## A simple formula for Sequences and Series

If you are given the initial terms of a sequence, then here is an insanely simple method to derive a general formula for the first N terms, as well as the sum of the first N terms of the sequence. ## Trigonometry in Pictures

This post shows how the core trigonometric definitions, relations and addition theorems can be simply and intuitively visualized.

## Lissajous Curves

This post illustrates and explains the beautiful Lissajous Curves – trajectories of points whose coordinates follow sinusoidal movements.  A simple but timeless classic curve that has numerous applications as well as artistic elegance. ## A Formula for the Perimeter of an Ellipse

Unlike for circles, there isn’t a simple exact closed formula for the perimeter of an ellipse. We compare several well-known approximations, and conclude that a formula discovered by Ramanujan is our favourite, due to its simplicity and extreme accuracy. ## Multiple Pendulums

This fun post illustrates the phenomenon of multiple uncoupled pendulums whose periods are all rational multiples of each other. Figure 1. Multiple uncoupled pendulums. All periods are rationally related. This entire motion has a period of precisely 60 seconds.