What is an arbelos?
Properties of an arbelos
Distances and areas
Dec 16, 2005
Math 308 by Dr. Bill Casselman
Construct a circle tangent to the two small interior semicircles and the enclosing semicircle.
Next, create another circle tangent to the first circle created, one of the two interior semicircle, and the enclosing semicircle.
Continue in this fashion until a chain of circles is created. This is the Pappus chain.
The Pappus chain's circles all have centers which lines on an ellipse which has foci at the centers of the circles bounding it.
The focus c1 is at the center of the semicircle with diameter AB.
The focus c2 is at the center of the semicircle with diameter AC.
The centers and the radii of the nth circle in the Pappus chain are