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 Dudeneyin 1931. A = 11/4 + 3/√2 = 4.871+Found by Trevor Greenin September 2000.

 8. 13. A = 3 + 2√2 = 5.828+Found by Trevor Greenin September 2000. A = 11/2 + 6/√2 = 9.742+Found by David Patersonin July 2002.

 14. 15. A = 10.860+Found by Michael Kearneyin July 2002. A = 11.806+Found by Maurizio Morandiin October 2010.

 21. 22. A = 17/2 + 6√2 = 16.985+Found by David Patersonin July 2002. A = 17.821+Found by David Cantrellin August 2002.

 23. 24. A = 19.001+Found by David Cantrellin July 2002. A = 20.008+Found by Maurizio Moranndiin October 2010.

 31. 32. A = 25.527+Found by David Patersonin September 2002. A = 83/4 + 9/√2 = 27.113+Found by David Patersonin September 2002.

 33. 34. A = 27.988+Found by Maurizio Morandiin October 2010. A = 18 + 8√2 = 29.313+Found by David Patersonin September 2002.

 35. 43. A = 30.247+Found by Maurizio Morandiin October 2010. A = 36.608+Found by David Patersonin September 2002.

 44. 45. A = 41/2 + 24/√2 = 37.470+Found by David Patersonin September 2002. A = 39.042+Found by David Patersonin September 2002.

Back to Erich's Packing Center.