Talk:Logarithmic spiral
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What type of spirals do subatomic particles track in cloud chambers?
- a log spiral -- if the drag force is proportional to speed (which I doubt). (If a uniform magnetic field runs perpendicular to the complex plane, with Im(z) the strength of the field, -Re(z) the drag coefficient, and <math>x'<math> the velocity, then <math>x''=zx'<math>. Integrating twice is trivial.) 142.177.124.178 21:05, 20 Jul 2004 (UTC)
Is it "spiralis mirabilis" or "spira mirabilis"? I've seen both, which is correct?
I urge caution with the pedal curve comment (I merely preserved it); I suspect it's only so if the pedal point is the center/origin of the spiral. 142.177.124.178 20:27, 20 Jul 2004 (UTC)
- D'oh, it's so obvious. If the pedal point is not the spiral's center then the pedal curve passes through the pedal point an infinite number of times. No log spiral passes through any point more than once. 142.177.124.178 06:58, 23 Jul 2004 (UTC)
I fixed my mistake in the differential geometric definition of the logarithmic spiral.MathMartin 21:50, 20 Jul 2004 (UTC)
Presumably some log spirals are exactly their own evolute (no rotation needed) ... anyone know which? They're the only such curves, ya? 142.177.124.178 07:33, 23 Jul 2004 (UTC)
- 'Cording to my ciphering, the evolute of <math>t\mapsto e^{zt}<math> is <math>t\mapsto {\bar z+z\over\bar z-z}e^{zt}<math>; if that's right, then the spiral is exactly its evolute iff <math>{\Re z\over\Im z}\left(2n+\frac12\right)\pi=\ln {\Re z\over\Im z}<math> for some integer n. 142.177.124.178 18:05, 23 Jul 2004 (UTC)