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Browse Classroom Capsules and Notes

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

Many naive ways used by students in their mathematical proofs

A common mistake in graphing a positive trigonometry function.
Minimize the length of wire to hang a bird feeder without calculus

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...

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...

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

Recursive computation of derivatives for a family of functions

Find arbitrarily large patches of invisible lattice points.

A solution to a difficult trigonometric integral