Browse Classroom Capsules and Notes

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A Differentiation Test for Absolute Convergence

The author presents an easy absolute convergence test for series based solely on differentiation, with examples.

A Certain Type of Number Expressible as the Sum of Two Squares

Integers equaling the sum of the squares of their contiguous parts (a generalization of two-digit numbers which are the sum of the squares of their digits) are discussed, with several examples...

What Goes Up Must Come Down; Will Air Resistance Make It Return Sooner, or Later?

The author investigates the time needed for an object to travel when being thrown vertically in the air when the air resistance is taken into consideration.

A Method of Duplicating the Cube

The authors use analytic geometry to construct two curves and the bonus product is the duplication of a cube.

Permutable Primes

The article discusses prime numbers which remain prime after the permutation of the digits.

How to Win (or Cheat) in the Solitaire Game of "Clock"

A criterion is given to determine in advance whether a game of "clock" will result in a win.

Proofs without Words: Count the Dots

This article contains a geometric demonstration of an identity for integers.

On a Family of Polygons

The author uses vectors to prove a charactering property for polygons.

A Number-Theoretic Sum

The author presents a new Identity for integer functions and their inversion formulas.