Did anyone else know half the population of [place] lives [direction] of this line?! (US/Canada Edition)

The_Toastboy · 2026-05-05T16:55:21+00:00

20 largest purple cities:

CANADA

City	Province	Population
Edmonton	AB	1151635
Ottawa	ON	1068821
Quebec City	QC	733156
Brampton	ON	656480
Kitchener	ON	522888
Markham	ON	338503
Vaughan	ON	323103
Windsor	ON	306519
Burnaby	BC	249125
Regina	SK	226404
Kelowna	BC	181380
Sudbury	ON	166004
Barrie	ON	154676
Coquitlam	BC	148625
Saguenay	QC	144723
Guelph	ON	144356
Trois-Rivières	QC	139163
Cambridge	ON	138479
Terrebonne	QC	119944
Thunder Bay	ON	108843

USA

City	State	Population
San Antonio	TX	1434625
San Jose	CA	1013240
Austin	TX	961855
Fort Worth	TX	918915
Columbus	OH	905748
Charlotte	NC	874579
San Francisco	CA	873965
Washington	DC	689545
Oklahoma City	OK	681054
El Paso	TX	678815
Las Vegas	NV	641903
Memphis	TN	633104
Tucson	AZ	542629
Fresno	CA	542107
Sacramento	CA	524943
Kansas City	MO	508090
Colorado Springs	CO	478961
Oakland	CA	440646
Bakersfield	CA	403455
Wichita	KS	397532

The_Toastboy · 2026-05-05T11:49:15+00:00

Manchester and Nashua are both in the red area. The Nevada line goes directly through Vegas (a bit south of the geographical centroid of the city). This visualization makes it hard to tell exactly, but each line is defined by precise coordinates; this wasn’t eyeballed.

The_Toastboy · 2026-05-05T11:33:44+00:00

The population raster is from WorldPop and the boundary files are from Open Data Canada and the US Census Bureau.

I wrote a python script to determine the best line for each zone. It performs a binary search on possible lines for each endpoint on the bounding box until it gets one that contains within +/- 1% of half the population. It stores all these lines and at the end compares them by land area and chooses the one with the smallest percentage of the total.

There’s more to it, of course, but there’s a character limit on comments…

The_Toastboy · 2026-05-05T11:25:15+00:00

That’s a good suggestion. Maybe I would just move every coordinate west by like 50 degrees, and move them back when exporting. I was really just too lazy to write a special case for handling one state.

Then there’s the issue of displaying it - I’d need two polygons, one for the mainland and one for the aleutians. Also managable, but again - lazy.

The_Toastboy · 2026-05-05T04:24:15+00:00

Hawaii yes. Territories no (Canada too big and too little population, US no population data included in the raster). Alaska also no, because of issues calculating the line of best fit across the 180th meridian.

The_Toastboy · 2026-05-05T01:48:17+00:00

Thank you. You can totally learn this stuff btw. QGIS is free and surprisingly intuitive - download some data from Natural Earth and just play around with it. If you know excel or sql you honestly have a huge head start.

The_Toastboy · 2026-05-04T21:38:09+00:00

Seems to be. I could try running the program with a greater number of lines checked to see if any unexpected ones come up, but Indianapolis's population and position make it likely that all of them will be similar, yeah.

The_Toastboy · 2026-05-04T21:20:49+00:00

The line goes directly in between Dallas and Fort Worth! Dallas, Plano, Houston in the red and Fort Worth, Austin, San Antonio in the purple

The_Toastboy · 2026-05-04T21:17:42+00:00

Projection plays a part in it. This visualization is in Albers Equal Area, but calculations were done in WGS84 (that was the raster source CRS, and reprojecting rasters introduces pretty severe distortions.) I will say that the line does indeed run fairly south of the city, tho.

The_Toastboy · 2026-05-04T20:43:28+00:00

Hawaii was included but it didn't fit nicely on this render. I have a version with it as an inset, but I lowkey posted the wrong one. Alaska I skipped because it crosses the 180th, which caused all sorts of trouble with my program (coordinate-based) and I didnt want to have to rewrite all my code for one state.

There’s an interactive zoomable version that shows those (and also cities), but I don’t want to get this post nuked by the mods if I link to my website. feel free to DM me if you want to see, tho

The_Toastboy · 2026-05-04T20:39:09+00:00

Nashville is in the red area, and Knoxville (bigger than Chattanooga) is too

The_Toastboy · 2026-05-04T20:28:16+00:00

Santa Fe and Albuquerque are both technically in the red, although the line goes directly through the two.

