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curvature of Nielsen's spiral

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

Mathematics Subject Classification

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Comments

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

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

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

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