<p>Comparison of the Archimedean spiral generated by the equations <tt>x=θcosθ</tt> and <tt>y=θsinθ</tt> with the Involute of a circle, generated by the equations <tt>x=cosθ+θsinθ</tt> and <tt>y=sinθ-θcosθ</tt> (where "θ" is an angle expressed in radians).  The Archimedean spiral is shown in red, and corresponds to the values <tt>0 ≤ θ ≤ 8π</tt> of the angle parameter, while the Involute of the circle is shown in black, and corresponds to the values <tt>0 ≤ θ ≤ 17π/2</tt> of the angle parameter.  The x-axis extends from -25 to +28 and the y-axis from -26.4 to +23.4, and there are tick marks at -20, -10, +10, +20 along the axes.
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The curves are 1 unit apart at their start points, while they are slightly more than 1.5 (and slightly less than π/2) units apart where they intersect the x-axis for the final time in this plot.
AnonMoos
<p>Self-made graphic converted from the following vector PostScript source code:
</p>
<pre>%!
300 396 translate 10 dup scale .6 setgray .3 setlinewidth
-25 0 moveto 28 0 lineto stroke 0 -26.4 moveto 0 23.4 lineto stroke
0 setgray/radians 57.2957795131 def/q{2 div/x exch def/c x cos
def/s x sin def/x x radians div def}def 1 setlinejoin
1 0 moveto 1 1 3060{q c x s mul add s x c mul sub lineto}for stroke
1 0 0 setrgbcolor 0 0 moveto 1 1 2880{q x c mul x s mul lineto}for
stroke showpage
%EOF</pre>