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Browse Classroom Capsules and Notes

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Displaying 1041 - 1050 of 1135

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.

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

Mengoli`s Series is presented visually .

A wide-ranging discussion of the question in the title of the paper is presented.
The probability of losing in exactly \(n\) steps of the gambler`s ruin game is investigated.
The author discusses the effect of moving the roots of a polynomial in a Java applet.
The authors exhibit two differentiable functions for which the integration by parts formula does not apply.
The author analyzes the motion of a hollow ball with a viscous fluid center as it slowly rolls down a slightly inclined plane.

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.