Now suppose I need to multiply length times width to get the area (A = L x W). Simple - right? But that is multiplication for scalar variables. How do you multiply vectors? There are two common ...

In 1843, William Rowan Hamilton had a four-dimensional flash of insight that still shapes our three-dimensional world. When you purchase through links on our site, we may earn an affiliate commission.

Imagine winding the hour hand of a clock back from 3 o’clock to noon. Mathematicians have long known how to describe this rotation as a simple multiplication: A number representing the initial ...