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Browse Classroom Capsules and Notes

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The Pythagorean theorem is proved geometrically in yet another way. This article originally appeared as "Proof without Words: \(a^2 + b^2 = c^2\)."

A general version of the gambler's ruin problem is solved by elementary means.

The authors show that for every continuous function with irrational period, the set of images of integers is dense in the range.

The author applies basic group theory ideas to a variety of card tricks.

The authors show that a function between vector spaces that maps lines to lines is either a collineation or has one-dimensional range.

The paper presents a guided collection of problems investigating when groups are isomorphic to proper subgroups.

The author explores integration of radially symmetric functions of several variables.

This is a discusion of the importance of the existence of limits in L'Hôpital's Rule.

An analytic proof of the fact that for any triangle \(ABC\), \(G=\frac{1}{3}(A+B+C)\) is the centroid of the triangle.

A simple characterization of the condition that, for an integer-sided triangle, one angle is twice another.