Ellipson

This flash shows a slide of an ellipson along it z-dimension. Each slide is an ellipse which lies entirely inside the unit square. The equation for the ellipson as follows:

$$(x + y + z)^2 = 2 (x^2 + y^2 + z^2) + 4xyz$$ (1)

As special case, when $z = 0$, the ellipse reduces to the line $x = y$. Similarly, when $z = 1$, the ellipse reduces to the line $x + y = 1$.

The flash has two text boxes which show the value of $z$ and the step (for which $z$ increases). The default value for ``step'' is $0.02$ and the value of $z$ will range between $0$ and $1$. When the value of $z$ reach $1$, it will come back to $0$.

There are three buttons for control the flash.

• Dec Step: Decrease the value of step by $0.01$. You cannot decrease the value of ``step'' below $0.01$.

• Inc Step: Increase the value of step by $0.01$. You cannot incrase the value of ``step'' above $0.49$.

• Pause/Resume: In order to pause/resume the flash animation.

The printed version of this document can be found here.