2951: Bad Map Projection: Exterior Kansas

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Bad Map Projection: Exterior Kansas
Although Kansas is widely thought to contain the geographic center of the contiguous 48 states, topologists now believe that it's actually their outer edge.
Title text: Although Kansas is widely thought to contain the geographic center of the contiguous 48 states, topologists now believe that it's actually their outer edge.


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This is the seventh comic in the series of Bad Map Projections displaying Bad Map Projection #45: Exterior Kansas.

Projection of the world from the same perspective as the comic. This uses an azimuthal equidistant projection, so distances from the center point (39°50′S 98°35′E) are correct but areas are distorted.

This comic portrays an unusual projection of a map of the contiguous United States based loosely on an azimuthal projection. Maps of individual countries are common, especially in academic settings. It is typical for such maps, which only display a limited area of the globe, to use a projection that does not severely distort the shape of the country or its internal borders, but a country that is large enough (as with the United States) will always noticeably suffer from certain distortions of at least one element chosen from distances, areas or angles. This usually occurs at its extremities (though some projections can be made more faithful to its extremities at the expense of distorting its interior).

Here, however, Randall has opted for a much different projection. Rather than placing the geographical center of the country in the middle and the borders on the outside, this map has gone the opposite direction, with the border of the US toward the center, and the geographical center of the contiguous US (Kansas) and surrounding states distorted to surround the entire map. This, understandably, results in the shape of both the national and state borders being largely unrecognizable as it effectively puts every bit of the chosen map features out towards the distorted extremities. Much of the internal area of Kansas itself (should one wish to display further internal features) may be located far beyond the comic's edges, perhaps even to infinitely far away on the projected plane.

Polar azimuthal equidistant projection, as on the flag of the United Nations, but with an "exterior Antarctica"

If Alaska and Hawaii were present in this map and represented in geographically accurate locations (as opposed to inset, as is common in many maps of the United States), Alaska would in the upper right of the empty space, between Minnesota and Washington, while Hawaii would be in the center to the right, off the coast of California. Both would be rather small, with Hawaii particularly compressed (to an extent dictated by the exact projection method used). Additionally, if all 50 states were included, the geographical center would be further to the northwest, resulting in an "Exterior South Dakota" projection.

The map in 1335: Now shows an exterior Arctic Ocean and Antarctica in the center


Ambox notice.png This transcript is incomplete. Please help editing it! Thanks.
[A distorted map of the contiguous United States with the states labeled, where the Atlantic and Pacific coasts and the Canadian and Mexican borders are located closest to the center, with there being a gray void in the middle of the map, while the central U.S. states are distributed in the edges of the panel, with Kansas being in all of the four corners of the map.]
[Caption below the panel:]
Bad Map Projection #45:
Exterior Kansas

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Seems weird that it's just the contiguous US, with "hints" about what lies within. I hope Randall will release another version with the rest of the world included. 03:20, 27 June 2024 (UTC)

Would the center be both poles and Kansas's antipode? -- 03:58, 27 June 2024 (UTC)

Including Hawaii would have been the cherry on the cake. 05:42, 27 June 2024 (UTC)

As the center of the map corresponds to Kansas' antipode (Kerguelen in the Indian Ocean https://www.geodatos.net/en/antipodes/united-states/kansas-city), Hawaii isn't really "near the center", but rather to the right of the center (in the direction of the "Pacific Ocean" tag). -- 05:58, 27 June 2024 (UTC)
Admittedly, I guessed where they would be. 06:09, 27 June 2024 (UTC)

I don't think the middle part is meant to be seen as 'water', just 'out of scope'. Jaap-Jan (talk) 07:44, 27 June 2024 (UTC)

Yeah, this is similar to a map like https://suncatcherstudio.com/uploads/patterns/us-maps/pdf-png/usa-map-states-names-color-010101.png In that map, Canada and Mexico aren't "rendered as water", they're not rendered at all, and neither are the oceans. I'm going to edit that. 13:34, 27 June 2024 (UTC)

How would the rest of the world look?[edit]

Currently the center is all water. If I understand correctly the rest of the world could be added, but how would it look? For example, would Europe and Asia cover a good part of the water or would they be tiny specs in the middle (almost making this a world map already)

