About the squares in square packing problem with 11 squares

In this web site there are the solutions of a lot of packing squares problems. I know a very simple method to calculate with pen and paper the solution for the ten squares in a square using the same method than for five squares.

But now I try the eleven squares and the problem seems to be difficult, I try some approximations but they were not very conclusive. So I made a "puzzle" with eleven piece of paper and tried some configurations but they were not really interesting.

So I searched online but I find nothing about Walter Trump's method and I don't want to buy a book for $40 just to know the solution. Have you got some ideas which can help me ? Thank you in advance • Are you trying to calculate$s$or to prove$s$is optimal? Jun 3, 2015 at 12:51 • I'm trying the both ! :) Jun 3, 2015 at 12:55 1 Answer It seems like there is no proof$^1$that this result is actually optimal. There also seems to be an unpublished proof that no$45^\circ$solution is better than that of Trump, but the actual optimality proof is still out there. The attached reference also gives a hint to finding the angle ($40.182^\circ\$) and configuration:

1. "Which Way Did the Bicycle Go?: And Other Intriguing Mathematical Mysteries", pp. 105
• Is it difficult to find these two equations ? :) Jun 3, 2015 at 15:46
• @Shadock - difficult? no. tedious? very. Jun 3, 2015 at 15:52
• OK i will try and if I don't find them you will give me :P Thank you for your help ! Jun 3, 2015 at 15:54