Parabolic mirrors — While it can be considered common knowledge that mirrors bundling incoming parallel rays into a unique focal point need to be parabolic in shape, it is less commonly known how to arrive at such a result. In this article we start with the desired condition on such a mirror and derive an equation for a function f : ℝ → ℝ describing the shape of it.

Nicomachus' equation — We prove the identity 1³ + 2³ + … +  n³ = (1+2+…+n)², which is attributed to the antique philosopher and mathematician Nicomachus of Gerasa (c. 60 – c . 120 BCE).