# Math Insight

### Applet: Sphere with inward normal vector

#### Applet loading

The sphere of a fixed radius $R$ is parametrized by $\dlsp(\theta,\phi) = (R\sin \phi \cos\theta, R\sin\phi \sin\theta, R\cos\phi)$ for $0 \le \theta \le 2\pi$ and $0 \le \phi \le \pi$. In this case, we have chosen the inward pointing normal vector $\vc{n} = (-\sin \phi \cos\theta, -\sin\phi \sin\theta, -\cos\phi),$ orienting the surface so the inside is the positive side. You can change the values of $\theta$ and $\phi$ by moving the base of the normal vector or by dragging the points on the sliders.

#### Applet links

This applet is found in the pages

List of all applets

#### Notation systems

More information on notation systems

#### General information about three.js applets

The applet was made using three.js and requires Javascript as well as a browser that supports WebGL. For most three.js applets, you can drag with the mouse to rotate the view, drag with the right button to pan, and zoom in/out with the mouse wheel. Many applets contain points that you can drag to change values of variables.