The Fermat spiral script is now converted into the more general Archimedean spiral, based upon the polar equation r = a * Math.pow( theta, b ).

There are names for four of the spirals.

For the lituus curve, b = -1/2.

For the hyperbolic spiral, b = -1.

For Archimedes' spiral, b = 1.

For Fermat's spiral, b = 1/2.

The script NO LONGER adjusts the aValue by PI, so that half whorls come to the aValue entered, e.g. 6 units. (Removed this division by PI)

The Chinese yinyang symbol is explained as the lengths of the shadow cast by a pole, over the course of a year. Say at high noon.

The shadows vary due to the tilt of the earth. Does the elliptical orbit change the shadow lengths enough to measure?

http://www.chinesefortunecalendar.com/yinyang2.htm
After some study, it becomes clear that the curve is an Archimedes' spiral, with b = 1.

For an aValue of 6, (/PI inside script), the Archimedes spiral matches up exactly with the yinyang curve.

The .3dm shows the red curve rotated slightly to show the match with the blue curve.

- Brian

UPDATE Sept 12, 2014, The ArchimedeanSpirals script is revamped, with Sliders and lots of improvements.

The exponent is the reciprocal, to avoid division by zero.

UPDATE Sept 13, 2014: Replaced the script with MaxSmirnof's 3 improvements, per post #7 and #8.