arbelos
What is an arbelos?
Properties of an arbelos
Distances and areas
Archimedes' circles
Apollonius circle
Bankoff circle
Pappus chain
References
Stephen Tan
42373027
Dec 16, 2005
Math 308 by Dr. Bill Casselman
Final Project

Page 11
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 c_{1} is at the center of the semicircle with diameter AB.
The focus c_{2} is at the center of the semicircle with diameter AC.
The centers and the radii of the nth circle in the Pappus chain are


