Recent content by Ahmidahn

Thanks again for all the replies. I will be pondering this one for a while.

Are you wondering why I write the power in the exponent (theta) over "n"? Or what?

"Logarithmic spiral"= r = a(exp)-b(theta) in polar coordinates Parametric form: x(t) = r(t) \cos(t) = ae^{bt} \cos(t)\, y(t) = r(t) \sin(t) = ae^{bt} \sin(t)\,

I'm going to have to suss that out for the arc length...hmm...getting closer.

Yes. That would seem to make sense. Correct me if I'm wrong reinterpreting the equation. e-a + i\theta = (e-a)(ei\theta)= (e-a)(cos\theta + i sin\theta) What kind of variable is "a" in this situation? Is this a three dimensional curve, or rather, can it be visualized in 3 dimensions...

The Wikipedia entry for "Circular Polarization" has the "classical sinusoidal plane wave solution of the electromagnetic wave equation" - and the math behind it as well. It's similar, in general, to what I'm looking for. The math is beyond me. I actually know what some of those things are...

Maybe something like: (cos \theta + i sin\theta)/w would translate into: [exp(i\theta)] / w where w is some decreasing function related to \theta? I don't know. I've been stuck on this one for almost two years. Thanks for your help.

Is there a way to take Euler's formula "e^(i∅)" -which gives a circle; and change it into a logarithmic spiral? Does a simple modification like " e^-(i∅/n) " make any sense mathematically? If it actually does, my other question would be; supposing that such a logarithmic spiral is in fact just...