Loxodrome Question: Unraveling the Definition

[kkz23691]

Hello,

On this site http://mathworld.wolfram.com/SphericalSpiral.html
the loxodrome is given by(1)
$x=cos(t)cos(c)$
$y=sin(t)cos(c)$
$z=-sin(c)$
(oblate spheroidal coordinates in the limit when the spheroid is actually a sphere. A bit unusual though, putting a "minus" sign in z )

and
(2)
$c\equiv tan^{-1}(at)$

Why did they choose this second condition in this form oo)?
It must be a matter of definition, judging by the "$\equiv$" sign in it. But why exactly this and not something else oo)?

Would anyone know? Thanks!

 

[Greg Bernhardt]

Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?

 

[kkz23691]

Yes, I posted another thread on this... it seems this curve, the way it is defined, is not a loxodrome. The angle btw curve/meridian doesn't seem to be constant as the curve's parameter changes.