The golden earring A disk of radius r is removed from a larger disk of radius R to form an earring (see figure). Assume the ear- ring is a thin plate of uniform density. a. Find the center of mass of the earring in terms of r and R. (Hint: Place the origin of a coordinate system either at the center of the large disk or at Q; either way, the earring is symmetric about the x-axis.) b. Show that the ratio – such that the center of mass lies at the R point P (on the edge of the inner disk) is the golden mean 1+ V3 * 1.618. (Source: P. Glaister, Golden Earrings, Mathematical Gazette, 80, 1996) Radius r Radius R

The golden earring A disk of radius r is removed from a larger disk of radius R to form an earring (see figure). Assume the ear- ring is a thin plate of uniform density. a. Find the center of mass of the earring in terms of r and R. (Hint: Place the origin of a coordinate system either at the center of the large disk or at Q; either way, the earring is symmetric about the x-axis.) b. Show that the ratio – such that the center of mass lies at the R point P (on the edge of the inner disk) is the golden mean 1+ V3 * 1.618. (Source: P. Glaister, Golden Earrings, Mathematical Gazette, 80, 1996) Radius r Radius R