Category Archives: BMC Session

Adding together infinitely many numbers

It is often necessary to add more than two numbers together. For example, you might have made 137 deposits to your bank account this year, and wonder how much you contributed in total. But is it possible to add infinitely many numbers together? The answer is that sometimes it is possible, and sometimes it isn’t! In this discussion we investigated when, why, and how! Continue reading Adding together infinitely many numbers

Ovals upon ovals!

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!

The game SET

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

Multiplying points in the plane

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

Graph isomorphism

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.

Untitled Continue reading Graph isomorphism