# Browse Classroom Capsules and Notes

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Displaying 1111 - 1120 of 1209

Two proofs, one elementary, of the limit in the title are presented.

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

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

The paper presents an elementary solution to the Brachistochrone problem.

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.

Mengolis 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 gamblers ruin game is investigated.
The author discusses the effect of moving the roots of a polynomial in a Java applet.