Billiard balls versus the earth

“All balls must be composed of cast phenolic resin plastic and measure 2 ¼ (+.005) inches [5.715 cm (+ .127 mm)] in diameter and weigh 5 ½ to 6 oz [156 to 170 gms]. Balls should be unpolished, and should also not be waxed. Balls should be cleaned with a towel or cloth free of dirt and dust, and may also be washed with soap and water.”

That’s part of the official World Pool-Billiards Association specification for billiard balls. An analyst at the web site uses it in constructing a “Proof that the Earth is smoother than a billiard ball“. That proof says, in part:

… This means that balls with a diameter of 2.25 inches cannot have any imperfections (bumps or dents) greater than 0.005 inches. In other words, the bump or dent to diameter ratio cannot exceed 0.005/2.25 = 0.0022222

The Earth’s diameter is approximately 12,756.2 kilometres or 12,756,200 metres…. So, if a billiard ball were enlarged to the size of Earth, the maximum allowable bump (mountain) or dent (trench) would be 28,347 metres. Earth’s highest mountain, Mount Everest, is only 8,848 metres above sea level. Earth’s deepest trench, the Mariana Trench, is only about 11 kilometres below sea level. So if the Earth were scaled down to the size of a billiard ball, all its mountains and trenches would fall well within the WPA’s specifications for smoothness. [UPDATE: See the comments section for a possible correction.]

The Association’s very logo, reproduced here, seems to suggest as much:

[HT Cliff Pickover]

BONUS: Proof that Kansas Is Flatter Than a Pancake