*A visual demonstration of an inequality involving the tangent function and sums is presented.*

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*A visual demonstration of an inequality involving the tangent function and sums is presented.*

*Mengoli`s Series is presented visually .*

*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.*