### 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

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.
Regular tessellations
Regular tessellation means covering the plane with copies of a single regular polygon in such a way that the polygons meet edge to edge, with no overlap and no gaps. This can be done with triangles, squares, and hexagons. The shapes have N = 3, 4, and 6 sides, and the tessellations have C = 6, 4, and 3 shapes per corner, respectively. In all three cases, we can see that (N-2)(C-2)=4.