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Earth is not flat. So, representing it on a flat surface can be challenging and always requires compromises.

Hosted by: Hank Green
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Sources:
http://www.users.miamioh.edu/shermalw/honors_2001_fall/honors_papers_2001/pettita_2001.html
http://www.icsm.gov.au/mapping/map_projections.html
http://nationalgeographic.org/activity/investigating-map-projections/
http://www.progonos.com/furuti/MapProj/Normal/ProjCyl/ProjCEA/projCEA.html
http://xkcd.com/977/
http://www.businessinsider.com/mercator-projection-v-gall-peters-projection-2013-12?r=US&IR=T&IR=T
http://www.winkel.org/other/Winkel%20Tripel%20Projections.htm

Images:
https://commons.wikimedia.org/wiki/File:AnAlbumOfMapProjections.pdf
https://commons.wikimedia.org/wiki/File:Mercator-projection.jpg
https://commons.wikimedia.org/wiki/File:Mercator_projection_SW.jpg
https://ccsearch.creativecommons.org/image/detail/lGQeoEbPt2fwAzpFyA03Aw==
https://commons.wikimedia.org/wiki/File:Tissot_mercator.png
https://commons.wikimedia.org/wiki/File:Lambert-cylindrical-equal-area-projection.jpg
https://commons.wikimedia.org/wiki/File:Cilinderprojectie-constructie.jpg
https://commons.wikimedia.org/wiki/File:Tissot_indicatrix_world_map_Lambert_cyl_equal-area_proj.svg
https://commons.wikimedia.org/wiki/File:Winkel-tripel-projection.jpg
https://commons.wikimedia.org/wiki/File:Aitoff-projection.jpg
https://commons.wikimedia.org/wiki/File:Equirectangular_projection_SW.jpg
https://commons.wikimedia.org/wiki/File:Tissot_indicatrix_world_map_Winkel_Tripel_proj.svg
https://commons.wikimedia.org/wiki/File:Dymaxion_2003_animation_small1.gif
https://commons.wikimedia.org/wiki/File:Fuller_projection_with_Tissot%27s_indicatrix_of_deformation.png
https://commons.wikimedia.org/wiki/File:Map-of-human-migrations.jpg
https://commons.wikimedia.org/wiki/File:John_Newton_and_William_Palmer_SLNSW_globe_1782.jpg
Hank: The Earth is not flat, no matter what you might see people saying on twitter. And it turns out that it’s pretty tricky to make the world flat.

If you draw a map of Earth on a flat sheet of paper, you’re going to end up making some parts bigger, or smaller, or shaped wrong. It’s like trying to flatten an orange peel. You just can’t do it. So when you create a map, or even when you decide which map you want to use, you have to make a choice: which aspects of the world do you want to distort?

You have lots of different options, depending on what you want to do with your map. The type of map called the Mercator projection, for example, is famous because all its shapes are accurate. It’s made by cutting the globe into wedges along the meridians, the lines that run between the North and South Poles.

Then you flatten out those wedges. But once they’re flattened, the tips of the wedges are no longer touching, and you’re left with gaps in your map. So to fix this problem, so you have to stretch the tips of the wedges horizontally.

But if you’ve ever tried to stretch a photo in only one direction, you know that that seriously messes with the way things are shaped. To compensate, you have to stretch the tips of the wedges vertically, too. If you do it just right, then the map will have something called Constant True Direction.

That means that if you draw a straight line between any two points on a Mercator map, it’ll give the same direction as a compass would in real life — a feature that’s super useful for navigators. Which is why the Mercator projection’s original purpose was to help navigators figure out where they were going. These days, the Mercator map is also popular among navigation apps like Google Maps or websites like Mapquest. How old are you? Are you old enough for that?

See when you’re trying to plot a route, it’s really important to know which direction you’re supposed to be aiming for. Plus, the Mercator map’s stretching doesn’t make too much of a difference over short distances. But the downside is that when you look at the map as a whole, the North and South Poles look much larger than they are in real life. Like, according to the Mercator, Greenland looks about the same size as Africa. But Africa is actually nearly 14 times the size of Greenland!

There are maps that show everything with the right size, like Lambert’s Cylindrical Projection. But you have to compromise a lot on shape. This type of map is made by placing the globe in an imaginary cylindrical tube of paper. Anything on the globe that lines up with the cylinder gets projected onto the paper. The biggest distortion happens at the poles, where you end up with a lot of horizontal stretching and some vertical squishing.

But it all works out in the end — the map shrinks in the vertical direction just enough to compensate for the stretching in the horizontal direction. So the total area is actually preserved, and everything is the right size. It’s just shaped wrong.

Other maps go for a nice compromise between shape and size. Like the Winkel Tripel Projection, which is what National Geographic use in their maps. The projection was developed by German cartographer Oswald Winkel in 1921, and the “Tripel” in the map name is not a last name, it’s just how you spell “triple” in German.

It refers to the 3 things Winkel wanted to compromise between: area, distance, and direction. To do that, he just averaged out two other map projections. One was the Aitoff projection, which tries to minimize distortion by bending all the latitude and longitude lines and turning the world into a big curvy oval. The other was the Equirectangular projection, which keeps the latitude and longitude lines very straight and spaced out evenly so the world becomes a rectangle.

When Winkel combined these projections, he ended up with a map that’s rounded at the edges, with slightly curved latitude and longitude lines. Because of the rounded edges, the poles don’t need to be stretched out so much, and the curving of the latitude and the longitude lines helps correct shape and size. It also adds a slightly spherical effect, which helps show that the world isn’t flat.

And then there are some extra weird-looking projections out there: The Dymaxion projection basically reshapes the globe so it looks like a 20-sided die, then strategically cuts up the die in places where there’s just ocean and no continent. It’s bad at navigation, though, because some things that are actually quite close to each other get separated by huge areas of not-map. But because the Dymaxion ends up making the land look like one continuous strip, it helps show how interconnected the world’s land really is, and it’s sometimes used to plot early human migration.

If you’re looking for something that’s truly accurate, though, then the best map of the world you can get is a globe. No matter how hard you try, you just can’t make Earth flat. It’d be really nice if everybody agreed with that sentence.

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