Mathographics 2

further exercises from
Dixon, R. (1991). Mathographics (Dover ed.). New York: Dover Publications

2. False daisies with polygons. Use a hundred minimum polygons. Adjust K (spiral tightness) until the polygons are nearly touching.
2a. C= SQR (2)
2b. C = e = 2.718
2c. c= pi
2d. C=cube root 2
2e. C=5
2f. C=5/8


Fermat’s spiral,


in polar coordinates where, R is the radial distance, theta is the angle from the starting horizontal line.
Polygons are placed on the spiral (not actually drawn) at degree intervals that Dixon calls Divergence and defines as


Dixon’s method (1980s) was to use a fixed polygon and experiment with a constant K to enlarge the spiral. We can use a polygon sub routine that allows variable size polygons in addition to varying the size of the spiral with a constant.






dixon says the “true daisy” is accomplished by a radial spacing of 360/1.618 or 222.49 degrees. 1.618 is the famous number,

phi \phi or tau \tau


the beautiful and scholarly “The Algorithmic Beauty of Plants” by Prusinkiewicz and Lindenmayer uses the number 137.5 degrees which is 360/1.618^2

here are both numbers for comparison.




Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.