A circle has a center c and a radius r. The points on the circle are all a distance of exactly r units from c. What if we start with two fixed center points? The set of points on an ellipse have a fixed sum-distance to two center points c1 and c2 (called foci). An ellipse has kind of an oval shape. Ellipses occur in nature – the Earth’s orbit is not a perfect circle but rather an ellipse, with the Sun being just one of the two foci.
In this activity we investigated how to draw ellipses using pushpins and string. We also asked whether it is possible to have more than two fixed center points. Continue reading Ovals upon ovals!
Suppose you are sending a crew of scientists to the moons of Mars: Phobos and Deimos. The scientists are botanists, geologists, and mathematicians, or any combination of the three. You want to divide the crew into to halves so that each moon gets an equal number of each scientists. When can this be done? Continue reading Mars moon mission
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.
The card game SET is well-known amongst game players. Each card has four characteristics, and each characteristic has three outcomes. Twelve cards are placed face up, and players try to find a set of three cards with each characteristic all the same or all different. It turns out there is a lot of math going on! For example, are twelve cards enough to guarantee you will be able to find a set? If not how many do you need? Continue reading The game SET
What kinds of games can be played using just stones? It turns out quite a few! In this session we investigated three games in particular. Continue reading Cave person games
Suppose you have a room, and you need to guard it using ceiling mounted cameras. Assume the cameras can see in 360 degrees. If the room is very simple, such as a square shape, you can get away with just one. But if the room is more complicated, say with nooks and crannies, you may need many cameras. How can you find how many? Continue reading Taking in the whole room
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