Length and area of an Apollonian packing. (English) Zbl 07921341
Summary: 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.
MSC:
| 51M04 | Elementary problems in Euclidean geometries |
| 51M25 | Length, area and volume in real or complex geometry |
References:
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