Let M = {(x,y) ∈ ℝ × ℝ : x² + y² ≤ r²}, where r > 0. Consider the geometric progression aₙ = 1/2ⁿ⁻¹, n=1,2,3,… . Let S₀=0 and, for n≥1, let Sₙ denote the sum of the first n terms. Let Cₙ have center (Sₙ₋₁,0) and radius aₙ, and Dₙ have center (Sₙ₋₁,Sₙ₋₁) and radius aₙ.
For r=1025/513, let k be the number of circles Cₙ inside M and l the maximum number among them with no two intersecting. Then