A representation of the Earth’s surface, or a part thereof, in the plane. As a consequence of the Theorema Egregium, such a projection cannot be isometric. (The plane has zero Gaussian curvature and a sphere has positive curvature.) In different contexts, different projections might be preferred; Mercator’s projection was preferred for navigation as it is conformal with latitudes remaining horizontal, but area is severely distorted at the poles; equiareal projections (such as Mollweide’s projection) arguably give a truer geopolitical representation of the world; alternatively, a projection may trade off between the possible extremes.
The representation on a plane surface of part or all of the surface of the Earth or a celestial body. Various projections have been used in the Earth sciences because of their particular suitability for certain work, e.g. equal-area projections for the global distributions of different sedimentary deposits, polar stereographic projection for the relationships within Gondwana, Mercator’s projection for the absolute movements of the lithospheric plates, and conical projections for the Himalayan–Alpine fold belt. Projections based on Mercator’s are most frequently used because of their general familiarity, unless the information portrayed is peculiarly distorted.
Both a method of mapping a large area and the result of doing so. The Earth is a sphere; a map is flat, so that it is impossible to produce a map which combines true shape, true bearing, and true distance. ‘The usefulness of a particular map projection and the justification behind its transformation from a three-dimensional spherical surface to a two-dimensional plane surface is all too often judged from the aesthetic or suspicious eye of a naïve map reader rather than by the science behind its creation’ (M. Monmonier 2004). See also Monmonier (2005) PHG 29, 2.
Mercator’s projection exaggerates the size of the northern continents; it has been criticized as overemphasizing the importance of Europe and North America, although such was not Mercator’s intention. No projection is perfect: for example, Mollweide’s and Peters’ are equal area projections (correct in area), but distort shapes. Azimuthal projections show true direction; gnomic projections show the shortest straight-line distance between two points; orthographic projections convey the effect of a globe. Interrupted projections show the Earth as a series of segments joined only along the equator. Details of the projection used are given below each map in a good atlas.
Map projection. Mercator’s projection is drawn from the shapes and shadows of landmasses that are projected onto a cylinder of paper encircling the earth, when the earth is lit from the centre.