Browse Classroom Capsules and Notes

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Angling for Pythagorean Triples

Use the double angle formula for the tangent to construct Pythagorean triples.

Proofs by _Tion

Many naive ways used by students in their mathematical proofs

Sin^2: A Sheep in Wolf's Clothing

A common mistake in graphing a positive trigonometry function.

Hanging a Bird Feeder: Food for Thought

Minimize the length of wire to hang a bird feeder without calculus

Determinants of Sums

An interesting formula for the determinant of the sum of any two matrices of the same size is presented. The formula can be used to obtain important results about the characteristic polynomial...

On Uniformly Filled Determinants

Given a square matrix \(U\) and column vectors \( \alpha\) and \( \beta\), the author shows that \( \det(U + \alpha \beta^T) = \det U + \beta^T\) Cof\( (U) \alpha \). This...

Ways of Looking at \(n!\)

Use probability to find the volume of the standard \(n\)-dimensional simplex.

A Recursively Computed Limit

Recursive computation of derivatives for a family of functions

Strings of Strongly Composite Integers and Invisible Lattice Points

Find arbitrarily large patches of invisible lattice points.

Moments on a Rose Petal

A solution to a difficult trigonometric integral