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Re: [Phys-L] Halfway point ???



Another resource showing distances large and small, in
logarithmic steps:
http://apod.nasa.gov/apod/ap120312.html
It is well done. The lack of a soundtrack detracts from the
entertainment value ... but the fact that it is interactive
adds to the pedagogical value. The user is not a completely
passive couch potato.

On 04/04/2015 07:27 AM, Donald Polvani wrote:
the harmonic mean

There is also the closely related /harmonic sum/
i.e. 1 over the sum of the reciprocals.

An application to physics is resistors in parallel
(or capacitors in series). For three resistors in
parallel, the effective resistance is the harmonic
sum of the resistances, i.e. three times the harmonic
mean.

1/x_HM = (1/x_1 + 1/x_2)/2 or x_HM = 1/(1/x_1 + 1/x_2)/2
^^^^
The last factor there is either a typo or an abuse of
the notation. The rule is than in an expression such as

0 - a - b - c - d

you keep on subtracting, and in an expression such as

1 / a / b / c / d

you keep on dividing. Therefore the reciprocal of
a / b is 1 / b * a or 1 / (a / b) ... not simply
1 / a / b.