Algebraic theorems obtained by use of extended analytic geometry



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Texas Tech University


Te understand the theorems presented here one must first understand the basic principles which have been developed by Dr. Ralph Underwood. The basic process is a method by which equations with three or more variables may be represented on the XY plane. While the process does not represent a true projection many of the basic features of the loci, in the case of three variables, are preserved. The two basic methods which have been used previously are called System A and System B, (9:527) however, an infinity of methods or plotting rules are available. In the first ten theorems presented here a more flexible method is employed. In graphing the locus of the equation a point on the locus is first found, and the equation of a tangent hyperplane is written by the method illustrated below« one then may use a graphing rule so that the locus of the tangent hyperplane is a straight line on the XY plane.



Analytic, Geometry, Algebra