Start with a right triangle ∆ABC, with hypotenuse AB = 1, and AC = b. Draw a parallel to AB through C. Draw a circle centered at C, with radius b. Label the intersection of the line and the circle D. Drop a perpendicular from D to line AC, intersecting it at E. What is the length of CE? Draw the line BD. Draw a parallel to CD through E, intersecting line BD at F. Drop a perpendicular from F to line AC, intersecting it at G. What is the length of EG? Continue in this manner: parallel, perpendicular, parallel, perpendicular, and so on.

Where does the sum of the infinite geometric series b + b^2 + b^3 + … appear in the figure?