Tangent Circles

It is impossible to make a straight edge out of the silhouettes of several small circles. However, if we have infinitely many circles, we could resize and rearrange them in a way that they make a straight edge. This problem is related to the Apollonius' Problem, the Descartes Theorem and the Soddy circles.

The infinite number of circles is a necessary requirement for this construction. The animation shows the first few hundreds of circles (well, semispheres). However, it is possible to make a straight edge with just a single circle - a circle with ... an infinite radius.

The infinity is so important, that the possibility to avoid it is infinitely small. The shape of the circle is not relevant. We can make an edge with any finite shape - like the silhouette of a giraffe, or a star, or the Greek letter "ξ".

Category:

Education

Tags:

• Elica
• Logo
• demo
• Apollonius
• Problem
• Decartes
• Theorem
• Sobby
• circles
• tangent
• infinity