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ERIC Number: EJ976801
Record Type: Journal
Publication Date: 2012-Jan
Pages: 11
Abstractor: As Provided
ISBN: N/A
ISSN: ISSN-0143-0807
EISSN: N/A
Two-Dimensional Crystallography Introduced by the Sprinkler Watering Problem
De Toro, Jose A.; Calvo, Gabriel F.; Muniz, Pablo
European Journal of Physics, v33 n1 p167-177 Jan 2012
The problem of optimizing the number of circular sprinklers watering large fields is used to introduce, from a purely elementary geometrical perspective, some basic concepts in crystallography and comment on a few size effects in condensed matter physics. We examine square and hexagonal lattices to build a function describing the, so-called, dry area fraction of the field to be irrigated, providing a simple concept for first-year undergraduate students to understand the similarities between the arrangement of atoms/molecules in two dimensions and that of sprinklers. It is shown that the search for the most efficient (least-overlap) sprinkler configuration is equivalent to the search for the Wigner-Seitz cell covering the largest area of its own circumcircle. (Contains 10 figures.)
Institute of Physics Publishing. The Public Ledger Building Suite 929, 150 South Independence Mall West, Philadelphia, PA 19106. Tel: 215-627-0880; Fax: 215-627-0879; e-mail: info@ioppubusa.com; Web site: http://www.iop.org/EJ/journal/EJP
Publication Type: Journal Articles; Reports - Descriptive
Education Level: Higher Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A