Browse Classroom Capsules and Notes

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A Cross-Number Puzzle

This is a cross-word puzzle with natural number entries rather than words.

Proof Without Words: The Cauchy-Schwarz Inequality

Simple geometric proof of the Cauchy-Schwartz Inequality

A Differential Equation in Group Theory

The authors use a technique from differential equations to find topological isomorphisms.

Triangle Constructions with Three Located Points

The authors show how to use some of the data from a triangle to reconstruct the original triangle. See also the 1996 paper...

A Papal Conclave: Testing the Plausibility of a Historical Account

The author applies basic probability theory to the papal election of 1458.

An Application of Desargues' Theorem

The author interprets a result in projective geometry to obtain one in euclidean geometry.

Tiling Rectangles with Rectangles

The authors investigate and discuss the complexities of tilings called `simple tilings`.

An Advanced Calculus Approach to Finding the Fermat Point

The author uses the concept of maximum and minimum values to find Fermat points for a triangle. (The Fermat point of a triangle is the point such that the distances from the vertices have a...

The Hiding Path

Interesting example of fox-chasing-rabbit differential equation questions.

How Few Transpositions Suffice?... You Already Know!

The problem is to find the minimal number of transpositions, whose product equals a given permutation.