### Student's circle (BMC)

The Boise Math Students' Circle is for Treasure Valley young people with some experience with algebra who want to experience creative mathematics.

### Teacher's circle (BMTC)

The Boise Math Teachers' Circle is a community for Treasure Valley K–12 math educators.

## Recent sessions

Fractals
We looked at fractals, and even made our own! This session was led by Teri Willard and Mandy McDaniel. We cut and folded pieces of paper to illustrate the first four “phases” in the iteration for a fractal. We used our models to investigate a number of patterns, such as counting the number of rectangular faces and determining their measurements at each step, to finding the total area or volume of the fractal. That involved geometric series. We discussed how this activity could go into a classroom and the many things that a student might get from it. This was a “low floor, high ceiling” activity—anyone can have fun making the paper models, and the mathematical investigation can go as far as you want it to go.
Rationals and Irrationals
We looked at irrational and rational numbers. We figured out which real numbers have terminating, repeating, or eventually repeating decimal expansions. And we found some patterns in the periods of repeating decimal expansions: for a prime number $p$, the decimal expansion of $1/p$ always has a period which is a factor of $p-1$. We saw how to prove that some numbers are irrational, including $\sqrt{2}$ and $\log_2(3)$ (the logarithm of $3$ in base $2$).
Introduction to trees
Continuing with our introduction to combinatorics, this time we explored the structure side of things and introduced graph theory.
Introduction to graph theory
Continuing with our introduction to combinatorics, this time we explored the structure side of things and introduced graph theory.
Voting Systems
We looked at different voting and election systems, including first-past-the-post, two-round runoff, instant runoff, Borda count, and the Condorcet criterion. We voted for the best candy (the winner was chocolate peanut butter cups, but it was close!). We watched a PBS Infinite Series video about voting, and worked through some puzzles and problems. The video is here:
Introduction to combinatorics
In the first meeting of Fall 2018, we introduced the theme for the semester: Combinatorics. This is a fancy word in mathematics that encompasses counting problems, enumerations, as well as structure and design problems.