Some applets

Well, currently only one applet...

Embedding a 2D metric in 3D Euclidean space

The following applet tries to embed a 2D metric in a 3D Euclidean space. More specifically, the 2D metric is of the following type:

dS2 = dθ2+f(θ)22 .

The applet lets you embed such a surface in a three-dimensional Euclidean space for different kinds of f(θ) definitions. Note that in the applet, the variable x is used instead of θ and that mathematical functions use the Java syntax: for example, use Math.sin(x) instead of sin(x).

Some interesting expressions to try are:

  • Math.sin(x)*(1-0.75*Math.sin(x)*Math.sin(x)): this will draw a peanut-shaped surface (this is the default setting)
  • Math.sin(x): this draws a sphere
  • Math.sin(x)*(1+0.1*Math.sin(x)*Math.sin(x))
  • 0.8*Math.sin(x)-0.1*Math.sin(x*2)

Spring pendulum