Map Projections Explained

Correction: The azimuthal equidistant projection is actually defined by θ = a and r = 90° - b. I got b mixed up with phi.

This video was made for 3blue1brown's summer of math exposition contest. It was selected as one of the top 100, and that has really helped kickstart my channel, so a huge thank you goes out to 3blue1brown.

Note: If the title changes, it's because I'm testing out different video titles to see what works the best.

In this video, I explain map projections: what they are, how they work, and the math behind them. This video connects 2 of my favorite subjects: math and geography. If you want to do further research, this wikipedia page is very helpful:

The images of each projection come from that page, and are made by Daniel R. Strebe.

Chapters:
0:00 Intro
0:41 The Problem
3:37 Equirectangular Projection
7:15 Literal Projection
9:49 Mercator Projection
18:51 Sinusoidal Projection
21:24 Lambert Equal Area Projection
23:33 Azimuthal Equidistant Projection
24:30 Compromises
29:30 Perspectives
31:21 Conclusion

[PrimalPeashoter]

I kill for anything geography in-depth without unecessary bullshit and to me you pulled it off perfectly. Concise.

I'm saving this in my internet gems folder

[bettercalldelta]

Lol I was going to comment about flat earthers claiming the earth is the Azimuthal projection but then you said it. Awesome video btw

[ValkyRiver]

Remember: whenever you look at a globe, you are actually seeing a perspective projection of it

[error.]

"You might think math and [insert literally anything] are [not connected], but they are more connected than you think" true.

[angelradness]

How does this channel only have less than 2000 subscribers? This is fantastic Level of presentation for such a low subscriber channel. Great job!

[HelmutNevermore]

I like the azimuthal equidistant projection, its only flaw is that it's centered at the North pole, whereas it should be centered at the point that the world revolves around - which is, of course, me.
Joking aside, such map centered at any given point of particular interest may distort shapes and areas and directions and distances between two random points on the map, but it tells you accurately how far things are from you and in which direction you should go to reach them. What else could you possibly want from a map?

[zyxw]

Web maps are a use case for Mercator that it (obviously) wasn't designed for, but suites well — its conformal and orientation-preserving properties mean that you can have a map where you can zoom in at any point without reprojecting, all while maintaining directions and shapes.

[andrewchapman]

Actually needed a map for a project that didn't distort distances or shapes, and came back to this video for a recommendation! I'll have to add arrows so I don't forget which bits connect where, but Dynmaxion's the map for me!

[swagatochatterjee]

The Kavrayskiy is way way simple to compute without scarificing loads of quality. That's huge!!

[borja]

Great job, I wish I had found a video like this years ago, when I first tried to understand about the Mercator projection. There were some Interesting factshere, and I think you got a nice balance between the rigour/math and a good pacing.

[rvamark]

Outstanding documentation of map projections, with a bit of history thrown in. This is the best explanation of a very complex subject that I have ever seen. Thank you for making it.

[GigueBits]

I remember I had a toy map which was a "can" projection instead of a cylindrical projection: there was a central stripe in cylindrical projection, but the poles were projected separately onto circles that you could rotate across the top and bottom edges of the map.

I wonder how all these maps would look if you could rotate the earth before projecting. For one, if you rotate the earth longitudinally by 180 degrees you automatically avoid eurocentrism. But a projection of a latitudinally rolling earth would also be fun to watch.

[dcterr]

Excellent comprehensive discussion of various types of map projections and their advantages and disadvantages! Besides being a mathematician, I've always loved geography as well as cartography. I already knew most of the mathematical formulas for these map projections, but I never thought too much about the overall advantages and disadvantages of each one, and I think you nailed this part! And I also agree for the most part with the scores you gave each one. Great job!

[ckq]

I've always been fascinated by map projections, but never found any resource with explanations about the math of it. Great video

[DialecticRed]

My favorite map projection is the Peirce Quincuncial projection. I think it is potentially the best map projection of the earth because even though distortion exists, it is relegated to relatively insignificant areas (all in oceans), and it has the great property that it can tile the plane making it a perfect fit for spherical geometry in 2d video games, working in a similar way to the naive approach of teleportation on either side to create a torus. It is also just very aesthetically pleasing imho

[FreyrDev]

I always love to see videos on map projections, so this is great, I need more places to spread the word of our lord and saviour the Kavrayskiy VII Projection lol

[sinox]

Keep doing that good videos! I personnally think this channel is one of the best channels in all YouTube, featuring all of the interesting subjects ever. Great job! I love your videos!

[Chitose_]

*I'VE BEEN WONDERING ABOUT ALL OF THIS FOR SO LONG TYSM!!!!*

[ocamlmail]

Probably the best video on this topic I've seen so far, thank you very much!

[Kostyurik]

I love Peirce quincuncial map projection the most, it is super aesthetically pleasing