Cylindrical equal area projection and Gall-Peters

Detail

What the projection is

• Map projection (a method of moving the network of latitudes and longitudes from the round globe onto a flat sheet). No flat map can keep area, shape, distance and direction correct all at once. Each projection chooses what to keep correct.
• Equal-area (homolographic) projection (a projection on which every region keeps its true size compared with other regions). The trade-off is that shapes and directions get distorted [2].
• Cylindrical equal area projection, also called Lambert's projection. It was devised by J.H. Lambert in 1772.

• Britannica describes Lambert as a Swiss German mathematician. He offered this projection as an equal-area alternative to the Mercator [2].

• How it is made:

• Imagine a paper cylinder wrapped around the globe so that it touches it along the equator.
• Parallel rays carry each point of the globe sideways onto the cylinder.

• The cylinder is then cut open and laid flat.

• Result: the parallels (lines of latitude) and meridians (lines of longitude) are all straight lines. They cross each other at right angles, so the map has a rectangular grid.

NCERT construction example (world map, 1:300,000,000, 15° interval)

• Step 1 – radius of the reduced globe: R = 2.1 cm.
• Step 2 – length of the equator: 2πR = 2 × 3.14 × 2.1 = 13.2 cm.
• Step 3 – meridians: 360° ÷ 15° = 24 parts, so each part is 13.2 ÷ 24 = 0.55 cm. The meridians are drawn as equally spaced vertical lines.
• Step 4 – parallels: each parallel is drawn at a height of R × sine of its latitude above (or below) the equator.

Latitude	Height above equator (R sin φ)	Gap from the previous parallel
15°	2.1 × 0.259 ≈ 0.54 cm	0.54 cm
30°	2.1 × 0.500 ≈ 1.05 cm	0.51 cm
45°	2.1 × 0.707 ≈ 1.48 cm	0.43 cm
60°	2.1 × 0.866 ≈ 1.82 cm	0.34 cm
75°	2.1 × 0.966 ≈ 2.03 cm	0.21 cm
90° (pole)	2.1 × 1.000 = 2.10 cm	0.07 cm

• What the table shows: the gaps get smaller and smaller towards the poles, so the parallels crowd together near the poles.
• The whole map is 13.2 cm wide and only 4.2 cm tall (2R). It is a long, flat strip.

Properties

• Parallels and meridians are straight lines that meet at right angles.
• The polar parallel is as long as the equator. On the globe the pole is only a point, but on this map it becomes a line 13.2 cm long.
• Scale is true only along the equator, the line where the cylinder touches the globe.
• Area is correct everywhere. Any two equal areas on the globe are equal on the map.

How area stays equal (and why shape breaks)

• East-west stretching:
• On the globe, parallels get shorter towards the poles. The 60° parallel is only half as long as the equator.
• On the map, every parallel is as long as the equator.

• So land is stretched east-west, and the stretching grows towards the poles (about 2 times at 60°).

• North-south squashing:

• Parallels are put closer together towards the poles (the R sin φ rule).

• So land is squashed north-south by the same amount it was stretched east-west (about half at 60°).

• Result:

• Stretching × squashing = 1, so area stays true.
• Shapes near the poles become wide and flat, so shape is badly distorted poleward.
• The projection is therefore not orthomorphic. Orthomorphic, or conformal, means that the shapes of small areas and the angles between lines stay true. Mercator's projection (1569) is the classic orthomorphic one.

Limitations and uses

• Limitations:
• Shapes are badly distorted towards the poles.
• Scale is correct only at the equator.

• The poles appear as long lines instead of points.

• Uses:

• The belt between 45°N and 45°S, where the distortion stays small.
• Distribution maps of tropical crops: rice, tea, coffee, rubber and sugarcane.
• These maps compare areas under each crop, so true area matters more than true shape.

Feature	Mercator (1569)	Cylindrical equal area (Lambert, 1772)
Property kept	Shape and direction (orthomorphic)	Area (homolographic)
Spacing of parallels	Increases towards the poles	Decreases towards the poles
High latitudes	Area greatly enlarged	Area true, shape squashed
Typical use	Navigation charts	Tropical distribution maps

Gall-Peters projection (beyond NCERT)

• Gall-Peters projection (an equal-area cylindrical map that is a stretched version of Lambert's projection). It keeps true area, but it is not conformal, so local angles are not kept [2].
• Origin: in the 1800s James Gall, a Scottish clergyman and mapmaker, made a similar equal-area map by stretching landmasses north-south (Gall described it in 1855) [2].
• Revival: in the 1970s (from 1973), German historian Arno Peters campaigned to replace the Mercator with "a new geography—based on the equal status of [the world's] peoples" [2].
• Why he called it "fairer":
• The Mercator projection enlarges high-latitude lands. Greenland (836,330 sq mi) looks about as big as Africa (almost 12 million sq mi) [2].
• In fact Greenland is only one-eighth the size of South America [2].

• This makes tropical regions such as Africa, South America and South Asia look smaller than they are. Peters' map shows them at their true size.

• Supporters: the World Council of Churches, UNESCO, UNICEF and several non-governmental organisations endorsed it [2].

• Critics:
• Tropical landmasses look stretched tall and thin.

• American geographer Arthur H. Robinson mocked its shapes as "reminiscent of wet, ragged, long winter underwear hung out to dry on the Arctic Circle" [2].

• Boston public schools, 2017:

• In March 2017, Boston public schools adopted the Gall-Peters map. It was part of a three-year effort to "decolonize the curriculum" and move away from a Europe-centred view [3].

• Officials said the usual maps show students' home regions as "small and insignificant" [3].

• Lesson: every world map carries a point of view. The choice of projection decides which regions look large and central.

Prelims Hooks

• Cylindrical equal area projection = Lambert's projection, 1772. Mercator's projection = 1569.
• The cylinder touches the globe at the equator, so scale is true only along the equator.
• The polar parallel equals the equator in length. This is true for both the cylindrical equal area and the Mercator projection.
• Spacing of parallels: decreases poleward in the cylindrical equal area projection (R sin φ), but increases poleward in the Mercator.
• Cylindrical equal area is equal-area (homolographic), not orthomorphic. Mercator is orthomorphic, not equal-area. This is a common trap.
• NCERT example: R = 2.1 cm, equator = 13.2 cm, 24 divisions of 0.55 cm at a 15° interval, scale 1:300,000,000.
• Best suited to the belt 45°N–45°S. Used for maps of tropical crops: rice, tea, coffee, rubber, sugarcane.
• Gall-Peters: James Gall (1855) → promoted by Arno Peters (1970s). It is equal-area but not conformal [2].
• On a Mercator map, Greenland looks as big as Africa, but in reality it is only one-eighth the size of South America [2].
• Peters' map was endorsed by UNESCO, UNICEF and the World Council of Churches [2]. It was adopted by Boston public schools in 2017 [3].

Mains Points

• No projection is perfect:
• Keeping area true (Lambert, Gall-Peters) costs shape.
• Keeping shape true (Mercator) costs area.

• So the map must suit the purpose: equal-area maps for distributions such as crops, population and forests; conformal maps for navigation.

• Equal-area maps for resource geography (GS-III):

• True area is needed to compare tropical plantation belts, such as tea in Assam and Sri Lanka, rubber in Kerala and Malaysia, and coffee in Brazil.

• An enlarged high-latitude map would mislead a reader about how big these belts are.

• The politics of maps (GS-I):

• The Mercator projection made Europe and North America look large and central.
• The Gall-Peters debate shows that maps shape how people see the Global South [2][3].
• It suggests using equal-area or compromise projections in school atlases.