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 + 2√2 = 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 = 11.806+
Found by Maurizio Morandi
in October 2010.


21.            22.
A = 17/2 + 6√2 = 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 = 20.008+
Found by Maurizio Moranndi
in October 2010.


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 = 27.988+
Found by Maurizio Morandi
in October 2010.
A = 18 + 8√2 = 29.313+
Found by David Paterson
in September 2002.


35.            43.
A = 30.247+
Found by Maurizio Morandi
in October 2010.
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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