This page presents the numerical results and visual solutions found for the problems considered in the paper

E. G. Birgin, J. L. Gardenghi, A. Laurain. "Asymptotic bounds on the optimal radius when covering a set with minimum radius identical balls", submitted.

Unitary-side triangles and squares Regular polygons Nonregular polygons

Triangles

Number of balls	Radius	Solution	Files
10	2.4997701995076060e-01	Image	data file	metapost
20	1.7878680768922903e-01	Image	data file	metapost
30	1.4008484869823193e-01	Image	data file	metapost
40	1.2068514874998985e-01	Image	data file	metapost
50	1.0709802485963880e-01	Image	data file	metapost
60	9.6987098008903080e-02	Image	data file	metapost
70	8.9118383655621372e-02	Image	data file	metapost
80	8.2742840493430600e-02	Image	data file	metapost
90	7.8189168873025378e-02	Image	data file	metapost
100	7.4008843955332526e-02	Image	data file	metapost

Squares

Number of balls	Radius	Solution	Files
10	3.0857138444278132e-01	Image	data file	metapost
20	2.1530345690511624e-01	Image	data file	metapost
30	1.7257864265589820e-01	Image	data file	metapost
40	1.4969178407786468e-01	Image	data file	metapost
50	1.3350622446273461e-01	Image	data file	metapost
60	1.1927812547975987e-01	Image	data file	metapost
70	1.1073452412028875e-01	Image	data file	metapost
80	1.0329912595118773e-01	Image	data file	metapost
90	9.6411730891149183e-02	Image	data file	metapost
100	9.1836292588113586e-02	Image	data file	metapost

Pentagons

Number of balls	Radius	Solution	Files
10	3.4715783423734442e-01	Image	data file	metapost
20	2.3669939900915044e-01	Image	data file	metapost
30	1.8945452383832928e-01	Image	data file	metapost
40	1.6250262564038362e-01	Image	data file	metapost
50	1.4500870015930528e-01	Image	data file	metapost
60	1.3153499487968667e-01	Image	data file	metapost
70	1.2111414316889081e-01	Image	data file	metapost
80	1.1318557920546178e-01	Image	data file	metapost
90	1.0631815787366881e-01	Image	data file	metapost
100	1.0053105212646550e-01	Image	data file	metapost

Hexagons

Number of balls	Radius	Solution	Files
10	3.6038556747695094e-01	Image	data file	metapost
20	2.4292672230255191e-01	Image	data file	metapost
30	1.9601505809206032e-01	Image	data file	metapost
40	1.6839839391765454e-01	Image	data file	metapost
50	1.5016081142684781e-01	Image	data file	metapost
60	1.3642861185641464e-01	Image	data file	metapost
70	1.2473383220573088e-01	Image	data file	metapost
80	1.1636889903930613e-01	Image	data file	metapost
90	1.1009806639758152e-01	Image	data file	metapost
100	1.0422086484453501e-01	Image	data file	metapost

Heptagons

Number of balls	Radius	Solution	Files
10	3.6667470932734703e-01	Image	data file	metapost
20	2.5202311978156949e-01	Image	data file	metapost
30	2.0398727902995242e-01	Image	data file	metapost
40	1.7441006887658922e-01	Image	data file	metapost
50	1.5431652613265504e-01	Image	data file	metapost
60	1.4042351594973407e-01	Image	data file	metapost
70	1.2945957057836413e-01	Image	data file	metapost
80	1.2069316899027367e-01	Image	data file	metapost
90	1.1389008079331175e-01	Image	data file	metapost
100	1.0757351118594374e-01	Image	data file	metapost

Octagons

Number of balls	Radius	Solution	Files
10	3.7106873576400423e-01	Image	data file	metapost
20	2.5546346856171898e-01	Image	data file	metapost
30	2.0530034783740053e-01	Image	data file	metapost
40	1.7814137271875297e-01	Image	data file	metapost
50	1.5792422579503798e-01	Image	data file	metapost
60	1.4244166201882108e-01	Image	data file	metapost
70	1.3188785034950201e-01	Image	data file	metapost
80	1.2351039494338467e-01	Image	data file	metapost
90	1.1533310587096408e-01	Image	data file	metapost
100	1.0934237300065705e-01	Image	data file	metapost

Nonagons

Number of balls	Radius	Solution	Files
10	3.8517662774680106e-01	Image	data file	metapost
20	2.5917466356904295e-01	Image	data file	metapost
30	2.1249735122267938e-01	Image	data file	metapost
40	1.8061272327275071e-01	Image	data file	metapost
50	1.5935302684466349e-01	Image	data file	metapost
60	1.4433078321169282e-01	Image	data file	metapost
70	1.3324203765110695e-01	Image	data file	metapost
80	1.2448754289142935e-01	Image	data file	metapost
90	1.1702222597908146e-01	Image	data file	metapost
100	1.1061995497716709e-01	Image	data file	metapost

Decagons

Number of balls	Radius	Solution	Files
10	3.8158869903257292e-01	Image	data file	metapost
20	2.6141939510741896e-01	Image	data file	metapost
30	2.1418412263449060e-01	Image	data file	metapost
40	1.8301088164790927e-01	Image	data file	metapost
50	1.6181215355015219e-01	Image	data file	metapost
60	1.4527298684061413e-01	Image	data file	metapost
70	1.3400602611532583e-01	Image	data file	metapost
80	1.2579127911106236e-01	Image	data file	metapost
90	1.1786939677013490e-01	Image	data file	metapost
100	1.1174493622481496e-01	Image	data file	metapost

Hendecagons

Number of balls	Radius	Solution	Files
10	3.8466135710223731e-01	Image	data file	metapost
20	2.6267770819407193e-01	Image	data file	metapost
30	2.1525089619409984e-01	Image	data file	metapost
40	1.8417375804785402e-01	Image	data file	metapost
50	1.6221972829501324e-01	Image	data file	metapost
60	1.4631050090330716e-01	Image	data file	metapost
70	1.3541646130407034e-01	Image	data file	metapost
80	1.2639560586973519e-01	Image	data file	metapost
90	1.1806673442929519e-01	Image	data file	metapost
100	1.1218305516807402e-01	Image	data file	metapost

Dodecagons

Number of balls	Radius	Solution	Files
10	3.8552557785453406e-01	Image	data file	metapost
20	2.6285798973659935e-01	Image	data file	metapost
30	2.1689519268927326e-01	Image	data file	metapost
40	1.8470301934600389e-01	Image	data file	metapost
50	1.6314364327183928e-01	Image	data file	metapost
60	1.4650053598350171e-01	Image	data file	metapost
70	1.3580247823925282e-01	Image	data file	metapost
80	1.2668344095932238e-01	Image	data file	metapost
90	1.1880674384054297e-01	Image	data file	metapost
100	1.1261677885702405e-01	Image	data file	metapost