articles
Long-form explorations of mathematical ideas that go beyond the curriculum. Some articles are free to read; others require a subscription.
derangements (part 1)
Exploring permutations where nothing stays in its original place.
derangements (part 2)
Continuing the exploration of derangements and their properties.
amazing arctans
Beautiful relationships between arctangent values.
Cassini
A journey through these fascinating curves and their properties.
functional equations (part 1)
An introduction to solving equations involving functions.
functional equations (part 2)
Continuing the exploration of functional equations.
the Josephus problem
A classic problem with surprising mathematical structure.
cardioids (part 1)
The beautiful mathematics behind spirograph patterns.
cardioids (part 2)
Further exploration of cardioids and related curves.
integration with tea (part 1)
A powerful technique for trigonometric integration.
integration with tea (part 2)
Further applications of the t-substitution technique.
a spring in a circle
A mechanics investigation exploring a bead on a circular wire with an attached spring.
differentiation without limits
Finding gradients and tangents using polynomial factorization.