Squares in Triangles

The following pictures show n unit squares packed inside the smallest known equilateral triangles (of side length s ).

1. 2. 3.
s = 1 + 2 / 3 = 2.154+
Trivial. s = 2 + 2 / 3 = 3.154+
Trivial. s = 3 / 2 + 3 = 3.232+
Found by Erich Friedman in 1997.

4. 5. 6.
s = 3 + 2 / 3 = 4.154+
Found by Erich Friedman in 1997. s = 2 + 4 / 3 = 4.309+
Found by Erich Friedman in 1997. s = 2 + 4/ 3 = 4.309+
Found by Erich Friedman in 1997.

7. 8. 9.
s = 4 + 2 / 3 = 5.154+
Found by Erich Friedman in 1997. s = 5.301+
Found by David Cantrell in July 2002. s = 3 + 4 / 3 = 5.309+
Found by Erich Friedman in 1997.

10. 11. 12.
s = 2 + 2 3 = 5.464+
Found by Erich Friedman in 1997. s = 5 + 2 / 3 = 6.154+
Found by Erich Friedman in 1997. s = 6.301+
Found by David Cantrell in July 2002.

13. 14. 15.
s = 4 + 4 / 3 = 6.309+
Found by Erich Friedman in 1997. s = 3 + 2 3 = 6.464+
Found by Erich Friedman in 1997. s = 3 + 2 3 = 6.464+
Found by Erich Friedman in 1997.

16. 17. 18.
s = 6 + 2 / 3 = 7.154+
Found by Erich Friedman in 1997. s = 7.301+
Found by David Cantrell in July 2002. s = 5 + 4 / 3 = 7.309+
Found by Erich Friedman in 1997.

19. 20. 21.
s = 4 + 2 3 = 7.464+
Found by Erich Friedman in 1997. s = 3 + 8 / 3 = 7.618+
Found by Erich Friedman in 1997. s = 3 + 8 / 3 = 7.618+
Found by Erich Friedman in 1997.

22. 23. 24.
s = 7 + 2 / 3 = 8.154+
Found by Erich Friedman in 1997. s = 8.301+
Found by David Cantrell in July 2002. s = 6 + 4 / 3 = 8.309+
Found by Erich Friedman in 1997.

25. 26. 27.
s = 5 + 2 3 = 8.464+
Found by Erich Friedman in 1997. s = 4 + 8 / 3 = 8.618+
Found by Erich Friedman in 1997. s = 4 + 8 / 3 = 8.618+
Found by Erich Friedman in 1997.

28. 29. 30.
s = 3 + 10 / 3 = 8.773+
Found by Erich Friedman in 1997. s = 8 + 2 / 3 = 9.154+
Found by Erich Friedman in 1997. s = 9.301+
Found by David Cantrell in July 2002.

31. 32. 33.
s = 7 + 4 / 3 = 9.309+
Found by Erich Friedman in 1997. s = 6 + 2 3 = 9.464+
Found by Erich Friedman in 1997. s = 5 + 8 / 3 = 9.618+
Found by Erich Friedman in 1997.

34. 35. 36.
s = 4 + 10 / 3 = 9.773+
Found by Erich Friedman in 1997. s = 4 + 10 / 3 = 9.773+
Found by Erich Friedman in 1997. s = 4 + 10 / 3 = 9.773+
Found by Erich Friedman in 1997.

Back to Erich's Packing Center.

1.		2.		3.
s = 1 + 2 / 3 = 2.154+ Trivial.		s = 2 + 2 / 3 = 3.154+ Trivial.		s = 3 / 2 + 3 = 3.232+ Found by Erich Friedman in 1997.

4.		5.		6.
s = 3 + 2 / 3 = 4.154+ Found by Erich Friedman in 1997.		s = 2 + 4 / 3 = 4.309+ Found by Erich Friedman in 1997.		s = 2 + 4/ 3 = 4.309+ Found by Erich Friedman in 1997.

7.		8.		9.
s = 4 + 2 / 3 = 5.154+ Found by Erich Friedman in 1997.		s = 5.301+ Found by David Cantrell in July 2002.		s = 3 + 4 / 3 = 5.309+ Found by Erich Friedman in 1997.

10.		11.		12.
s = 2 + 2 3 = 5.464+ Found by Erich Friedman in 1997.		s = 5 + 2 / 3 = 6.154+ Found by Erich Friedman in 1997.		s = 6.301+ Found by David Cantrell in July 2002.

13.		14.		15.
s = 4 + 4 / 3 = 6.309+ Found by Erich Friedman in 1997.		s = 3 + 2 3 = 6.464+ Found by Erich Friedman in 1997.		s = 3 + 2 3 = 6.464+ Found by Erich Friedman in 1997.

16.		17.		18.
s = 6 + 2 / 3 = 7.154+ Found by Erich Friedman in 1997.		s = 7.301+ Found by David Cantrell in July 2002.		s = 5 + 4 / 3 = 7.309+ Found by Erich Friedman in 1997.

19.		20.		21.
s = 4 + 2 3 = 7.464+ Found by Erich Friedman in 1997.		s = 3 + 8 / 3 = 7.618+ Found by Erich Friedman in 1997.		s = 3 + 8 / 3 = 7.618+ Found by Erich Friedman in 1997.

22.		23.		24.
s = 7 + 2 / 3 = 8.154+ Found by Erich Friedman in 1997.		s = 8.301+ Found by David Cantrell in July 2002.		s = 6 + 4 / 3 = 8.309+ Found by Erich Friedman in 1997.

25.		26.		27.
s = 5 + 2 3 = 8.464+ Found by Erich Friedman in 1997.		s = 4 + 8 / 3 = 8.618+ Found by Erich Friedman in 1997.		s = 4 + 8 / 3 = 8.618+ Found by Erich Friedman in 1997.

28.		29.		30.
s = 3 + 10 / 3 = 8.773+ Found by Erich Friedman in 1997.		s = 8 + 2 / 3 = 9.154+ Found by Erich Friedman in 1997.		s = 9.301+ Found by David Cantrell in July 2002.

31.		32.		33.
s = 7 + 4 / 3 = 9.309+ Found by Erich Friedman in 1997.		s = 6 + 2 3 = 9.464+ Found by Erich Friedman in 1997.		s = 5 + 8 / 3 = 9.618+ Found by Erich Friedman in 1997.

34.		35.		36.
s = 4 + 10 / 3 = 9.773+ Found by Erich Friedman in 1997.		s = 4 + 10 / 3 = 9.773+ Found by Erich Friedman in 1997.		s = 4 + 10 / 3 = 9.773+ Found by Erich Friedman in 1997.