The size of ISO 216 B series paper is such that the length and width of Bn paper are the geometric means of the lengths and widths of An and An-1 paper. Since the geometric mean of products is the product of geometric means, the area also follows this relation.
JIS has a paper size system (JIS P 0138-61) very similar to ISO 216, except that B pages are a different size. In JIS, the area of Bn paper is the arithmetic mean of the areas of An and An-1 paper; B0 is 1030 × 1456 mm.
The U.S. engineering system has sizes A = 11 × 8.5 inches, B = 17 × 11 inches, up to E = 44 × 34 inches. The proportions alternate between approximately 1.29:1 and approximately 1.55:1. The U.S. architectural system is similar, but starts with A = 12 × 9 inches; it thus alternates between (exactly) 4:3 and 3:2.
Paper. . . it's what's for dinner.