Circles in Ellipses

The following pictures show n unit circles packed inside the ellipse with smallest known area A (with semi-axes a and b).

1.
           2.
           3.
A = π(1)
a = 1     b = 1
Trivial. 		A = π(3√3/2)
a = 3/√2     b = √(3/2)
Found by James Buddenhagen in June 2004
Proved by Tej Stead in June 2026 		A = π(16√6/9)
a = 8/√6     b = 4/3
Found by James Buddenhagen
in June 2004

4.
           5.
           6.
A = π(2+2√3)
a = 1+√3     b = 2
Found by David W. Cantrell
in June 2007 		A = π(7.279+)
a = 3.822+     b = 1.904+
Found by David W. Cantrell
in June 2007 		A = π(7.803+)
a = 2+√3     b = 2.090+
Found by David W. Cantrell
in June 2007

7.
           8.
           9.
A = π(9)
a = 3     b = 3
Found by David W. Cantrell
in June 2007 		A = π(10.546+)
a = 4.718+     b = 2.235+
Found by David W. Cantrell
in June 2007 		A = π(12.270+)
a = 5.878+     b = 2.087+
Found by Imre Pólik
in January 2026

10.
           11.
           12.
A = π(12.826+)
a = 4.117+     b = 3.115+
Found by David W. Cantrell
in June 2007 		A = π(14.578+)
a = 4.772+     b = 3.054+
Found by David W. Cantrell
in June 2007 		A = π(15.921+)
a = 4.905+     b = 3.245+
Found by David W. Cantrell
in June 2007

13.
           14.
           15.
A = π(17.008+)
a = 5.168+     b = 3.291+
Found by David W. Cantrell
in June 2007 		A = π(18.014+)
a = 4.730+     b = 3.808+
Found by David W. Cantrell
in June 2007 		A = π(19.762+)
a = 6.995+     b = 2.824+
Found by Imre Pólik
in January 2026

16.
           17.
           18.
A = π(20.761+)
a = 7.289+     b = 2.847+
Found by David W. Cantrell
in June 2007 		A = π(22.033+)
a = 7.998+     b = 2.754+
Found by David W. Cantrell
in June 2007 		A = π(22.819+)
a = 5.730+     b = 3.982+
Found by David W. Cantrell
in June 2007

19.
           20.
           21.
A = π(23.655+)
a = 1 + √2 + √6     b = 1 + √2 + √6
Found by David W. Cantrell
in June 2007 		A = π(25.723+)
a = 9.005+     b = 2.856+
Found by David W. Cantrell
in June 2007 		A = π(27.084+)
a = 6.497+     b = 4.168+
Found by David W. Cantrell
in June 2007

22.
           23.
           24.
A = π(27.998+)
a = 6.751+     b = 4.146+
Found by David W. Cantrell
in June 2007 		A = π(29.514+)
a = 9.918+     b = 2.975+
Found by David W. Cantrell
in June 2007 		A = π(30.224+)
a = 5.996+     b = 5.040+
Found by David W. Cantrell
in June 2007

25.
           26.
           27.
A = π(32.166+)
a = 8.378+     b = 3.839+
Found by Yanis Gomes
in October 2026. 		A = π(33.281+)
a = 7.718+     b = 4.311+
Found by Yanis Gomes
in October 2026. 		A = π(34.754+)
a = 9.260+     b = 3.752+
Found by Yanis Gomes
in October 2026.

28.
           29.
           30.
A = π(35.682+)
a = 9.530+     b = 3.744+
Found by Yanis Gomes
in October 2026. 		A = π(36.901+)
a = 6.900+     b = 5.347+
Found by Yanis Gomes
in October 2026. 		A = π(37.843+)
a = 6.546+     b = 5.780+
Found by Yanis Gomes
in October 2026.

31.
           32.
           33.
A = π(39.574+)
a = 10.643+     b = 3.718+
Found by Yanis Gomes
in October 2026. 		A = π(40.408+)
a = 10.627+     b = 3.802+
Found by Yanis Gomes
in October 2026. 		A = π(41.987+)
a = 11.134+     b = 3.770+
Found by Yanis Gomes
in October 2026.

34.
           35.
           36.
A = π(43.151+)
a = 9.125+     b = 4.728+
Found by Yanis Gomes
in October 2026. 		A = π(44.230+)
a = 7.720+     b = 5.728+
Found by Yanis Gomes
in October 2026. 		A = π(44.774+)
a = 7.620+     b = 5.875+
Found by Yanis Gomes
in October 2026.

37.
           38.
           39.
A = π(45.680+)
a = 6.758+     b = 6.758+
Found by Yanis Gomes
in October 2026. 		A = π(48.086+)
a = 12.600+     b = 3.816+
Found by Yanis Gomes
in October 2026. 		A = π(49.298+)
a = 10.141+     b = 4.861+
Found by Yanis Gomes
in October 2026.

40.
           41.
           42.
A = π(50.346+)
a = 10.736+     b = 4.689+
Found by Yanis Gomes
in October 2026. 		A = π(51.532+)
a = 10.778+     b = 4.781+
Found by Yanis Gomes
in October 2026. 		A = π(52.474+)
a = 8.685+     b = 6.041+
Found by Yanis Gomes
in October 2026.

43.
           44.
           45.
A = π(54.176+)
a = 7.797+     b = 6.948+
Found by Yanis Gomes
in October 2026. 		A = π(54.782+)
a = 7.888+     b = 6.944+
Found by Yanis Gomes
in October 2026. 		A = π(56.451+)
a = 12.018+     b = 4.697+
Found by Yanis Gomes
in October 2026.

46.
           47.
           48.
A = π(57.571+)
a = 12.432+     b = 4.630+
Found by Yanis Gomes
in October 2026. 		A = π(58.966+)
a = 12.665+     b = 4.655+
Found by Yanis Gomes
in October 2026. 		A = π(60.008+)
a = 9.577+     b = 6.265+
Found by Yanis Gomes
in October 2026.

49.
           50.
A = π(61.459+)
a = 13.066+     b = 4.703+
Found by Yanis Gomes
in October 2026. 		A = π(62.405+)
a = 11.173+     b = 5.585+
Found by Yanis Gomes
in October 2026.