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arXiv · 2202.10822

Neighbors

Gábor Fejes Tóth·Lázló Fejes Tóth·Włodzimierz Kuperberg
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Abstract

Two members of a packing are neighbors if they have a common boundary point. A multitude of problems arises in connection with neighbors in a packing. The oldest one concerns a dispute between Newton and Gregory about the maximum number of neighbors a member can have in a packing of congruent balls. Other problems ask for the average number of neighbors or the maximum number of mutually neighboring members in a packing. The present work gives a survey of these problems.

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Gábor Fejes Tóth, Lázló Fejes Tóth, Włodzimierz Kuperberg. 2022-02-22. Neighbors. https://arxiv.org/abs/2202.10822

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