When we want to create a beautiful image by drawing line segments or circles, we can use sawtooth waves. The sawtooth wave is a useful waveform to introduce an unlimited number of symmetrical shapes. Let S(x)=2x-2[x]-1, where [x] is the largest integer less than or equal to x. S(x) is a sawtooth wave. This periodic function is not continuous at the integers. I have created the following images by using S(x) in their formulas. At the end of this post you can see the mathematical descriptions of "3,000 Line Segments (III)" and "7000 Circles (II)".
and the radius of the k-th circle is: