Minimizing the Ratio of
Maximum to Minimum Distance

The following pictures show n points in the plane so that the ratio r of maximum distance (shown in red) to minimum distance (shown in blue) is the smallest known.

2.

r² = 1
Trivial.

3.

r² = 1
Trivial.

4.

r² = 2
Trivial.

5.

r² = (3 + √5) / 2 = 2.618+
Trivial.

6.

r² = (5 + √5) / 2 = 3.618+
Trivial.

7.

r² = 4
Trivial.

8.

r² = 1 / (2 - 2cos(π/7)) = 5.048+
Trivial.

9.

r² = 6.600+
Found by David Cantrell
in February 2009.

10.

r² = 7.713+
Found by David Cantrell
in February 2009.

11.

r² = 8.222+
Found by David Cantrell
in February 2009.

12.

r² = 5 + 2√3 = 8.464+
Found by David Cantrell
in February 2009.

13.

r² = 9.930+
Found by David Cantrell
in February 2009.

14.

r² = 10.994+
Found by David Cantrell
in February 2009.

15.

r² = 12.038+
Found by David Cantrell
in February 2009.

16.

r² = 12.890+
Found by David Cantrell
in February 2009.

17.

r² = 14.090+
Found by David Cantrell
in February 2009.

18.

r² = 14.725+
Found by David Cantrell
in February 2009.

19.

r² = 8 + 4√3 = 14.928+
Found by David Cantrell
in February 2009.

20.

r² = 16.734+
Found by David Cantrell
in February 2009.

21.

r² = 17.774+
Found by David Cantrell
in February 2009.

22.

r² = 19.053+
Found by David Cantrell
in February 2009.

23.

r² = 20.039+
Found by David Cantrell
in February 2009.

24.

r² = 20.960+
Found by David Cantrell
in February 2009.

25.

r² = 22.121+
Found by David Cantrell
in February 2009.

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