*The author shows that the ratio of the area under a catenary curve to the arc length is independent of the interval over which they are measured.*

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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.*