Browse Classroom Capsules and Notes

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Fibonacci Powers and a Fascinating Triangle

A modified Fibonacci triangle is created by squaring Fibonacci numbers. Interesting numbers such as Lucas numbers appear.

Bounding the Roots of Polynomials

Some bounds on the roots of the polynomial functions are discussed.

Neither a Worst Convergent Series nor a Best Divergent Series Exists

A short geometric discussion of the convergent and divergent series is given.

A Note on Taylor's Series for \(\sin(ax+b)\) and \(\cos(ax+b)\)

Taylor series for sine and cosine functions and their derivatives are discussed.

Bargaining Theory, or Zeno's Used Cars

This capsule gives an elementary solution to the problem of negotiatiating the right price for the buyer and seller.

A Recurrence Relation in the Spinout Puzzle

Solving a puzzle which deals with \(n\) interlocking gates

Critical Points of Polynomial Families

Using graphing calculators or computers to discuss critical points of polynomials

The Rental Car Problem

How to minimize the cost of filling up a rental car

Complex Eigenvalues and Rotations: Are Your Students Going in Circles?

The author shows that every \(2 \times 2\) real matrix with nonreal eigenvalues represents the composition of the following three operations: (1) a vertical “lift” to a plane...

Countability via Bases Other Than 10

The author uses base 12 and base 14 to show that certain sets are countable.