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Three new proofs of the fact that the point \(A\) on the circular arc \(BC\) for which \(AB + AC\) is maximum is the midpoint of the arc are presented.
This note uses the Gauss sums to evaluate certain sums of trigonometric functions. It includes a short history of Gauss sums.
The result in the title is demonstrated graphically.
By exploiting the geometry of the cobweb plot, the author provides a simple and elementary derivation of the parameter for the period-three cycle of the logistic map.
The author gives a mapping of the ordered pairs of positive integers onto the positive integers which is immediately recognizable as a bijection.