Squares in Circles

The following pictures show n squares packed inside a unit circle, so that the total sum of the sides of the squares is as large as possible.

 1. 2. 3. s = √2 = 1.414+Trivial. s = 4 / √5 = 1.788+Trivial. s = 2.331+Found by Erich Friedmanin June 2011.

 4. 5. 6. s = 2√2 = 2.828+Found by Erich Friedmanin June 2011. s = 3.204+Found by Maurizio Morandiin July 2011. s = 3.597+Found by Maurizio Morandiin July 2011.

 7. 8. 9. s = (2√10 + √190) / 5 = 4.021+ Found by Erich Friedmanin June 2011. s = (10√2 + 5√10 + √190) / 10 = 4.373+ Found by Erich Friedmanin June 2011. s = (10√2 + 3√10) / 5 = 4.725+Found by Erich Friedmanin June 2011.

 10. 11. 12. s = 4.970+ Found by Erich Friedmanin June 2011. s = 5.185+Found by Maurizio Morandiin July 2011. s = 5.419+Found by Maurizio Morandiin August 2011.

 13. 14. 15. s = 5.720+ Found by Maurizio Morandiin August 2011. s = 6.005+Found by Erich Friedmanin June 2011. s = 6.218+Found by Maurizio Morandiin July 2011.

 16. 17. 18. s = 6.435+ Found by Maurizio Morandiin July 2011. s = 6.595+Found by Maurizio Morandiin July 2011. s = 6.816+Found by Maurizio Morandiin July 2011.

 19. 20. 21. s = 7.069+ Found by David W. Cantrellin July 2011. s = 7.271+Found by Maurizio Morandiin July 2011. s = 7.473+Found by Maurizio Morandiin July 2011.

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