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.

This applet requires Sun's Java VM 2 which your browser may perceive as a popup. Which it is not. If you want to see the applet work, visit Sun's website at https://www.java.com/en/download/index.jsp, download and install Java VM and enjoy the applet.

What if applet does not run?

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.)

Convex Sets

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