Why is a geometric progression called geometric? Wikipedia's answer is "A geometric progression gains its geometric character from the fact that the areas of two geometrically similar plane figures are in "duplicate" ratio to their corresponding sides; Given two squares whose sides have the ratio 2:3, then their areas will have the ratio 4:9; we can write this as 4:6:9 and notice that the ratios 4:6 and 6:9 both equal 2:3; so by using the side ratio 2:3 "in duplicate" we obtain the ratio 4:9 of the areas, and the sequence 4, 6, 9 is a geometric sequence with common ratio 3/2. Furthermore, the volumes of two similar solid figures are in "triplicate" ratio of their corresponding sides. Similar to with the squares, you can take two cubes whose side ratio is 2:5. Their volume ratio is 8:125, which can be obtained as 8:20:50:125, the original ratio 2:5 "in triplicate", yielding a geometric sequence with common ratio 5/2." but there's no citation given, and I'm not sure I believe that. The terminology is older than higher-dimensional geometry, I think, so there would be no reason to think of a progression of more than 4 terms as being "geometric". Any evidence for wikipedia's theory? Any alternate theories? Andy