A Convex Polygon Is the Intersection of Half Planes

The applet below is a tool that helps verify that the intersection of any (finite) number of half planes constitutes a convex polygon, which might be empty, too. Lines in the applet can be moved by pointing and dragging the cursor. If you point close to the border of the drawing area, the lines will rotate around the opposite point. Otherwise, they will translate preserving the orientation.

In fact, the intersection of any number of convex shapes is again convex. This follows directly from the definition of convexity. For a finite number of shapes there is also a simple proof by induction.

(The applet requires Java 2, jre 1.4.2 or higher. Check with the Sun's site.)

Copyright © 1996-2009 Alexander Bogomolny