to draw a picture of it. Here's what it looks like:
If you want to walk a straight path in this world, follow the fish! This
means that the white "stripes" are tracing out the shortest distance paths
in this geometry.
Consider the 4-sided figure in the center. It has four sides that are congruent.
This means it is a rhombus.
If you look at the angles of the triangles traced out (next to the rhombus
for instance), you will see that in this geometry the sum of the angles in
a triangle is NOT 180 degrees! This geometry is full of these amazing surprises.
Fractals
Fractals are objects that contain smaller copies of themselves.
The Fourth Dimension
UNDER CONSTRUCTION