[Phys-L] Re: Unit conversion in Excel /cool discoveries

[David Bowman <David_Bowman@GEORGETOWNCOLLEGE.EDU>]

Regarding Tim's discovery:

> I'm sure many of you knew this, but in all my years of using Excel,
> I had never realized that there was a built-in function to convert
> units.  It is amazing what you can get Excel to do if you just know
> the right tricks!
>
> From the Excel Help:
>
> CONVERT(1.0, "lbm", "kg") equals 0.453592
> CONVERT(68, "F", "C") equals 20
> CONVERT(2.5, "ft", "sec") equals #N/A

So apparently Excel doesn't know that 2.5 ft = 2.5417584 ns  :) .

Speaking of neat discoveries, I only recently discovered the
cool identity: arcsinh(tan(x)) = arctanh(sin(x)) (& a bunch of
other equivalent identities generated by that one).

For another, consider the *discrete* Gaussian probability
distribution on the set of all integers whose probability for integer
n is given by p_n = K*exp(-[pi]*n^2) where K is the appropriate
normalization constant.  It ends up that the variance of this
distribution is exactly 1/(4*[pi]) even though the normalization
constant K can't be found exactly in terms of commonly known numbers.

This latter identity (and a whole infinite series of other analogous
ones) can be generated from the remarkable fact that the function F(x)
defined by:

F(x)== x/4 + ln(1 + 2*SUM{n = 1, infinity| exp(-[pi]*exp(x)*n^2)})

is, amazingly, an *even* function of x (i.e. F(x ) = F(-x)) and
is analytic.  This comes from an application of the Poisson Summation
formula for the Fourier series of a periodic series of delta functions
(along the real line with its spikes at the integers) in the integrand
of a normal Gaussian integral.

Do others have any unusual or cool discoveries they happened upon that
they wish to announce?

David Bowman