Pappus chain
In geometry, the Pappus chain is a ring of circles between two tangent circles investigated by Pappus of Alexandria in the 3rd century AD. == Construction == Given two circles CU and CV, let the inner circle CU be enclosed by the outer circle CV, and let the two circles be tangent to each other at point A. Let the radii of these two circles be denoted as rU, rV, respectively, and let their respective centers be the points U, V. The Pappus chain consists of the circles in the shaded grey region, which are externally tangent to CU (the inner circle) and internally tangent to CV (the outer circle). Let the radius, diameter and center point of the nth circle of the Pappus chain be denoted as rn, dn, Pn, respectively.