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.
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 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.
Sequence of Sequences
This session was led by Jerod Morehouse of Timberline High School. We looked at a sequence of sequences: the magic square numbers, the lazy caterer’s sequence, and more.
Division with Remainders
In this session we looked at division problems with remainders. First, Zoe’s three children—Alice, Bob, and Charlotte—tried to divide some cookies evenly, but there were two cookies left over. Thinking quickly, Zoe realized that she and the children could share the cookies so that everyone got the same number. We figured out that there could have been 8 cookies. Other possible numbers were 20, 32, 44…