Greenland and a Grapefruit
When she was in elementary school, my daughter brought home a map of the world. Her homework assignment was to color in all of the continents, and a list of these was provided. In the process, she asked why Greenland, which was obviously much bigger than Australia, was not on the list to be colored in. Possible answers flooded my mind (Is it because Greenland is not considered important politically? No, because Antarctica is a continent, and no one lives there...). Stuck, and thinking this was a very good point, I said to her, “Well, let’s find out.”
We looked up “continent” in the Encyclopedia Britannica and found “Continent: One of seven large continuous masses of land: Asia, Africa, North America, South America, Antarctica, Europe, and Australia (listed in order of size). Europe and Asia are sometimes considered a single continent, Eurasia.” Good enough, but this did not explain the Greenland problem.
We looked up the size of Greenland (2,130,800 SQ. KM) and Australia (7,682,300 SQ KM). I tried to explain that in reality, Australia is nearly four times the size of Greenland, and now my daughter was getting upset. Why, if Australia was so much bigger, would the map her teacher had given her be so wrong? How could a school do that?
My daughter was becoming increasingly teary: if Greenland isn’t that big, why did they make it so big? I had to explain to her that she was right. The map was wrong, and that I was truly sorry that she, (and everyone else) was given this wrong piece of information. Somehow the issue of map distortion came into my mind. I tried to explain the problem of trying to represent a sphere on a flat piece of paper. “They want to show you a picture of the world, but it’s hard to do on a flat piece of paper, so when they try, some things end up looking bigger than they really are.” This wasn’t really helping-it was as if her brain was short-circuiting.
Finally I got a different idea, and I sat her down with me at the kitchen table with a pen, a nickel and a grapefruit. The grapefruit was our model of the Earth, I explained, and I drew an equator around the middle. Next I traced the nickel with the pen, drawing perfect circles near the top, the “North Pole” of the grapefruit, to approximate where Greenland is. Then I drew one near the “equator” and finally in the “Southern Hemisphere” where Australia is.
I explained to my daughter that we were now going to try to take the skin off of the grapefruit and make it flat. I cut down the meridian lines from pole to pole, allowing the skin to stay connected around the equator, except on one meridian line. Finally I removed the skin and flattened it out on a piece of paper. There were significant spaces between the three segments of skin where the northern hemisphere nickel had been traced. I showed my daughter how, in order to make the Mercator projection map she had, they just filled such spaces in, creating a shape far bigger than the original nickel. That’s why Greenland looked much larger that it actually is.
I now know that my daughter, at around age ten, had discovered what cartographers call “the Greenland problem,” the distortion of size presented on a Mercator projection map. The Mercator projection map was developed in 1569 and is notorious for making Greenland and Africa, which is eleven times larger, look about the same size. Today, more than four hundred years after the development of this highly distorted map, it is still being used in schools. What’s worse, in this particular case, it was being used for an assignment which specifically dealt with the size of Earth’s land masses.