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March 20, 2006
Yet more discussion of coordinate systems, with the goal of showing that in any affine coordinate system every straight line is the set of solutions to a linear equation and the set of solutions to any linear equation is a straight line. We call a coordiante system affine if it is EITHER a standard coordinate system with perpendicular axes and the same unit of distance on each OR what we have called a skew coordinate system. By "linear equation" we mean an equation in the variables x and y that can be put in the form Ax + By + C = 0, where A, B, and C are constants and either A or B (or both) are nonzero.
This class also included a discussion (45 minutes) on functions. Key concepts included:
Second handout on coordinates.