We've been looking at map projections for my masters course and I continue to be blown away by how embedded mathematics truly is in our every day lives. As a self-identified directionally-challenged individual, geography and anything like it is to be avoided at all costs. I find myself at my wit's end now and have to admit that even maps hold a lot of mathematically intriguing ideas that are worth exploring. The course I'm taking now is called "Math for Global Citizens", offered at the University of Waterloo to MMT students, taught by Judith Koeller and is arguably one of my favourites in the program.
The problem of the "flat earth" has been around for centuries. It is believed that as early as the year 354, pre-medieval scholars asserted that the earth was in fact spherical (University of Waterloo). The problem for map-makers, then, is to find a way to depict a spherical object on a 2D surface, and this is turns out to be an impossible task. Take a look at the animation below for what's called a "Myriahedral projection" developed by Jack Van Wijk from the Netherlands.
The idea behind a "Myriahedral projection" is to split the earth up into polygons, thousands of them, in order to preserve both shape and size of major land masses or bodies of waters (see article here). Map projections have not always been so advanced however.
In trying to depict a spherical surface onto a 2D plane, one can try to preserve distances, shape, areas, or shortest distances between points by straight lines. It is impossible to have all these desirable properties in one map. For instance, the Mercator projection map is the one that we are probably all most familiar with as it preserves angular distances, making it easy for navigation, but it drastically skews areas the further away the land masses are from the equator. See this true size (thetruesize.com) comparison below, showing how large the continent of Africa actually is compared to the US, China and India:
On that note, I would highly recommend checking out thetruesize.com and just playing around.
Here's another great video explaining "Why all world maps are wrong" that was recommended to me by Mr. Schwartz, a geography teacher and the humanities Department Head at my school.
International math educator who writes, occasionally.