Elements and classification

Elements of a map projection:

• Reduced earth: a model of the earth at a reduced scale, from which the graticule is drawn. (In constructions, its radius is the earth's radius, about 640,000,000 cm, divided by the scale's denominator.)
• Parallels of latitude: circles parallel to the equator, of unequal length, from 0° to 90° N and S.
• Meridians of longitude: semicircles from pole to pole; Greenwich is taken as 0°.
• Global properties to be kept: distance, shape, area and direction.

Four ways to classify projections:

• Drawing technique: perspective (drawn with a source of light, projecting the graticule onto a developable surface), non-perspective (no light or shadow used), and conventional or mathematical (worked out from formulae).
• Developable surface: a surface that can be flattened without shrinking, breaking or creasing. A cylinder, a cone and a plane are developable; a globe is not. So projections are cylindrical, conical or zenithal (a plane touching the globe at a point, usually a pole). By where the surface touches: normal or equatorial (at the equator), oblique (between the equator and a pole) and polar (at a pole).
• Global property: no projection keeps all four properties at once. Equal-area (homolographic) projections keep areas true; orthomorphic (true-shape) keep shapes, usually at the cost of area; azimuthal (true-bearing) keep directions from the centre; equidistant (true-scale) keep distance, but only along certain lines.
• Source of light: gnomonic (light at the globe's centre), stereographic (light on the globe's surface, diametrically opposite the point where the plane touches) and orthographic (light at infinity).

Two route lines: a rhumb line (loxodrome) is a line of constant bearing, straight on Mercator's projection; a great circle is the shortest route between two points on the globe, used in air and sea navigation.

From the video: the teacher's memory tip is that 'ortho-' words are about shape; and to picture a conical projection, think of unrolling a paper ice-cream cone.

Example (new): a map made to compare the land under rice in different countries must keep areas fair, so it should be equal-area; a map used to plot a ship's course needs true directions instead.