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Style of vase painting that flourished in Athens *circa* 1000–700 *BC*. Vases decorated in this style feature horizontal bands filled with geometric patterns such as zigzags, triangles, and swastikas in dark paint on a light ground. The rhythmic effect is similar to that of basketry. The abstract motifs developed into stylized animal and human forms in such narrative scenes as funerals, dances, and boxing matches. Small bronze and clay figurines, elaborately decorated fibulas, and limestone seals were also produced. The patterns remained popular and influenced much later Greek art.

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Encyclopedia Britannica, 2008. Encyclopedia Britannica Online.

In mathematics, the geometric-harmonic mean M(x, y) of two positive real numbers x and y is defined as follows: we first form the geometric mean of g_{0} = x and h_{0} = y and call it g_{1}, i.e. g_{1} is the square root of xy. We then form the harmonic mean of x and y and call it h_{1}, i.e. h_{1} is the reciprocal of the arithmetic mean of the reciprocals of x and y.## See also

## External links

Now we can iterate this operation with g_{1} taking the place of x and h_{1} taking the place of y. In this way, two sequences (g_{n}) and (h_{n}) are defined:

- $g\_\{n+1\}\; =\; sqrt\{g\_n\; h\_n\}$

and

- $h\_\{n+1\}\; =\; frac\{2\}\{frac\{1\}\{g\_n\}\; +\; frac\{1\}\{h\_n\}\}$

Both of these sequences converge to the same number, which we call the geometric-harmonic mean M(x, y) of x and y.

M(x, y) is a number between the geometric and harmonic mean of x and y; in particular it is between x and y. If r > 0, then M(rx, ry) = r M(x, y).

If AG(x, y) is the arithmetic-geometric mean, then we also have

- $M(x,y)\; =\; frac\{1\}\{AG(frac\{1\}\{x\},frac\{1\}\{y\})\}$

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Last updated on Friday September 26, 2008 at 05:52:48 PDT (GMT -0700)

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This article is licensed under the GNU Free Documentation License.

Last updated on Friday September 26, 2008 at 05:52:48 PDT (GMT -0700)

View this article at Wikipedia.org - Edit this article at Wikipedia.org - Donate to the Wikimedia Foundation

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