# Rigid Circles in Squares

The following pictures show n unit circles packed inside the largest known square (of side length s) so that the circles are rigid.

 1. 2. 3. s = 2Trivial. s = 2 + √2 = 3.414+Trivial. s = 2 + 1/√2 + √6/2 = 3.931+Trivial.

 4. 5. 6. s = 4Trivial. s = 2 + √2 + √6 = 5.863+Found by Erich Friedmanin 1998. s = 4 + √3 = 5.732+Found by Erich Friedmanin 1998.

 7. 8. 9. s = 5.985+Found by David Cantrellin August 2006. s = 6.946+Found by Craig Clappin August 2006. s = 7.022+Found by Erich Friedmanin 1998.

 10. 11. 12. s = 4 + √3 + √2/2 + √6/2 = 7.663+Found by Craig Clappin October 2006. s = 4 + √2 + √6 = 7.863+Found by David Cantrellin July 2002. s = 7.983+Found by Craig Clappin August 2006.

 13. 14. 15. s = 8.992+Found by Craig Clappin August 2006. s = 9.055+Found by Craig Clappin August 2006. s = 9.032+Found by Craig Clappin August 2006.

 16. 17. 18. s = 9.177+Found by David Cantrellin July 2002. s = 2 + 2√6 + 2√2 = 9.727+Found by Clint Weaverin July 2002. s = 10.276+Found by Craig Clappin August 2006.

 19. 20. 21. s = 10.348+Found by Craig Clappin August 2006. s = 10.497+Found by Craig Clappin August 2006. s = 10.530+Found by Craig Clappin September 2006.

 22. 23. 24. s = 10.764+Found by Craig Clappin August 2006. s = 10.982+Found by Craig Clappin September 2006. s = 8 + 2√3 = 11.464+Found by David Cantrellin July 2002.

Are these circle packings by Craig Clapp rigid? 15   16   16   16   19   20   21   22   22   22