page_title: Packing problems
section_title: Circles in equilateral triangle
hierarchical_section_title: Packing problems / Packing in 2-dimensional containers / Packing circles / Circles in equilateral triangle
caption_attribution_description: 5 cirkloj en 60 60 60 triangulo, varianto 1
context_page_description: Packing problems are a class of optimization problems in mathematics that involve attempting to pack objects together into containers. The goal is to either pack a single container as densely as possible or pack all objects using as few containers as possible. Many of these problems can be related to real life packaging, storage and transportation issues. Each packing problem has a dual covering problem, which asks how many of the same objects are required to completely cover every region of the container, where objects are allowed to overlap.
  In a bin packing problem, you are given:
  'containers'
  A set of 'objects' some or all of which must be packed into one or more containers. The set may contain different objects with their sizes specified, or a single object of a fixed dimension that can be used repeatedly.
  Usually the packing must be without overlaps between goods and other goods or the container walls. In some variants, the aim is to find the configuration that packs a single container with the maximal density. More commonly, the aim is to pack all the objects into as few containers as possible. In some variants the overlapping is allowed but should be minimized.
context_section_description: Pack n unit circles into the smallest possible equilateral triangle. Optimal solutions are known for n<13, and conjectures are available for n < 28.
caption: The optimal packing of five circles in an equilateral triangle
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