On Wed, Mar 2, 2011 at 7:10 PM, Mike Stay <metaweta@gmail.com> wrote:
Does the OED have anything to say on it? They're a pretty canonical arbiter of such things...
I don't think the OED is really the best source for what is essentially a question of history of mathematics. There is a definition of elliptic, but it won't tell you that elliptic functions are called that because they are the inverses of the integrals used to describe the arc length of ellipses. The OED says, in explaining "geometrical ratio": "The term geometrical points to the fact that problems involving multiplication were originally dealt with by geometry and not by arithmetic". But I think that's just wrong. The babylonians knew how to multiply, and did it arithmetically, rather than by use of geometry. Andy
On Wed, Mar 2, 2011 at 3:49 PM, Andy Latto <andy.latto@pobox.com> wrote:
On Wed, Mar 2, 2011 at 5:52 PM, Adam P. Goucher <apgoucher@gmx.com> wrote:
Why is a geometric progression called geometric?
....
Any evidence for wikipedia's theory? Any alternate theories?
Each term is the *geometric mean* of the terms either side of it, which in turn gains its name from the fact that the geometric mean has an elegant compass-and-straight-edge construction.
This sounds much more plausible to me than the etymology in wikipedia. I had thought of geometric progression as the primary one, with geometric mean being called that because the geometric mean of a and b is the number c such that a, c, b is a geometric progression (with positive ratio). But the theory that the geometric progression gets its name from the geometric mean, rather than the other way around, seems quite plausible.
I've edited wikipedia to reflect this. Hoping this doesn't produce an edit war...
Andy
Sincerely,
Adam P. Goucher
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