I have often run into the equivalent equations $\frac{1}{a} + \frac{1}{b} = \frac{1}{c}$ and $c = \frac{1}{\frac{1}{a} + \frac{1}{b}}$ (e.g. focal length, equivalent resistance, etc). Does this relationship have a name?
Edit: wording
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It's not a function, it's an equation with an infinite number of real solutions. – barak manos Dec 04 '14 at 13:08
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sorry, fixed. thanks – woojoo666 Dec 04 '14 at 13:10
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2Such fractions are, if $a, b$ and $c$ are natural numbers, called Egyptian fractions. If I was to call the equation anything, it would be something like "Egyptian Diophantine equation" or "Egyptian fractional equation". But I don't think they have a commonly accepted name. – Arthur Dec 04 '14 at 13:15
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$\frac{1}{n}$ is called a unit fraction. – Fred Daniel Kline Dec 04 '14 at 13:29
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Sometimes $2c$ is called the harmonic mean of $a$ and $b$. It is called the harmonic mean to distinguish it from the arithmetic mean $(a+b)/2$ and geometric mean $\sqrt{ab}$. If we write HM, AM and GM respectively for the means of $a$ and $b$, and we take $a$ and $b$ to be positive, then
$$HM \leq GM \leq AM$$
Simon S
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ah, I totally forgot about the harmonic series and the like. Thanks for all the info! – woojoo666 Dec 04 '14 at 13:21
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