## Hip to be square: American edition

Earlier this year, programmer David Barry released a fun estimation of how rectangular each country’s borders are.

Ignoring some outlying islands (and archipelago nations whose shape isn’t approximated by any shape) it turns out that between 60 and 95 percent of national borders fit within that blockiest of shapes.

But many national boundaries have been set by things such as “coastlines” or “mountains” or “colonial compromises.” Much of the United States — especially west of the original 13 colonies — has been set by more geometric criteria, such as lines of latitude and longitude.1 (For more information, Mark Stein’s “How the States Got Their Shapes” is a quick, breezy read.)

So I modified Barry’s code to estimate how well each state can be approximated by a rectangle. To score well, a rectangle has to include as much of the state’s land as possible — while excluding as much area outside the state as possible. (This account for why California, a sort of angled box shape, scores so poorly. You can easily draw a rectangle that takes in most of California — but you’ll also get a bunch of not-California in the rectangle, too.)

As it turns out, U.S. states ARE somewhat more rectangular than world countries. The median rectangularness index for countries in Barry’s estimations was 0.843 (on a scale from 0 to 1). The median U.S. state, by contrast, is 0.861. Setting aside Alaska (which the code just couldn’t handle), the range runs from Hawaii’s 0.581 to nearly perfect Wyoming, 0.999.

After the jump, view the data for yourself — plus keep scrolling for an even deeper dive into the rectangularness of U.S. counties.

Rank State Index Rectangle-ness
50 Hawaii 0.581
49 California 0.622
48 Michigan 0.699
47 Maryland 0.715
46 New York 0.761
45 Virginia 0.767
44 Delaware 0.768
42 Idaho 0.778
43 Florida 0.778
41 Louisiana 0.812
40 Massachusetts 0.816
39 North Carolina 0.83
38 New Hampshire 0.837
37 Kentucky 0.848
36 South Carolina 0.852
35 Vermont 0.854
34 Rhode Island 0.855
33 West Virginia 0.86
32 New Jersey 0.864
31 Texas 0.866
30 Maine 0.871
29 Missouri 0.884
27 Minnesota 0.887
26 Wisconsin 0.888
25 Illinois 0.889
24 Georgia 0.89
23 District of Columbia 0.902
22 Ohio 0.906
21 Tennessee 0.907
20 Oklahoma 0.914
18 Washington 0.921
17 Mississippi 0.924
16 Arkansas 0.932
15 Alabama 0.935
14 Connecticut 0.937
13 Indiana 0.94
12 Utah 0.941
11 Iowa 0.942
10 Montana 0.947
9 Arizona 0.953
8 Oregon 0.956
7 New Mexico 0.972
6 Pennsylvania 0.98
5 South Dakota 0.981
4 North Dakota 0.986
3 Kansas 0.988
1 Wyoming 0.999

(How does it work? The code basically draws a rectangle, calculates how good a fit it is, then draws another one and compares. It keeps doing this until each iteration no longer makes improvements.)

Things get even squarer when we zoom in one level: to the counties. Again, particularly west of the Appalachians, American political subdivisions have often been often drawn based on geometry rather than geography or culture.

Indeed, while the typical state scored 0.861 on the rectangularness scale, the typical U.S. county scores a 0.907. The overall scale runs from 0.297 to 1.000, with almost 94 percent of counties being at least 80 percent rectangular.

There’s more than 3,000 counties and county-equivalents in the United States, so I won’t share all of them here. But here you can see each state’s average county rectangularness:

The state with the most rectangular counties is Kansas, with an average of 0.981. The state with the least rectangular counties is, unsurprisingly, Hawaii, with 0.771. My current home state of Minnesota is 11th-best with 0.927; my former home of South Dakota is fourth with 0.951. View a full list here.

Finally, a special gift to Minnesotan readers: a breakdown of the rectangularness of each of Minnesota’s 87 counties.

A number of them are almost 100 percent rectangular. Even Minnesota’s least-rectangular county (Polk, in northwestern Minnesota) is about 75 percent rectangular, far better than California or Michigan, or Laos or Denmark.

(I know enough, however, not to venture any opinions on what this rectangularness data says about which counties are the worst places to live.)

Take a look!

Rank County Index Rectangle-ness Location
87 Polk 0.765
86 Big Stone 0.776
85 Lake of the Woods 0.814
83 Cook 0.817
83 Traverse 0.817
82 Scott 0.818
81 Yellow Medicine 0.819
80 Cass 0.822
79 Nicollet 0.832
78 Renville 0.84
77 Morrison 0.855
75 Brown 0.857
75 Winona 0.857
74 Chisago 0.859
73 Goodhue 0.86
72 Itasca 0.862
70 Pine 0.864
70 Redwood 0.864
68 Beltrami 0.866
68 Dakota 0.866
67 Chippewa 0.885
66 Sherburne 0.887
64 Hennepin 0.888
64 Carver 0.888
62 Wright 0.893
62 Wabasha 0.893
60 Lac Qui Parle 0.898
60 Mille Lacs 0.898
59 Sibley 0.901
57 Lake 0.904
57 Red Lake 0.904
56 Anoka 0.907
54 Isanti 0.909
54 McLeod 0.909
53 Wilkin 0.91
52 Meeker 0.911
51 Olmsted 0.915
50 Stearns 0.916
49 Cottonwood 0.922
48 Rice 0.925
47 Kanabec 0.926
46 Le Sueur 0.936
45 Washington 0.937
44 Roseau 0.946
43 Saint Louis 0.947
42 Ramsey 0.951
40 Koochiching 0.952
40 Benton 0.952
39 Aitkin 0.96
38 Blue Earth 0.961
37 Clearwater 0.97
36 Kittson 0.972
35 Crow Wing 0.975
33 Pennington 0.98
33 Clay 0.98
32 Houston 0.983
31 Otter Tail 0.986
29 Grant 0.988
29 Stevens 0.988
28 Mower 0.989
26 Swift 0.991
23 Douglas 0.992
23 Pope 0.992
23 Lincoln 0.992
17 Marshall 0.993
17 Norman 0.993
17 Hubbard 0.993
17 Becker 0.993
17 Todd 0.993
17 Lyon 0.993
15 Carlton 0.994
15 Kandiyohi 0.994
8 Pipestone 0.997
8 Murray 0.997
8 Steele 0.997
8 Nobles 0.997
8 Jackson 0.997
8 Fillmore 0.997
8 Waseca 0.997
4 Mahnomen 0.998
4 Dodge 0.998
4 Watonwan 0.998
4 Rock 0.998
1 Martin 0.999
1 Faribault 0.999
1 Freeborn 0.999
1. An infamous French Revolution proposal to divide France into square départements would have given America a run for its money.