My impression (without measuring/replicating) is that this is mathematically (or whatever) a gnomonic projection (which can only show half the world, anyway, even on a sheet stretching up to infinity) radially inverted. As such quite a lot of features that aren't shown ('beyond/within' the 'coastline'/borders) couldn't be, anyway, as more than half the world away. Map-centre would be the compressed singularity of the Great Circle exactly 90° off the 'centre of Kansas' that itself now exists at infinite-radius-every-angle far off the page.
Though it could just be stereographic with any negatively positioned projection origin. Instead of -1, for gnomonic, with a -2 radii origin you would get the whole surface (at infinity!) in ways that whatever you do to radially invert (probably the direct reciprocal) and otherwise scale (clearly choosing the additional 'zoom level' factor that neatly brings the Kansas border more or less into frame) to compress all offshore/over-border territories into the 'oceanic' centre. Or it could just be a useful rescale of a -2r projection of the Kansas-antipode, such that all borders of Kansas are pulled into frame.
(Regarding Hawaii, if quick googling is right about Hawaii being 3,600km from Kansas(-centre?), then that puts it at various preskewed factors towards the 'hemispherical horizon' of ~10,000km or the antipodal point at ~20,000km, before then being further squashed by the particular coordinate conversion system in use. If it's a near-side orthographic projection and, say approaching +1 radii up from the surface-tangent, then it could perhaps be 'over the horizon' in the direct projection and thus 'beyond the singularity' of the inverted-radius version.)
I'd have to mess with some map data, to be sure the existing features fit either idea of projection (or find the actual one (ab)used), but this'd probably be what I'd do, straight off the bat. And then I could apply it to extraterratorial features, also. I've got some of the necessary data and mungable code handily sitting on a machine that I am unhandily not going to next use until at least the weekend, and reimplimenting it on this tablet would mean starting from first principles again/testing/etc... ;) 09:23, 27 June 2024 (UTC)
Check out the Wikipedia article "Azimuthal equidistant projection" and scroll to "Sample azimuthal equidistant projection maps". There is an inverse example, that puts California at the center of a world map. Now imagine everything else in the "great sea" of Randall's map, using a similar projection. 13:48, 27 June 2024 (UTC)
Yay! A task for a geography teacher (i.e. me, and I'm a big fan of Randall's work with maps), and I just happen to have the right bookmarks for this kind of thing in my browser. So here's a little toy to play around with: [1] I hope my settings got preserved in the link as they should, else whoever added all those letters and numbers clearly has something to answer for! If the link works as it should it'll show you what a map of the whole wide world would look like in an Azimuthal Equidistant Projection with Kansas on the exterior. That is, I first used this Antipodes Map [2] to locate the point opposite to Lebanon, Kansas at 39°48'35"S, 81°26'39.8"E , which is quite literally in the middle of the Indian Ocean, near the islands of Saint Paul and Nouvelle Amsterdam (which, incidentally, belong to France and are mainly known for being as far away from anything as you can possibly get on this planet*) and then set the centre of the worldmapgenerator.com map approximately there. It's not a very precise tool, but it'll do - it's precise enough for me to use in lessons anyway. Surprisingly, you actually get a more or less usable map for much of the world (if you're not too fussy or trying to navigate with it or anything), except only for North and Middle America. :D PaulEberhardt (talk) 16:04, 27 June 2024 (UTC)
* At least, you can say that if you happen to land there, you're really not in Kansas any more. ;) PaulEberhardt (talk) 16:30, 27 June 2024 (UTC)
Oh, I really like map stuff, but: "This site uses cookies to improve the results of our bakery. With your acceptance we can add more honey, sugar and flour to improve the website. [Accept]". Only "[Accept]", no other options (even long-winded 'deselect "things we suggest are important" options that I might disagree with'). I really don't like that. And then it also offers to install an App, apparently... Oh, website builders, just because I'm currently on a mobile device, it doesn't mean I'm eager to "app everything"; entirely the opposite, perhaps! Yeah, I know script/cookie blockers or specialist browsers exist to avoid these things, but... Anyway, nice to see a geography teacher taking it seriously, even if I've got my own conflicting issues in picking up on what you've found. (Behind/before the popup stuff, it truly looked interesting. Don't know if there's a legit way to get a screenshot of it. Don't break any Ts&Cs in doing so!) 17:03, 27 June 2024 (UTC)
The joke is that worldmapgenerator doesn't store ANY cookies. Meanwhile the site you are posting from stores 63 kB of browser data just visiting the homepage. Quantum7 (talk) 21:08, 27 June 2024 (UTC)
Hmm, I get the "This site uses cookies to improve the results of our bakery." too. If they don't use cookies, then they shouldn't have that.
I am actually on a desktop system, I can probably go in there and remove the "don't do anything until the Accept is clicked" popover without clicking on the popover, and even check out what it tries to store, or doesn't... I'm not even overly paranoid about these things, but I agree with above poster that it's bad form. Especially if it's a joke (no reason to suppose it is).
Yeah, I'll accept Cookies if essential, but often they aren't, so it's not even a very good joke to make. Maybe they do just do everything in URL-encoded/GET data. It's my own prefered method, to make fully transparent GET data on websites I use (barring anything that needs to be POST-submitted), and if I ever use cookies it's a single own-site-only cookie for session control, not the mass of "Legitimate Use" (as if!) items.
Have you ever gone and looked in the list? (Assuming the "Do you accept cookies" doesn't do a "Yes, accept all"/"No, reject all (inessential)" and gives you the 'option' to painstakingly turn off half a dozen "default cookie sets".) It's frightening how many 'interested parties' are potentially getting info (dozens to hundreds, at a time). And, realistically, I'm not sure I even believe that by selecting 'off' on that kind of dialogue that I'm actually not being Cookified just as much as if I accidentally clicked on the prominent "Accept All".
Sorry, the above comment just resonates with me, too. Decided I had to vent a bit. 23:51, 27 June 2024 (UTC)
I checked the cookies it uses, none of them contain any sort of tracking identifier. It stores the selected language, whether you accepted cookies, and for which screens of the wizard you've seen the tutorial screen. Zmatt (talk) 03:14, 28 June 2024 (UTC)
Whoa! Sorry about that. I had my browser set to block trackers and automatically delete all cookies upon closing it, so I tend not to pay attention to this kind of thing very much (I probably should anyway, so most of the time I reject everything just in case), and my malware detector thingies didn't sound the alarm. However, I have to agree this is really bad form of them and does look a bit fishy. Again, sorry. It's 'cause I'm dumb (see above) ;). PaulEberhardt (talk) 18:11, 30 June 2024 (UTC)
Thanks for the wonderful link. I suggest we include an image from this in the article. Your settings were preserved nicely. Given how little of north America is visible, I suspect that Randall must have used an even more extreme azimuthal protection than the equidistant one to shrink the center. Quantum7 (talk) 21:18, 27 June 2024 (UTC)
Added File:Exterior_Kansas_Azimuthal_Projection.pngQuantum7 (talk) 07:53, 28 June 2024 (UTC)

