Crop Circles Art: Apollonius Circles, Taiji Diagram

By Xah Lee. Date:

Circles touching circles is a common plane geometry problem. They are not as easy to design than grid patterns or radiating patterns, because the problem of finding the right circle center and size takes some advanced plane geometry to known. See: Problem of Apollonius.

Touching Circles

nat geo 09
This one is called Apollonian gasket. image source
SedonaEvents crop circle 8
In this one, you have tangent circles around 2 large circles, with the tangent circles increasing in size. Once you decided that you want n circles to go around, the problem is how do you determine their center and radius. This would be a interesting exercise.

Taiji Diagram Designs

crop circle 3yingyang hackpenhill2003
In this design, it is made of 3 taiji diagrams of different sizes and positions. The taiji diagram , aka Yin Yang symbol, is a simple circle composition.
crop circle tri-yin-yang
This design is another variation based on the taiji diagram design. Instead of using 2 circles, it uses 3.
〔►see Geometry: Transformation of the Plane II
crop circle-Wallpaper 1
crop circle 060720 berkshire straight soley