Circles in Ellipses

The following pictures show n circles with the largest possible sum of radii packed inside an ellipse with perimeter 2π.


1.
           2.
           3.
Σ r = 1
Circular.
Σ r = 1.185+
Found by David W. Cantrell
in September 2011.
Σ r = 1.407+
Found by David W. Cantrell
in September 2011.


4.
           5.
           6.
Σ r = 1.684+
Found by David W. Cantrell
in September 2011.
Σ r = 1.887+
Found by David W. Cantrell
in September 2011.
Σ r = 2.110+
Circular.
Found by Veit Elser
in November 2009.


7.
           8.
           9.
Σ r = 7 / 3 = 2.333+
Circular.
Found by Veit Elser
in November 2009.
Σ r = 2.512+
Circular.
Found by Veit Elser
in November 2009.
Σ r = 2.660+
Circular.
Found by Veit Elser
in November 2009.


10.
           11.
           12.
Σ r = 2.809+
Found by David W. Cantrell
in September 2011.
Σ r = 2.950+
Found by David W. Cantrell
in September 2011.
Σ r = 3.103+
Circular.
Found by Veit Elser
in November 2009.


13.
           14.
           15.
Σ r = 3.231+
Found by David W. Cantrell
in September 2011.
Σ r = 3.370+
Found by David W. Cantrell
in September 2011.
Σ r = 3.485+
Found by David W. Cantrell
in September 2011.


16.
           17.
           18.
Σ r = 3.231+
Circular.
Found by David W. Cantrell
in April 2011.
Σ r = 3.732+
Found by David W. Cantrell
in September 2011.
Σ r = 3.851+
Found by David W. Cantrell
in September 2011.


19.
           20.
           21.
Σ r = 3.981+
Circular.
Found by David W. Cantrell
in May 2011.
Σ r = 4.077+
Found by David W. Cantrell
in September 2011.
Σ r = 4.182+
Found by David W. Cantrell
in September 2011.


22.
           23.
           24.
Σ r = 4.287+
Circular.
Found by David W. Cantrell
in June 2011.
Σ r = 4.378+
Found by David W. Cantrell
in September 2011.
Σ r = 4.478+
Found by David W. Cantrell
in September 2011.


25.
           26.
           27.
Σ r = 4.570+
Found by David W. Cantrell
in September 2011.
Σ r = 4.667+
Found by David W. Cantrell
in September 2011.
Σ r = 4.762+
Circular.
Found by David W. Cantrell
in June 2011.


28.
           29.
           30.
Σ r = 4.849+
Found by David W. Cantrell
in September 2011.
Σ r = 4.938+
Found by David W. Cantrell
in September 2011.
Σ r = 5.030+
Found by David W. Cantrell
in September 2011.


31.
           32.
Σ r = 5.105+
Found by David W. Cantrell
in September 2011.
Σ r = 5.192+
Found by David W. Cantrell
in September 2011.


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