The Boise Math Circle is excited to announce we’ll be continuing our program throughout the 2016–17 school year! The BMC is open to middle and high school students with some experience in algebra. If you like solving problems and want to learn more about the creative side of math, please consider applying. If you have a friend that does, invite them to apply too!
We will begin on Saturday morning, September 10, and meet approximately every two weeks. See our schedule of meeting dates.
Please help us recruit participants by letting your students know about the program. If you’d like attendance reports for your students (e.g., for extra credit), please send us an email. You’re of course welcome to join the sessions.
It is easy to add points in the plane “coordinatewise”, that is, by writing (x,y)+(z,w)=(x+z,y+w). This even has a very nice geometric interpretation: completing the parallelogram with first three corners (0,0), (x,y), and (z,w). But it isn’t easy to multiply points because the simple rule (x,y)*(z,w)=(xz,yw) doesn’t allow division. In this activity we looked for something better. Continue reading Multiplying points in the plane
A graph is a collection of dots (called vertices) joined by curve segments (called edges). It doesn’t matter how you name the vertices and it doesn’t matter where you put them in your drawing. Two graphs are called isomorphic if you can rearrange the way one of them is drawn to make it look like the other. So for example you might convince yourself that a pentagon and pentagram are isomorphic to each other.
Continue reading Graph isomorphism
Today our guests Liljana Babinkostova and Marion Scheepers (both BSU math professors) led a discussion of sudoku and counting. Continue reading Sudoku and latin squares
Today we didn’t have a lesson, but instead toured the campus science fair! Check out the pictures after the jump. Continue reading STEM exploration day
This may sound like a fancy title, but it just means figures with flat sides and a hole in the middle! Continue reading Toroidal polyhedra
Imagine three friends play a game. Mia beats Alex, Alex beats Siki, and Siki beats Mia. Which one of the three, if any, should we consider to be overall winner? In this session, we consider the idea of a tournament, which is a series of one-on-one win-or-lose games in which every player plays everyone else one time. Continue reading Tournament Winners
We all know that many fractions can be simplified, for example, 6/20 may be better written as 3/10. So how many fractions (less than 1) really use a denominator of 20? The answer turns out to be exactly eight… 1/20, 3/20, 7/20, 9/20, 11/20, 13/20, 17/20, and 19/20. But is there a rhyme or reason to this answer? Continue reading Counting simplified fractions
It is hard to believe that this was only our first discussion using Geogebra, the all-powerful program for visualizing geometry problems. In fact we used just a tiny fraction of the tool’s capabilities to explore four-sided figures, or quadrilaterals. Continue reading Quadrilaterals
For our Halloween session, presenter Gary Thomas shared some wonderful skills and the abstract concepts that support day-to-day arithmetic. Continue reading Spook-tacular Mental Math