Ellipse Game

The Foci: What are They?

Suppose you have a loop of string (shown in blue in the animation) looped around two posts (shown as blue dots) and a third point (shown as a black dot) which is free to move provided the string stays taut. Then the moving point will trace out an ellipse or oval (shown in red).

You can easily try it out for yourself. Place a loop of string around two pins stuck through a piece of paper into a drawing board. Use a pencil to keep the loop taut. If you move the pencil carefully, it should trace out an ellipse. The pins correspond to the blue points and the pencil corresponds to the black point in the animation.

Every ellipse has such a pair of points. They are called the foci of the ellipse (The singular is "focus"). The foci are unique. There are always precisely two of them. A taut loop of string of appropriate length stretched about the foci as shown in the animation will draw the ellipse.

The Game

Your mission, should you choose to accept it, is to find a focus. You will be given an ellipse of random dimensions and you will have to try to click on one of the foci. Should you fail in this mission at first, you will be given some clues.

Should you be discovered by your employer or teacher wasting time on this mission, we will disavow all knowledge of you. We will also deny any responsibility for holes or other damage caused should you decide stick pins into into a drawing board or any other item of household equipment.

This game was developed by John Banks at the suggestion of Andrej Panjkov.

This page has been hit (mostly by the author) times since it was published on 14 August 1996.

Last updated 21 August 1996.