Apollonian GasketDrop a circle into the gap between three touching circles, then into every new gap that makes, forever. The result is a frozen foam — endlessly many circles, each one snug against its neighbours.Around 200 BC Apollonius of Perga asked which circle touches three given circles. Descartes answered with an equation in 1643: the four bend values (1 ÷ radius) of any touching quartet obey (k₁+k₂+k₃+k₄)² = 2(k₁²+k₂²+k₃²+k₄²). Iterate that rule and the packing builds itself — a shape whose “dimension” is a fraction, about 1.31.