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.

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