René Descartes1596–1650
Circle theorem
Mathematician and philosopher whose circle theorem relates the curvatures of four mutually tangent circles, enabling recursive circle packing.
Orbital Packing
A few generous circles give way to constellations of smaller ones. Tangency creates a continuous rhythm, with soft neutral discs adding weight and depth.
About this pattern
Apollonian packing · Descartes’ circle theorem
Four mutually tangent circles form a Descartes configuration, including a negatively curved enclosing circle. Replacing one circle with the other solution recursively fills the gaps. A disc-preserving Möbius transformation changes the balance while preserving every tangency.
Behind the mathematics