pack

every circle is the same size. click where you want the next one — it only lands if it doesn't overlap and stays inside the square. nothing is saved.

// the idea

Packing equal circles as densely as possible is an old problem with a settled answer — in an infinite plane, no arrangement beats the hexagonal lattice (each circle touching six neighbors), which covers π/(2√3) ≈ 90.69% of the plane. Axel Thue sketched a proof in 1890 (with a gap later found in it); László Fejes Tóth gave the first fully rigorous proof in 1940.

That number is a limit for an infinite plane, not a promise for a small square. A finite container always loses some ground at its edges — a circle near the wall wastes the space it can't fill on that side. So reaching 90.69% here by hand is unlikely, and that's fine; the game is in how close you can get, not in matching a number that was never a guarantee for a box this size.