Multiplication with a slide rule

Anyone can see how to add using a pair of rulers. Say we want to add 3+5. If you slide the “0” of one ruler underneath the “3” of the second ruler, then the “5” of the first ruler appears underneath the “8” of the second ruler. But can we multiply this way?

In this special session of the BMC, Dr. Brandy led us to discover a way to do it. First we explained the ruler addition by looking at an addition table. If you look at the table, you see that the SW-NE diagonal lines have just one constant number in them. You could say that the level sets of the addition function are diagonal lines. We observed that this fact was somehow letting us use the two rulers to add.


But then we looked at the multiplication table, we found that the level sets are actually curves and not lines.


Therefore, we asked the question: can you redraw the multiplication table in a way that stretches the level sets to be lines? Try it!