Squares in Dominoes

The following pictures show n unit squares packed inside the smallest known domino (of shortest side length s).

 1-2 s = 1Trivial. 3 s = 3/2 = 1.5Trivial. 4 s = 1.930+Found by Evert Stenlundin June 2010.

 5-8 s = 2Trivial. 9 s = 2 + √2/3 = 2.471+Found by Evert Stenlundin June 2010. 10 s = 5/2 = 2.5Trivial.

 11 s = 2.779+Found by Evert Stenlundin June 2010. 12 s = 6 (1 + √2) / 5 = 2.897+Found by Maurizio Morandiin June 2010. 13 s = 2.976+Found by David W. Cantrellin July 2012 (after MaurizioMorandi in June 2010.)

 14-18 s = 3Trivial. 19 s = 3 + 1/√5 = 3.447+Found by Maurizio Morandiin June 2010. 20-21 s = 7/2 = 3.5Trivial.

 22 s = 3.745+Found by David W. Cantrellin July 2012 (after MaurizioMorandi in June 2010.) 23 s = 3.849+Found by Maurizio Morandiin June 2010. 24 s = 3.882+Found by DC after MMin August 2012.

 25 s = 3.939+Found by DC after MMin August 2012. 26 s = 3.981+Found by David W. Cantrellin July 2012 (after MaurizioMorandi in July 2012.) 27-32 s = 4Trivial.

 33 s = 3 + √2 = 4.414+Found by Maurizio Morandiin July 2012. 34 s = 4 + √2/3 = 4.471+Found by David W. Cantrellin July 2012. 35-36 s = 9/2 = 4.5Trivial.

 37 s = 10 / 3 + √2 = 4.747+Found by Maurizio Morandiin August 2012. 38 s = (13 + √2) / 3 = 4.804+Found by Maurizio Morandiin August 2012. 39 s = 4.839+Found by David W. Cantrellin August 2012.

 40-41 s = (10 + 7√2) / 4 = 4.974+Found by David W. Cantrellin August 2012. 41-42 s = 4.989+Found by David W. Cantrellin August 2012. 43-50 s = 5Trivial.

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