Mercator's projection

Mercator's projection was developed in 1569 by the Flemish cartographer Gerardus Mercator. It is a mathematical projection and is orthomorphic: shapes of small areas are kept true.

The book's construction (world, 1 : 250,000,000, interval 15°): the reduced earth's radius is 1 inch; the equator is 2πR, about 6.28 inches, divided into 24 parts. Each parallel is drawn at a distance taken from a table, which grows towards the poles: 15° at 0.265", 30° at 0.549", 45° at 0.881", 60° at 1.317", 75° at 2.027".

Properties:

• Parallels and meridians are straight lines at right angles.
• Every parallel is as long as the equator, so scale is true only along the equator. (The 30° parallel, for instance, is drawn 1.154 times too long.)
• The spacing between parallels increases towards the poles, so that the stretch north-south matches the stretch east-west: that is how shape is kept.
• A straight line between two points is a rhumb line (loxodrome), a line of constant bearing: a ship can follow one compass direction along it.
• The book also lists it as 'azimuthal'; strictly, it keeps local angles and rhumb-line bearings, not true directions from one centre.

Limits: scale is greatly exaggerated in high latitudes, so countries near the poles look far too big: Greenland looks about as big as the USA, though it is much smaller. The poles cannot be shown, because the parallel spacing grows without limit.

Uses: world maps and atlases; navigation (sea and air routes); and world patterns of drainage, ocean currents, temperature, winds and rainfall.

From the video: the teacher points out that the great circle route, though curved on a Mercator map, is actually the shortest, which is why long flight routes look curved on such a map; and that a version of Mercator (Universal Transverse Mercator, UTM) is widely used in GIS.

Example (new): on a Mercator map, Africa and Greenland can look roughly similar in size, but Africa is about fourteen times larger; an equal-area map would show the true difference.