Tag Archives: multiplication

The geometry of numbers in Euclid

This is about how the Elements of Euclid shed light, even on the most basic mathematical activity, which is counting. I have tried to assume no more in the reader than elementary-school knowledge of how whole numbers are added and multiplied.

How come 7 ⋅ 13 = 13 ⋅ 7? We can understand the product 7 ⋅ 13 as the number of objects that can be arranged into seven rows of thirteen each.

Seven times thirteen

Seven times thirteen

If we turn the rows into columns, then we end up with thirteen rows of seven each; now the number of objects is 13 ⋅ 7. Continue reading