Re: capacitance of horned toroid

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: Mddeming-at-aol-dot-com 

In a message dated 3/15/04 10:15:33 AM Eastern Standard Time, 
tesla-at-pupman-dot-com writes:
Original poster: "Godfrey Loudner" <ggreen-at-gwtc-dot-net>

Hello Antonio

C = 8(permittivity)(1.3677)d is about (96.8790)d, which is about 97d.

The curious formula (37D + 23d)pF in the MKS system of units becomes
97d when D = 2d. So the curious formula is explained the case
of a horned toroid.

I found a way around the first difficulty with Mathematica rounding
off too early. Now Mathematica will not carryout the hard parts of
the calculation with increased precision. Its says at some point that
the numbers encountered are smaller than machine numbers. This begins
even with n = 1. So I cannot proceed with calculating a more
accurate value of 1.3677 by my method. I'm going to send the
calculation problem to the Borwein brothers in Canada. They
are the authors of "Pi and the AGM" and are experts in severe
calculations. Anything they say will be the best possible and
they might even run the calculation.

Godfrey Loudner

 >The formula:100e-12*(0.37*D+0.23*d) pF
 >gives 48.4977000000 pF for 1x0.4999 and 48.5000000000 pF for 1x0.5.
 >Not bad.

 >Antonio Carlos M. de Queiroz

Hi Godfrey,

     Pardon my ignorance, but, since d & D are, in reality, measurable only 
to about 4-digit accuracy, what is the problem with "only" having 
calculations accurate to 6 digits?

Matt D.
2 + 2 = 3.99999999999999