Circle and Waves

Splashery stretches a drumhead over this Splash's outline, twelve inches across, and finds the ways it can ring. Its lowest is 413.7 Hz, 93 cents sharp of G4, the nearest tine on the comb. The next fifteen are its overtones, and each one draws its own figure: sand gathers on the lines that stay still.

Tap to send the point round. Hands-on: drag the point round; the waves follow.

The unit circle is a circle with a radius of 1. As a point goes around it, turning through an angle called θ, its height is the sine of θ and its left-right place is the cosine. Traced out over time, they make two waves, the same shapes as sound and light waves.

Tap it and the point goes once around while its height draws the sine wave and its left-right place draws the cosine wave. For the circle, Euler's formula, e^(iθ) = cos θ + i sin θ, lights up piece by piece. In the Splash tab, try a 3D helix, another path, up to three turns, or type your own: x = …, y = … with t, or r = … with θ.

Made in Splashery. Its code is MIT.

This link opens it in the Playground. To put it on your own page, add the element and one script tag. Every option.