Return to my Cinderella pages
Return to my Mathematics pages
Go to my home page
© Copyright 2003, Jim Loy
The set of points (locus) a given ratio from two other points is the Apollonius circle. The solutions to Apollonius' problem (which is much more difficult than this, and which I will write about later) are also called Apollonius circles, and so I call this one Apollonius' "lonely" circle. Apollonius problem is much more difficult than this, by the way.
You can change the ratio by moving the bottom bright red point. The green circle is the locus of points that are that ratio from the other two points. For example, if the ratio is 2.2, then the distance from the left point to a point on the circle, divided by the distance from the right point to the same point on the circle, is 2.2. At a ratio of 1, the circle has an infinite radius; in other words it is a straight line, as you might have guessed.
The above Java interactive demonstration was created with Cinderella (a geometry program).
Return to my Cinderella pages
Return to my Mathematics pages
Go to my home page