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The Principle of Linearity: A Short Cut to Determine Dependent Angles

Brian R. Stonebridge, The Principle of Linearity: A Short Cut to Determine Dependent Angles . CSTR-96-005, Department of Computer Science, University of Bristol. May 1996. PDF, 116 Kbytes.

Abstract

We propound the principle that ``if there is a relationship between angles of a planar figure, composed of straight lines set at angles (which may be constructed to be rational multiples of each other) then the relationship will be linear''. We contend that this principle holds a similar status to a law of Physics, in that it is accepted because has been found to supply consistent answers and no counterexample, which cannot be accommodated, has yet been found. Some simple examples are given of the use of the principle as a proof mechanism. We then use it to prove more complex theorems of Desargues, Johnson (1995) and finally Morley (1904). Morley's Trisector Theorem is a very simple and elegant result. However, almost all published proofs lack the motivation provided by a natural forward development towards a clear goal, and the length and complexity of others suggests that some new viewpoint is desirable. The method presented dramatically reduces the length of the proof compared with previous methods. [An extended version has been submitted to "The Mathematical Gazette", March 1996.]

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