TITLE: Why is a geometric progression called so?
QUESTION [107 upvotes]: Just curious about why geometric progression is called so. Is it related to geometry?

REPLY [7 votes]: The arithmetic and geometric adjectives come from the Pythagoreans before the Christian Era. Apparently, the expression “geometric progression” comes from the “geometric mean” (Euclidean notion) of segments of length $a$ and $b$: it is the length of the side $c$ of a square whose area is equal to the area of the rectangle of sides $a$ and $b$. The construction
of the geometric mean with ruler and compass is well known for high school students; it involves "multiplication" and not "addition".