curvature of Nielsen's spiral

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Defines:
Nielsen's spiral
Keywords:
arc length
Synonym:
arc length of Nielsen's spiral
Type of Math Object:
Example
Major Section:
Reference
Groups audience:

Mathematics Subject Classification

\parametricplot in pstricks

I have tried to use \parametricplot in pstricks for making the Nielsen's spiral (http://planetmath.org/encyclopedia/CurvatureOfNielsensSpiral.html), but not succeeded. Are there some masters of pstricks who knows what is the cause? Please feel free to correct the code (the equations are seen in "version 7").
Jussi

Re: the Nielsen's spiral plot

I think you will find it easier to plot analytically complicated curves like Nielsen's spiral with numerical software rather than with Postscript directly. (This is what I have done in the entry.)

In particular, I'm not sure those approximating equations that you have work for "large" $t$, say $0< t < 1/2$, as they are based on Taylor series expansions of $sin$ and $cos$ about $0$. The interesting part, of course, is for large $t$, say $t > 6.0$. For this part, I evaluate the functions with their asymptotic series as displayed on their Wikipedia entry (without proof :). For $t < 6.0$, I use direct numerical integration to compute the function values.

I can post the Octave code (should also run in MatLab) once I clean it up a bit.

// Steve

Re: the Nielsen's spiral plot

Steve,
Thousands of thanks to you for the beautiful picture of the Nielsen's spiral! I am very happy about it.
I believe now that pstricks isn't rather good for making such graphs, especially when they require uncomfortable functions and when the author is so inexperienced as I am :) Before I have made only one graph (cissoid of Diocles).
Jussi