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M4005 Geometry

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.