Starting with the circle P_1 tangent to the three semicircles forming the arbelos, construct a chain of tangent circles P_i, all tangent to one of the two small interior circles and to the large exterior one. This chain is called the Pappus chain. In a Pappus chain, the distance from the center of the first inscribed circle P_1 to the bottom line is twice the circle's radius, from the second circle P_2 is four times the radius, and for the nth circle P_n is 2n times the radius. Furthermore, the centers of the circles P_i lie on an ellipse.

arbelos | Coxeter's loxodromic sequence of tangent circles | Pappus's centroid theorem | Pappus's harmonic theorem | Pappus's hexagon theorem | six circles theorem | Soddy circles | Steiner chain

Pappus