Abstract
The general mathematical problem of finding the densest packing of equal objects in a bounded shape arises in many fields of the natural sciences, in engineering design, and also in everyday life. Some applications that involve the packing of identical circles are the following:
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coverage: place radio towers in a geographical region such that the coverage of the towers is maximal, with as little interference as possible;
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storage: place as many identical objects as possible (e.g. barrels) into a storage container;
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packaging: determine the smallest box into which one can pack a given number of bottles;
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tree exploitation: plant trees in a given region such that the forest is as dense as possible, but the trees allow each other to grow up to their maximal desired size;
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cutting industry: cut out as many identical disks as possible from a given (in the general case, irregular) piece of material.
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© 2007 Springer Science+Business Media, LLC
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(2007). Introduction and Problem History. In: New Approaches to Circle Packing in a Square. Springer Optimization and Its Applications, vol 6. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-45676-8_1
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DOI: https://doi.org/10.1007/978-0-387-45676-8_1
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-45673-7
Online ISBN: 978-0-387-45676-8
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