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Disk covering problem
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<h2 id="method">Method</h2> <p>The following picture shows an example of a dashed disk of radius 1 covered by six solid-line disks of radius ~0.6. One of the covering disks is placed central and the remaining five in a symmetrical way around it. </p><p>While this is not the best layout for r(6), similar arrangements of six, seven, eight, and nine disks around a central disk all having same radius result in the best layout strategies for r(7), r(8), r(9), and r(10), respectively.<a class="footnote-ref" id="fnref:3" href="#fn:3"><sup>3</sup></a> The corresponding angles θ are written in the "Symmetry" column in the above table. </p> <h2 id="external-links">External links</h2> <ul><li><a href="/facts/Eric_W._Weisstein/FbMuVDep">Weisstein, Eric W.</a> <a href="https://mathworld.wolfram.com/DiskCoveringProblem.html">"Disk Covering Problem"</a>. <i><a href="/facts/MathWorld/yc1jodbq">MathWorld</a></i>.</li> <li>Finch, S. R. "Circular Coverage Constants." §2.2 in Mathematical Constants. Cambridge, England: Cambridge University Press, pp. 484–489, 2003.</li></ul> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>Kershner, Richard (1939), "The number of circles covering a set", American Journal of Mathematics, 61 (3): 665–671, doi:10.2307/2371320, JSTOR 2371320, MR 0000043. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>Friedman, Erich. "Circles Covering Circles". Retrieved 4 October 2021. <a href="https://erich-friedman.github.io/packing/circovcir/" target="_blank">https://erich-friedman.github.io/packing/circovcir/</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> <li id="fn:3"><p>Friedman, Erich. "Circles Covering Circles". Retrieved 4 October 2021. <a href="https://erich-friedman.github.io/packing/circovcir/" target="_blank">https://erich-friedman.github.io/packing/circovcir/</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li> </ol>