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 $40 just to know the solution.
Have you got some ideas which can help me ?
Thank you in advance
It seems like there is no proof$^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 There also seems to be an unpublished proof that no $45^\circ$ solution is better than that of Trump, but the actual optimality proof is still out there.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: