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
28	Nevada	0.884
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
19	Nebraska	0.918
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
2	Colorado	0.998
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
27	Wadena	0.99
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