Partial covering of a circle by equal circles. Part I: The mechanical models

Zsolt Gáspár, Tibor Tarnai, Krisztián Hincz

Abstract


How must n equal circles of given radius be placed so that they cover as great a part of the area of the unit circle as possible? To analyse this mathematical problem, mechanical models are introduced. A generalized tensegrity structure is associated with a maximum area configuration of the n circles, whose equilibrium configuration is determined numerically with the method of dynamic relaxation, and the stability of equilibrium is investigated by means of the stiffness matrix of the tensegrity structure. In this Part I, the principles of the models are presented, while an application will be shown in the forthcoming Part II.

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DOI: http://dx.doi.org/10.20382/jocg.v5i1a6

ISSN: 1920-180X