"It blew my mind. 4-D. Wow." From January to March, come to our tuition-free 10-week on-campus program. This year, we will explore the relationships between ... knots and the geometry of special relativity, game theory and dynamical systems, and yarn and the geometry of art. "Math Circle was a fun and interesting experience for me. ... Whether I was working alone or in a group, the process of discovery was rewarding." Our students gain exposure to the process of conjecture and proof, learn to think critically about ideas presented, and develop skills for articulating mathematical concepts. Contact information Email: mathcircle@math.ucdavis.edu Phone: Monday-Friday (business office): (530) 752-0827

Now accepting applications! Go to our website's online application form The application takes 5 minutes. Applicants are accepted on a first-come first-serve basis. 2008 Classes: Knot Theory taught by Marion Moore Math Through Games taught by Yvonne Lai Perspectives in Geometry taught by Tom Denton

Visit our website for: class descriptions, instructor bios, and our math problem list.

Don't forget to check out our featured problem on the back.

Featured problem:

Drawing random points in the Sierpinski Gasket

Draw a triangle.

Pick a vertex (pink circle).

(a) Draw a point there.
(b) Pick another vertex (pink circle).
(c) Find the point half way between that vertex and the point you just drew.
(d) Draw a point there. Proceed to step (b).

You will only ever draw points in the Sierpinski Gasket. Why?

(A solution will be posted to our website in January 2008)

The Sierpinski Gasket

Step (1)

The Sierpinski Gasket is the set of points that are leftover after the following process.

(1) Start with a solid equilateral triangle.
(2) Take the triangle whose vertices are the midpoints of the boundary edges, and remove its interior.
(3) Repeat step (2) with all of the remaining triangles.

After step (2)

After step (3)

Repeating steps (2) and (3).

If you have any thoughts or questions about this, we encourage you to contact us.
... and if you found this problem interesting, you should join our Saturday workshops!