His favorite result, which he loved so much that he asked that it be carved on his tombstone, concerned the surface area and volume of a sphere. Picture a sphere sitting snugly in a cylindrical hatbox. Using the Method, Archimedes discovered that the sphere has ⅔ the volume of the enclosing hatbox, as well as ⅔ of its surface area (assuming the top and bottom lids are also counted in the hatbox’s surface area). Notice that he didn’t give formulas for the volume or the surface area of the sphere, as we would today. Rather, he phrased his results as proportions. That’s classic Greek style.
