Here are some brief descriptions of the Math Circles we have successfully held over the past two years. We hope they help to illuminate what this amazing program is all about.

#### Open Questions

Designed for ages 11-14, this Math Circle ran from 4/21 through 5/26, 2016

At an age when some kids feel disenfranchised from mathematics while others feel empowered by it, we will collaboratively attempt to solve currently unsolved (“open”) questions. The students will be essentially working mathematicians, with the stated hope of making some progress toward a solution and the unstated hope of experiencing joy in mathematics.

#### Parity, 3/3-4/14 (6 weeks, no class 3/24)

Designed for ages 7-8, this Math Circle ran from 3/3 through 4/14, 2016

The basic definition of parity is this: a property of a number that describes whether it is even or odd. Sounds simple and obvious, right? But parity has implications that are bigger in mathematics and science: alternating groups, or a way of putting things into 2 distinct groups. We will play games that depend upon this concept as a strategy in hopes of ending the course with a true conceptual understanding (vs. rote memorization) of parity. I suspect that the students will lead this discussion into how parity is related to infinity (is it even or odd, is it even a number?), as most Talking Stick math circles with this age group have done.

#### Cantor, 1/5-2/9 (6 weeks)

Designed for ages 14-18, this Math Circle ran from 1/5 through 2/9, 2016.

We’ll examine the life and work of this revolutionary mathematician once called a “corrupter of youth.” Come and have your teens corrupted with Georg Cantor’s ideas: set theory (a concept that seems fundamental and even obvious today); his most famous proof; and more. Cantor’s life story is sad because of his struggle with mental illness. In discussing his personal story, we’ll question (1) the stereotype that the most successful mathematicians are somehow unbalanced, and (2) the apocryphal “math gene.”

#### Compass Art, 9/17-10/22 (6 weeks)

Designed for ages 9-11, this Math Circle ran from 9/17 through 10/22, 2015

What do Michelangelo, Bernini, Zarah Hussein, feng shui practitioners, mapmakers, architects, astronomers, and mathematicians have in common? They all use compasses to construct and deconstruct circles. We’ll create our own compass art while learning about basic circle geometry and some math history. (Each student should bring a compass, sketch pad, and pencils.)

#### River Crossing Problems

Designed for ages 9-11, this Math Circle ran for 5 weeks from 4/28-5/26, 2015.

This Math Circle focused on the concept that classical composers incorporated variations on themes in their compositions just as mathematicians create them in their work. Isopmorphic problems appear dissimilar on the surface, but have the same underlying structure. We’ll tried out some traditional river-crossing problems, and and attempted to solve them. Then we tried some problems that were not about crossing a river, and compared and contrasted them. Finally we tried to create our own isomorphs.

#### Chromatic Number of the Plane

Designed for ages 7-8, this Math Circle ran for 6 weeks from 3/3-4/7, 2015.

Students will explore graph-coloring questions and tilings to lead up to an exploration of an open (unanswered) question in mathematics: the Chromatic Number of the Plane (aka The Hadwiger-Nelson Problem). But my real agenda here, as it is in just about every math circle, is to move children toward abstraction. We’ll start out by using manipulatives and then hopefully wean from those to explore the difference between objects and symbols and, more generally, the difference between things (the concrete) and ideas (the abstract).

#### Escher and Tesselations

Designed for ages 11 and up, this Math Circle ran for 6 weeks from 1/6-2/10, 2015.

In this math-meets-art circle, students will experiment with the four types of symmetry in a plane to create their own tessellations (tilings). We’ll look at the work of MC Escher and that of the mathematician whose work inspired Escher, George Polya. We’ll draw and draw and draw. We’ll also attempt to determine which regular polygons can tessellate a plane, and then verify our answer with proof.

#### Infinity

Designed for ages 5-6, this Math Circle rang for 5 weeks from 11/11-12/9, 2014.

We’ll explore the idea of infinity using drama (puppets!) and embodied mathematics. The kids will use their imaginations and physical movements to play with patterns that have limits and patterns that don’t. And we’ll work on verbalizing our mathematical ideas as we try to figure out what patterns exactly are.

#### Martin Gardner

Designed for ages 9-11, this Math Circle ran for 6 weeks from 9/23-10/28, 2014.

Before there was Vi Hart, there was Martin Gardner. Celebrate the Martin Gardner Centennial with an exploration of Recreational Mathematics. For 25 years, Gardner wrote the Mathematical Games column in Scientific American, and became legendary for his unconventional approach to mathematics. In this circle, we will explore his life, his influence, and of course, his mathematical puzzles. The goal of this math circle is the same as the goal for all of them: to develop mathematical thinking. Recreational mathematics is yet another avenue for seeking patterns when none are obvious, and for seeking ways to crush seemingly obvious patterns that aren’t really patterns at all.