02.16.08
February 16 roundup of Math 21a
We’re now firmly grounded in three-dimensional space. We talked this week about the various linear objects in 3D: lines, points, planes, and finding equations for them. Also, we showed how to define and calculate the distance between points and lines, lines and planes, etc.
Then we moved into the functional unit of the course. A function of two variables has as its graph a surface in three-dimensional space. Graphing these is a challenge of the brain but of the hands. But there are some tips, such as the method of traces.
Finally, we have other ways to measure space besides our boring old rectangular cartesian coordinates. We defined polar coordinates in the plane, and cylindrical and spherical coordinates in space, to better express certain surfaces. For instance, the cone in three-space can be described as 
in cartesian coordinates, but in cylindrical all you need to say is z=r.
Tags: math, math21a, geometry, surface, coordinates