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

## 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.

Continue reading “A simple formula for Sequences and Series”

## 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.

Continue reading “A Formula for the Perimeter of an Ellipse”

## Multiple Pendulums

This fun post illustrates the phenomenon of multiple uncoupled pendulums whose periods are all rational multiples of each other.