This article is cited in 6 papers

Multiple circle coverings of an equilateral triangle, square, and circle

Sh. I. Galiev, A. V. Khorkov

Kazan National Research Technological University, 10 K. Marx St., 420011 Kazan, Russia

Abstract: We study $k$-fold coverings of an equilateral triangle, square, and circle with $n$ congruent circles of the minimum possible radius $r^*_{n,k}$. We describe mathematical models for these problems and algorithms for their solving. We also prove optimality of the constructed coverings for certain $n$ and $k$, $1<k\le n$. For $n\le15$ and $1<k\le n$, we present the best found (possibly, improvable) values of circles radii ensuring the $k$-fold covering of the equilateral triangle, square or a circle. Ill. 4, tab. 3, bibliogr. 39.

Keywords: multiple covering with congruent circles, equilateral triangle, square, circle, minimum covering problem.

UDC: 519.7

Received: 17.03.2015
Revised: 20.08.2015

DOI: 10.17377/daio.2015.22.482

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