hello, I am a junior in precalculus. we started working on geometric sequences today, it makes perfect sense on how it works. but why is it called that? if you could send me an answer to why geometric sequences have that name, I would be much appreciative.
thanks
alan
Hi Alan,
Here's what the Oxford English Dictionary says: (The last sentence is all that is relevant here. The word geometric = geometrical was once used to describe figures that could be constructed by ruler and compass; anything else was called "mechanical.")
b. ... geometrical proportion: a proportion which involves an equality of geometrical ratio in its two parts, as 1:3::4:12. geometrical progression: a series in which the ratio between the successive quantities is constant, as 1:3:9:27:81, etc.
arithmetical progression, proportion, ratio, etc. (see ARITHMETICAL a.) relate to differences instead of quotients. The term geometrical points to the fact that problems involving multiplication were originally dealt with by geometry and not by arithmetic.