In last last week's episode of PBS Infinite Series, we talked about different flavors of multiplication (like associativity and commutativity) to think about when multiplying things that aren't numbers. My examples of multiplying non-numbers were vectors and matrices, which come from the land of algebra. Today I'd like to highlight another example:
It's true! To illustrate, here's the multiplication table for a point, a line, a circle, and a square.
I'm really stretching my art skills today, but the idea is hopefully clear: A 'circle $\times$ line segment' is a vertical cylinder: its horizontal cross sections are circles and its vertical cross sections are lines.
But what about associativity? Let's compare '(point $\times$ line segment) $\times$ circle' with 'point $\times$ (line segment $\times$ circle).' According to the multiplication table:
What shape, exactly?
You'll have to wait and see!
Thanks, John, for suggesting the idea for today's post!