# Triangles Covering Circles

The following pictures show n unit equilateral triangles covering the largest known circle (of radius r).

 1. 2. 3. r = √3/6 = .288+Trivial. r = √3/4 = .433+ Found by Erich Friedmanin 1997. r = (38√3 - 9) / 109 = .521+Found by Maurizio Morandiin June 2009.

 4. 5. 6. r = (9√3 - 2√22) / 10 = .620+Found by Trevor Greenin July 1999. r = (79√3 - 3√79) / 152 = .724+Found by Maurizio Morandiin June 2009. r = √3/2 = .866+Trivial.

 7. 8. 9. r = .892+Found by Maurizio Morandiin July 2009. r = (453√3 - 3√347) / 752 = .969+Found by Maurizio Morandiin June 2009. r = (81√3 - 6√30) / 106 = 1.013+Found by David Cantrellin July 2005.

 10. 11. 12. r = (31√3 - √103) / 40 = 1.088+Found by David Cantrellin July 2005. r = (177√3 - 2√586) / 226 = 1.142+Found by David Cantrellin July 2005. r = (7√3 - √7) / 8 = 1.184+Found by David Cantrellin July 2005.

 13. 14. 15. r = (40√3 - √165) / 45 = 1.254+Found by Maurizio Morandiin August 2009. r = 1.290+Found by Maurizio Morandiin August 2009. r = 1.343+Found by Maurizio Morandiin August 2009.

 16. 17. 18. r = 1.392+Found by Maurizio Morandiin August 2009. r = 1.434+Found by Maurizio Morandiin August 2009. r = 1.475+Found by Maurizio Morandiin August 2009.

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