Squares Covering Squares

The following pictures show n unit squares covering the largest known square (of area A). For the n not pictured, the trivial covering (with no tilted squares) is the best known.

3.            7.
A = 1/2 + 5/2 = 1.618+
Found by Dudeney in 1931. 		A = 11/4 + 3/2 = 4.871+
Found by Trevor Green in September 2000.

8.            13.
A = 3 + 22 = 5.828+
Found by Trevor Green in September 2000. 		A = 11/2 + 6/2 = 9.742+
Found by David Paterson in July 2002.

14.            15.
A = 10.860+
Found by Michael Kearney in July 2002. 		A = 11.659+
Found by David Cantrell in July 2002.

21.            22.
A = 17/2 + 62 = 16.985+
Found by David Paterson in July 2002. 		A = 17.821+
Found by David Cantrell in August 2002.

23.            24.
A = 19.001+
Found by David Cantrell in July 2002. 		A = 19.883+
Found by David Cantrell in July 2002.

31.            32.
A = 25.527+
Found by David Paterson in September 2002. 		A = 83/4 + 9/2 = 27.113+
Found by David Paterson in September 2002.

33.            34.
A = 27.794+
Found by David Paterson in September 2002. 		A = 18 + 82 = 29.313+
Found by David Paterson in September 2002.

35.            43.
A = 30.195+
Found by David Paterson in September 2002. 		A = 36.608+
Found by David Paterson in September 2002.

44.            45.
A = 41/2 + 24/2 = 37.470+
Found by David Paterson in September 2002. 		A = 39.042+
Found by David Paterson in September 2002.

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