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Browse Classroom Capsules and Notes

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Displaying 91 - 100 of 1211

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

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.

The paper presents an elementary solution to the Brachistochrone problem.

A visual proof for the sum of octagonal numbers is presented.

The authors investigate the occurrence of composite values of non-constant polynomials with integer coefficients evaluated at integer points.

The author gives a mapping of the ordered pairs of positive integers onto the positive integers which is immediately recognizable as a bijection.

The author uses Newton`s impact method to compute the centripetal force exerted on a particle moving uniformly on a circumference of a noneuclidean circle.

A discrete analog of integration by parts

This article uses four different methods to evaluate a type of Poisson integral: Riemann sums, functional equation, parametric differentiation, and infinite series.

An inductive proof is presented for the bounds of the remainder of Taylor expansion. This result, with Darboux's theorem, implies the classical formula for the remainder.