We prove two theorems about the circular Apollonian packing. The first states that the circles used in the packing have an infinite total length. The second states that the largest circle is covered by the other circles used in the packing, up to an area of Lebesgue measure zero. Our proofs are elementary and only use basic coordinate geometry.
No takes yet. Share an insight, caveat, or question.
Alexandru Tupan (2024) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: