Fig. 106. §6 Math
Circle and Waves
The unit circle is a circle with a radius of 1.
1Facts
- Shelf
- Math
- Kind
- Built from a recipe
- Your own
- Your own path
- Sound
- Yes
- Hands-on
- Yes
- Licenses
- Own work (made in the page)
2How to play
Tap to send the point round. Hands-on: drag the point round; the waves follow.
3Its controls
Table I. Every control on this Splash.
| Control | Kind | Range | Start |
|---|---|---|---|
| Go round | Tap | ||
| Turn | Button | ||
| View | List | 2 choices | 2D diagram |
| Path | List | 6 choices | Circle |
| Turns | Setting |
4About it
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.
5Details
- Splats
- Opens at 200,000 at Mid Detail, 60,000 at Low, and up to 590,000 at Max
- Your own files
- .txt
6Sources and credits
Made in Splashery. Its code is MIT.
