Excursions in Computing Science: Book 11c. Geometry and Gravity Part I. Fields, Complementary Coordinates, Curved Space

I. Prefatory Notes 1. Fields and slopes. A function of two variables is called a “field” by the physicists, maybe because it might be describing a topography in which the height of the surface above, say sea level, is a function of two coordinates, say the longitude and latitude. To be precise, physics would call this a scalar field (because the height is a single number at each point) in two dimensions (because of the two coordinates). We will soon encounter more ambitious types of field. An example is f(x, y) = xy Here is what the surface xy looks like, plus a few of its values.