WOLFRAM|DEMONSTRATIONS PROJECT

Disks Centered on Vertices of Regular Polygons

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rotation (degrees)
direction
cw
ccw
no. of vertices, n
6
view radius
1.
polygon perimeter
in color
Gray
inradius circle
circumradius circle
thick perimeter
background
White
enclosing disk
in color
LightPurple
nest n
trapped disk
in color
Purple
vertex-centered disks
disk edges
central disk
nest 1 level (1:n)
nest all n
automatic Tao coloring
or in color
Red
hexagon
This Demonstration draws patterns constructed from colored disks whose centers are the vertices of an origin-centered regular polygon where you can vary the number of vertices
n
from 1 to 60. All vertex-centered disks have the same radius, so that each disk is tangent to both its neighbors and to an enclosing circle of unit radius and, for
n>2
, to an origin-centered disk that is trapped by and tangent to the vertex-centered disks. You can vary the colors of the disks, the background, and the underlying polygon. The overall disk pattern may optionally be nested within the vertex-centered disks and/or the trapped origin-centered disk, zoomed in and out by a factor of from 1 to 3, rotated 360° in either direction, or colored by an automatic hue selection rule applied to a curved region taken from the Taoist symbol for yin and yang.