I have made an image adapting the comic to add the rest of the world if anyone was curious about it. I tried adding to the explanation but I don't have the permissions for such. If anyone wants it, feel free to grab it and put it here, since it's a derivative of Randalls work it is licensed as Creative Commons too. -- avsa


Adding an image?[edit]

Is it possible to add an image to the description? I'm looking at the Wikipedia article "Azimuthal equidistant projection" and the "external Antarctica" map is relevant. https://en.wikipedia.org/wiki/File:Azimuthal_equidistant_projection_SW.jpg Thanks! 13:43, 27 June 2024 (UTC)

You could use a variation on [[File:Azimuthal_equidistant_projection_SW.jpg|300px]] maybe. Add align/wrap options, as necessary, and use a size that seems to work. Remember to try it with Preview, before you're submitting it for real, lets you fine-tune to your liking without spamming the edit-history. Doesn't need (explicit) uploading to the wiki, this way. 17:11, 27 June 2024 (UTC)
I added File:Exterior_Kansas_Azimuthal_Projection.png. Is that what you had in mind? It's an equidistant projection; I haven't found a tool that lets you change the projection radius to better match Randall's projection.Quantum7 (talk) 07:51, 28 June 2024 (UTC)

Should Now [3] be mentioned? Same type of projection. 20:51, 27 June 2024 (UTC)

Actual azimuthal projection centered at Kansas' antipode[edit]

It turns out that, this being the internet, there's an actual tool for generating azimuthal projections ([4]). For the curious minds out there, here's what the exterior Kansas would look like as an actual azimuthal projection: [5]. 21:05, 27 June 2024 (UTC)

Here's one where the conformal lines are still latitude and longitude, from https://maps.ontarget.cc/azmap/en.html which releases it as CC-BY-SA if someone wants to upload it. 01:24, 28 June 2024 (UTC)
These one's are great, too. Thanks for the links! PaulEberhardt (talk) 18:11, 30 June 2024 (UTC)

Someone please call out the homage to Frank L. Baum. Dorothy started her trip from Kansas, house and all. She landed in the fabulous Land of Oz, a rectangle surrounded by the deadly desert. This map shows Kansas surrounding the rest of the USA. (My screen name's Trelligan, don't blame anyone else for this.) 12:18, 28 June 2024 (UTC)

😁 PaulEberhardt (talk) 18:11, 30 June 2024 (UTC)

New Flerf lore just dropped. RegularSizedGuy (talk) 15:54, 28 June 2024 (UTC)

Me being a geomatician and having a couple of friends who are map projection nerds, we had a short discussion (https://mastodon.social/@EvenRouault/112688667438256248) and I ended up implementing a web map version of a Oblique Stereographic map in the style of this: https://ivan.sanchezortega.es/2024-06-exterior-kansas/ . You'll notice that a Oblique Stereographic projection does create a coastline that matches the one in the comic much closer to the Azimuthal Equidistant projection (and therefore, I'll hypothesize that Randall used a compromise projection). I'd like to add an image of my map to this explanation, but I seem to lack permissions. Ivansanchez (talk) 14:47, 29 June 2024 (UTC)

Wow! That is so cool. 05:48, 3 July 2024 (UTC)