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Perfect Proportion

Since

(2a)/(a+b)=(2ab)/((a+b)b),
(1)

it follows that

a/((a+b)/2)=((2ab)/(a+b))/b,
(2)

so

a/A=H/b,
(3)

where A and H are the arithmetic mean and harmonic mean of a and b. This relationship was purportedly discovered by Pythagoras.

See also

Arithmetic Mean, Harmonic Mean

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Cite this as:

Weisstein, Eric W. "Perfect Proportion." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PerfectProportion.html

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