geometric mean (thing) by dev/eth0:

In simple terms, the geometric means are the terms between two nonconsecutive terms in a geometric sequence - a sequence where each number is multiplied by a common ratio rather than related by a common difference.
The formula for a geometric sequence is:
a_n=a₁r^n-1
a_n is the nth or last term in the sequence, a₁ is the first, r is the common ratio, and n is the number of the term - a₅ is the fifth term and n=5, for example.
Finding a geometric mean: Input values for the first and nth term, value of n (the number of geometric means you want between the two + 2 to represent the first and nth terms), and solve for the common ratio. Now you can use the common ratio and a₁ to find the means of that sequence.

harmonic mean	the sum of all positive even numbers is -2	Logarithmic mean	AM-GM inequality
arithmetic mean	Interdecile Mean	All I Know About Science I Learned From Michael Crichton	proof of the AM-GM inequality
arithmetic geometric mean	physical proof that the arithmetic mean is at least as large as the harmonic mean	Helping Everything2/Perl Monks/AnimeFu	Geometrical
Geometric	pi	mean	nth roots of a complex number
Cauchy sequence	Difference	Average	exponential
complex number	infinite series	probability	logarithm