The Mercator Projection

Ever wondered why we are bound to the usage of rectangular maps to represent Earth, and not any other weird shape? Unfortunately, I’m not the first. Gerardus Mercator is. 

Annoyed by the spherical inconvenience of carrying a map of Earth, Mercator, in 1569, introduced a rather convenient method of representing a map. The one dumped in your school files: A rectangular map. And there’s a pretty neat logic behind this brilliant substitute.

Consider a sphere whose diameter is equal to the height of a cylinder. Evolve the equations for the total surface area of the sphere and the lateral surface area of the cylinder in terms of the sphere’s radius. You’ll notice the equations tally. Also, when unwrapped, the lateral surface area of the cylinder matures to provide a rectangle. Thus, a sphere’s area is that of a rectangle! Bingo, your map is on the go, in perfect harmony with the sphere, disregarding any extensions to patch the proportionality.

… If you were too lazy to visualize
Unwrap the Earth!

Highlights? The Mercator projection is erroneous. Why? Take a look at a globe’s pole. The longitudes converge into a speckle. Visualize the globe unwinding to frame the rectangle. The longtitudes no longer have a speckle to unite. They spread out to keep the rectangle’s length consistent. Distortions occur. And the area of regions near the poles exaggerate while those nearing the equator minimize.

Greenland’s area explodes 14 folds. Alaska mushrooms its stretch five folds. Check out the Mercator Puzzle and manipulate the distortions yourself.

Thankfully, it has not triggered the distortion of Earthlings; it might!

~Shamoil Khomosi


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