The Defect of a Hyperbolic Triangle

This page requires a java-enabled browser for correct functioning. You can drag the points labelled A, B, and C around with the mouse, and the rest of the picture will adjust accordingly.

Please enable Java for an interactive construction (with Cinderella).

In hyperbolic geometry, the sum of the angles of a triangle is always strictly less than 180 degrees. The difference between this sum and 180 degrees is called the defect of the triangle. Notice as you move the vertices of the triangle around that there is a relationship between the size of the triangle and the defect.

Sorry, but the applet messes up if you drag a vertex across a side, and the defect becomes negative. This is my fault, but I couldn't think of another way to do it.

Java image created using Cinderella by Scott Sutherland on April 1, 2004 .