Circle packing coordinates for the moduli space of tori

Research output: Contribution to journalArticlepeer-review


We develop a set of natural coordinates (α, β) on the moduli space of Euclidean tori using the combinatorial structure of circle packings. Surfaces with rational coordinates support Brooks packings, while surfaces with rational a and irrational β coordinates support generalized Brooks packings with periodic singularities.

Original languageEnglish
Pages (from-to)2577-2585
Number of pages9
JournalProceedings of the American Mathematical Society
Issue number7
StatePublished - Jul 2011


  • Circle packing
  • Moduli space


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