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## Interlude 1: Spaces, Trigonometry, and Vectors

“Where are we, George?”

George pulled out his map and spread it out in front of Lenny. “We’re right here Lenny, coordinates 36.60709N, –121.618652W.”

“Huh? What’s a coordinate George?”

### Coordinates

To describe points quantitatively, we need to have a coordinate system. Constructing a coordinate system begins with choosing a point of space to be the origin. Sometimes the origin is chosen to make the equations especially simple. For example, the theory of the solar system would look more complicated if we put the origin anywhere but at the Sun. Strictly speaking, the location of the origin is arbitrary—put it anywhere—but once it is chosen, stick with the choice.

The next step is to choose three perpendicular ...

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