Browse Classroom Capsules and Notes

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A Note on the Gaussian Integral

An alternative way to evaluate the famous improper integral of Gauss, \(\int_{0}^{\infty} e^{-x^2} dx\)

Lemniscates and Osculatory Interpolation

The authors use the polynomial interpolation to discuss the circle of convergence.

Note on the Evaluation of \(I = \int_{0}^{x} \frac{1}{1+t^{2^n}} dt\)

The authors develop a general formula for integrals of \(1/(1 + t^m)\), where \(m\) is an integral power of \(2\).

How Expected Is the Unexpected Hanging?

The article discusses the paradox described in the title and two other similar paradoxes.

Smith Numbers

A Smith number is a composite number the sum of whose digits is the sum of all the digits of all its prime factors. The author reviews the history of these numbers, starting with the proof that...

An Introduction to Combinatorial Existence Theorems

The author discusses the connection between the pigeonhole principle and several theorems in combinatorics.

Dörrie Tiles and Related Miniatures

"Proofs without words" of areas of polygons described by Dörrie several other related constructions

On Linear Difference Equations with Constant Coefficients

The author gives a particular approach to the special solution for a nonhomogeneous difference equation.

A Note on the History of the Cantor Set and Cantor Function

Notes on the origin and ideas of Cantor Sets and Cantor Functions

Proof without Words: Pythagorean Triples via Double Angle Formulas

Geometric construction of Pythagorean Triples through the Double Angle Formula