World Map

A couple of weeks ago I saw a one man show about Buckminster Fuller. Great show, talked about the complete man. It got me thinking about maps of the world again. I never liked the standard maps of the world that are displayed in classrooms. As my teachers pointed out the tropical regions are fairly well depicted, but as you get closer to the poles, the land forms become much more distorted. Greenland (836,109 sq mi) is actually about as big as Mexico (761,606 sq mi). It is not bigger than China (3,704,427 sq mi).

Standard Horribly Distorted World Map

At one point I was playing with regular polyhedrons (icosahedron, dodecahedron) and I got to thinking that maybe this would be a good way to make a better world map.



Icosahedron is made of 20 equilateral triangles. Dodecahedron is made of a dozen regular pentagons.



Then I found out that Buckminster Fuller had already done that, so I ordered a copy of his map. It is an interesting exercise, but I can see why it never caught on. While it does portray the continents (and Greenland) with very low distortion, the cardinal directions (North, South, East and West) are somewhat randomized. One of things I learned in school was that the conventional way to layout a map is to have North at the top, South at the bottom, East to the right and West to the left. Bucky's map does not do this, which makes it a little hard to use. So back to the drawing board.

Buckmister Fuller's Dymaxion Map

After considerable thought and some experimentation, I came up with what I think is a superior layout for a world map. I even went to the trouble to write it up and send it off to a local map maker. Nothing came of it.

I talked to my friend Dennis about some of these ideas after the show. Last week he sends me a link to a website that has more world map projections than you can shake a stick at. Some of them are even similar to mine.



Of course none of them are as good as mine. Just keep listening to me, I will show you the one true way. I wish I had a drawing I could show you, but producing a map is time consuming. Perhaps I will scan my one paper drawing and post it here.

My idea is to start with a cylinder. The diameter and height are equal. The axis of the cylinder coincides with the axis of the Earth. Scribe the tropics on the cylinder wall. Scribe the arctic circles on the circular top and bottom of the cylinder. Now cut bevels around the top and bottom edges using the tropics and the arctic circles as guides. Project the surface of the Earth onto this three dimensional surface. Now with some judicious cutting, and little bit of fudging, we can unwrap this object and spread it onto a flat surface. Orientation is (mostly) preserved, or at least apparent. Distortion is low, and land masses are contiguous.

Update September 2016 replaced missing picture.