Classification by preserved property

Detail

Why maps must choose one property

• A globe is the only true model of the Earth. It shows area, shape, direction and distance correctly, all at once.
• A map projection is a way of moving the graticule onto a flat sheet. The graticule is the network of parallels (lines of latitude) and meridians (lines of longitude).
• A curved surface cannot be flattened without stretching or tearing. So every flat map gets at least one property wrong.
• The mapmaker therefore picks the property that matters most for the map's use. Projections are grouped by the property they keep. These are the global properties: area, shape, direction and distance.

Class	Other names	What stays true	What is lost	Typical use
Equal area	Homolographic; also called authalic or equivalent [4]	Area of every graticule cell is the same as on the globe	Shape	Distribution maps of population, crops and forests
Orthomorphic	True shape; conformal	Shape of small areas	Area	Navigation charts (Mercator)
Azimuthal	True bearing	Direction of every point from the centre	Direction from any other point	Maps centred on one place
Equidistant	True scale	Distance along chosen parallels or meridians only	Scale everywhere else	Distance measurement along set lines

1. Equal area (homolographic) projection

• Definition: a projection in which each cell of the graticule has the same area as the matching cell on the globe.
• Test: if you place a coin anywhere on the map, it covers the same real area of the Earth wherever you put it [4].
• Result:
• Area comparisons are true. For example, India's area can be fairly compared with Africa's.

• To keep area right, the cells are squeezed in one direction and stretched in the other. So shapes become distorted, mostly near the edges and towards the poles.

• Use: distribution maps, such as maps of population, crops and forests. On these maps the reader compares how much of something is spread over how much land.

2. Orthomorphic (true-shape, conformal) projection

• Definition: a projection that keeps the correct shape of small areas.
• How it works:
• At every point, the scale is made equal in all directions.
• So a tiny circle on the globe stays a tiny circle on the map. It does not become an oval.

• Meridians cut parallels at right angles (90°), just as they do on the globe [4].

• Cost: area is given up. Scale changes from place to place, so large regions look too big or too small.

• Classic example: Mercator projection.
• Gerardus Mercator introduced it in 1569 [5].
• Meridians are equally spaced vertical lines. Parallels are horizontal lines that get farther apart as you move away from the Equator [5].
• Cause → result:
  • Parallels are spread out towards the poles.
  • So high-latitude lands such as Greenland, Canada and Siberia look far bigger than they are.
  • The poles cannot be shown at all.

• Why sailors loved it: a rhumb line (loxodrome: a course that keeps the same compass direction the whole way) appears as a straight line. This made it the standard projection for sea charts [5].

• "Small areas" is the key phrase. A conformal map keeps local shape, not the shape of a whole continent.

3. Azimuthal (true-bearing) projection

• Definition: a projection on which the direction (azimuth) from one central point to every other point is correct [4].
• Azimuth is the angle of a direction measured clockwise from north.
• Limit: directions are true only from the centre point. Directions between any two other points are not true.

4. Equidistant (true-scale) projection

• Definition: a projection that shows true distance (true scale), but only along chosen parallels or meridians.
• Rule: no flat map can keep the scale true everywhere [4].
• Example: the simple (equidistant) cylindrical projection keeps true scale:
• along all meridians, and
• along the Equator.

• Away from the Equator, the parallels are drawn as long as the Equator. So east–west distances grow more and more wrong towards the poles.

• A more general form keeps true scale along every great circle (the shortest path between two points on a sphere) that passes through one or two chosen points [4].

5. Azimuthal equidistant projection (beyond NCERT)

• Definition: a projection that shows both true distance and true direction from its centre point.
• How it looks when centred on a pole: parallels become circles around the pole. They are spaced in proportion to their true distances along each meridian [4].
• UN emblem:
• The United Nations emblem is a world map drawn on an azimuthal equidistant projection centred on the North Pole [2].
• The map is set inside a wreath of crossed olive branches, which stand for peace. It is gold on a smoke-blue field, with all water areas in white [2].
• The map reaches 60° S latitude and has five concentric circles [2][3].

• The UN General Assembly approved the emblem by resolution 92 (I) of 7 December 1946 [2].

• Centred on a city: it is used to plan air routes and radio links.

• On a map centred on Delhi, the distance and direction from Delhi to any world capital can be read straight off the map with a ruler.
• This works because every straight line from the centre is a great-circle route at true scale.

Traps

• Trap 1: equal area and orthomorphic cannot both hold on one map. If shape is kept, area is lost, and the other way round [4]. A projection can still mix weaker properties. For example, azimuthal equidistant keeps both direction and distance, but only from the centre.
• Trap 2: NCERT's exercise "homolographic vs orthographic" most likely means orthomorphic. Orthographic is a different thing: an azimuthal projection drawn as if the light source is at infinity. It is a way of building a projection, not a property it keeps.
• Trap 3: "true-scale everywhere" is never correct in an answer option.

Prelims Hooks

• Homolographic = equal area. Orthomorphic = conformal, or true shape.
• Equal area projections suit distribution maps (population, crops, forests), because area comparisons stay true while shapes distort.
• Mercator (1569) is orthomorphic. It keeps local shape but exaggerates area towards the poles. Rhumb lines appear as straight lines [5].
• On a conformal projection, meridians and parallels cross at right angles, and scale is equal in all directions at each point [4].
• Azimuthal projection gives true direction only from the centre point.
• The simple cylindrical projection keeps true scale along all meridians and the Equator only.
• UN emblem: azimuthal equidistant projection, centred on the North Pole, reaching 60° S, inside olive branches. Approved on 7 December 1946 by UNGA resolution 92 (I) [2][3].
• "Which of the following cannot exist?" A map that is both equal area and conformal [4].
• No projection is equidistant everywhere [4].

Mains Points

• Choosing a projection depends on purpose (GS-I, mapping):
• Use equal area for resource and population distribution.
• Use conformal (Mercator) for navigation and large-scale topographic sheets.

• Use azimuthal equidistant for air-route, radio and missile-range planning from one centre.

• Mercator's distortion affects how people see the world:

• Area is enlarged at high latitudes.
• So tropical regions, including India and Africa, look smaller than they really are compared with Europe and North America.

• This is why equal-area world maps are preferred for comparing development or resources.

• Every projection is a trade-off:

• A flat map cannot keep all four global properties at once. Equal area and conformal cannot exist together [4].

• So map users must check which property a map keeps before measuring area, distance or direction on it.

• Geospatial use: azimuthal equidistant maps centred on Delhi help plan civil aviation routes and communication links. The UN uses the same projection, centred on the North Pole, as a neutral symbol that shows all nations together [2].