Squares in Dominoes

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


1-2

s = 1
Trivial.
 
3

s = 3/2 = 1.5
Trivial.
 
4

s = 1.930+
Found by Evert Stenlund
in June 2010.


5-8

s = 2
Trivial.
 
9

s = 2 + √2/3 = 2.471+
Found by Evert Stenlund
in June 2010.
10

s = 5/2 = 2.5
Trivial.
 

11

s = 2.779+
Found by Evert Stenlund
in June 2010.
 
12

s = 6 (1 + √2) / 5 = 2.897+
Found by Maurizio Morandi
in June 2010.
 
13

s = 2.976+
Found by David W. Cantrell
in July 2012 (after Maurizio
Morandi in June 2010.)

14-18

s = 3
Trivial.
 
19

s = 3 + 1/√5 = 3.447+
Found by Maurizio Morandi
in June 2010.
20-21

s = 7/2 = 3.5
Trivial.
 

22

s = 3.745+
Found by David W. Cantrell
in July 2012 (after Maurizio
Morandi in June 2010.)
23

s = 3.849+
Found by Maurizio Morandi
in June 2010.
 
24

s = 3.882+
Found by DC after MM
in August 2012.
 

25

s = 3.939+
Found by DC after MM
in August 2012.
 
26

s = 3.981+
Found by David W. Cantrell
in July 2012 (after Maurizio
Morandi in July 2012.)
27-32

s = 4
Trivial.
 
 

33

s = 3 + √2 = 4.414+
Found by Maurizio Morandi
in July 2012.
34

s = 4 + √2/3 = 4.471+
Found by David W. Cantrell
in July 2012.
35-36

s = 9/2 = 4.5
Trivial.
 

37

s = 10 / 3 + √2 = 4.747+
Found by Maurizio Morandi
in August 2012.
38

s = (13 + √2) / 3 = 4.804+
Found by Maurizio Morandi
in August 2012.
39

s = 4.839+
Found by David W. Cantrell
in August 2012.

40-41

s = (10 + 7√2) / 4 = 4.974+
Found by David W. Cantrell
in August 2012.
41-42

s = 4.989+
Found by David W. Cantrell
in August 2012.
43-50

s = 5
Trivial.
 

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