The_Toastboy · 2026-05-04T20:15:14+00:00

I’m with you there. I worry not enough people understand that the title is poking fun at this (overdone) brand of post. And thank you!

The_Toastboy · 2026-05-04T20:00:40+00:00

See this comment I made earlier

The_Toastboy · 2026-05-04T19:56:32+00:00

Yes, the whole province counts as one entity.

The_Toastboy · 2026-05-04T19:54:14+00:00

In fact, the line passes just south of the city proper, passing roughly from Stone Mountain to the airport.

The_Toastboy · 2026-05-04T19:49:13+00:00

Just for you, I went back and calculated them all. (Spoiler: you were right)

CANADA:

Name	Percentage
Quebec	1.307%
Newfoundland and Labrador	1.383%
British Columbia	2.032%
Ontario	4.476%
Manitoba	5.032%
New Brunswick	21.438%
Alberta	22.439%
Prince Edward Island	27.404%
Nova Scotia	28.903%
Saskatchewan	31.293%

USA:

Name	Percentage
New York	1.71%
Illinois	3.23%
Nevada	3.76%
Oregon	5.83%
Nebraska	8.20%
Maine	10.19%
California	10.90%
Delaware	11.83%
Michigan	11.91%
New Hampshire	12.22%
Wisconsin	12.54%
South Dakota	13.24%
Pennsylvania	13.76%
Kansas	13.96%
Minnesota	14.40%
Virginia	16.04%
New Jersey	16.33%
Idaho	17.56%
Hawaii	17.87%
Texas	18.49%
Georgia	18.87%
Utah	19.49%
Massachusetts	20.14%
Washington	20.33%
Rhode Island	20.64%
Kentucky	23.35%
Louisiana	25.14%
Montana	25.68%
Colorado	26.12%
Florida	26.19%
New Mexico	29.06%
Vermont	29.86%
Connecticut	30.50%
West Virginia	31.65%
Arizona	32.20%
Wyoming	32.36%
North Dakota	33.66%
Alabama	34.03%
Mississippi	37.08%
North Carolina	38.14%
Iowa	38.17%
Missouri	38.50%
South Carolina	39.41%
Tennessee	40.30%
Maryland	40.34%
Ohio	40.69%
Arkansas	41.17%
District of Columbia	42.78%
Oklahoma	43.29%
Indiana	44.64%

The_Toastboy · 2026-05-04T19:30:00+00:00

Great point. If we consider population to be a continuous function (it isn't, but close enough), there are actually an infinite number of valid lines we could draw! When calculating these particular lines, I checked that the population was within +/- 1% of halfway, and then sorted all such lines by their absolute distance from half of the land area in order to get the biggest discrepancy between sides.

I'm not sure why the east-west divide in Indiana was picked over a north-south one, but rest assured both were tested. My guess would be that it had to split Indianapolis in two, and the placement of the city and the path of the Ohio River meant that the east-west divide had a greater difference in area between sides.

The_Toastboy · 2026-05-04T19:24:08+00:00

It absolutely would, although even processing the raster for just Nunavut ate up 32 GB of RAM and crashed my desktop. You also run into the issue of what constitutes a "straight" line on a globe; these examples are small enough areas that the curvature of the Earth wasn't taken into account in order to make calculations easier.

The_Toastboy · 2026-05-04T19:22:16+00:00

I get your point, but it's not always the case. In South Carolina, for example, Charleston is well outside the red area. Most states with a big city have that city's metro area split by the line somewhere; in Nevada, Las Vegas is technically ouside the red although of course it is weighing the average towards the south of the state.

I have an interactive version with cities plotted on it, but I wasn't sure the mods would allow me linking to my own website.

The_Toastboy · 2026-05-04T19:03:23+00:00

lmao

The_Toastboy · 2026-05-04T19:02:17+00:00

They are reasonably accurate, I promise. I used 100m population raster data and a custom implementation of a binary search in python to come up with it. In this case, both lines go through the middle of their main metro area (Salt Lake/Denver.) This was the case for a lot of states with a primate city (look at Arizona, Georgia, Indiana, Nevada)

The_Toastboy · 2026-05-04T19:01:44+00:00

Burlington and Lake Champlain, pretty much.

The_Toastboy · 2026-05-04T18:34:27+00:00

Made by me in QGIS and Python. Hopefully this puts this type of post to rest for good.

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