How does one go about flattening the Earth? An absurd question on the face of it, yet one at the heart of cartography, as representing the spherical Earth on a two-dimensional flat map is a complex undertaking and always an imperfect one. Be they used for school, navigation or spatial analysis, maps are everywhere. And behind each map is a cartographic projection, a method of transformation that dictates which geometric properties are preserved and which are sacrificed.

Cylindrical projection
Imagine rolling a cylinder around the globe, so it envelops our planet tangentially to the equator or to another parallel

Conic projection
The Earth is projected onto a cone that touches one or two parallels (e.g., Lambert conformal conic projection).

Planar projection (azimuthal)
The projection is made onto a tangent (or secant) plane at a specific point, often a pole or a strategic point.

Conformal (Preserves shapes locally and angles)

Preserves the shapes of objects on a small scale, by preserving local angles.

Ideal for coastal, marine and topographic maps
Surfaces may appear quite exaggerated, particularly near the poles

Equivalent (Preserves surfaces)

The areas represented on the map are proportional to those in the real world.

Crucial for political, demographic and economic geography
Shapes may appear elongated, distorted or flattened

Equidistant (Preserves distances)

Preserves distances from a central point, but not those between two random points on the map.

Useful for direct flights, radial maps and analyses of proximity
Does not preserve shapes or surfaces overall

Azimuthal (Preserves directions)

Precise directions from a centre point are preserved, but local angles are accurate only at this point. Consequently, the shape of objects is progressively distorted with increasing distance from the centre.

Practical for aviation routes, satellite maps and polar views
Accuracy diminishes with distance from the central point

The Mercator projection: conformal, useful, yet misleading on a small scale

The Mercator projection, created in 1569, is a conformal cylindrical projection. It was intended for marine navigation: thanks to its preservation of angles, loxodromes (paths of constant compass bearing) appear as perfectly straight lines. This has made it a reference for marine maps for centuries.

However, this projection significantly distorts surfaces, particularly as distance from the equator increases. For instance, Greenland appears as large as Africa, even though it is 14 times smaller. Thus, it provides a false representation of the spatial importance of regions situated at high latitude.

This distortion is spectacular on a small scale (that is, on maps of the world or of continents), yet it becomes almost imperceptible on a large scale, on a map covering a limited territory, such as a city or a region.

For this reason, services such as Google Maps use a variant of the Mercator projection: on a local scale, the angular conformity makes it possible to preserve shapes and orientations, and surface distortions are negligible.

For maps of small territories with still greater accuracy, adapted local projections are often used. These are designed to limit as much as possible distortions within a well-defined zone. Examples include the UTM (Universal Transverse Mercator) and MTM (Modified Transverse Mercator) systems.

The UTM system divides the globe into 60 longitudinal zones each 6° wide. Inside each zone, a conformal cylindrical transverse projection is used, centered on a meridian, which makes it possible to ensure very good accuracy for distances and local shapes. This is the system used for most modern topographic maps.

In Québec, the MTM system is often preferred, which is based on the same principle, but with narrower zones of 3° longitude each, for greater accuracy. Each MTM longitudinal zone is assigned a false central meridian value and is adapted to the singular geometry of Québec’s territory, particularly as regards cadastral surveys, land use and engineering works.

These systems are not designed for representing the entire world, but they are excellent for detailed cartography on a large scale (e.g., a city, region, or infrastructure corridor). It is a perfect example of projection that is optimized for a very localized use, with parameters that are calibrated according to geographical location.

Lambert conformal projection: ideal for national maps of Canada

Unlike Mercator, the Lambert conformal projection is a conic projection, ideal for vast east-to-west expanses. It is widely used in Canada, particularly in the mapping of Québec, Ontario and the Western provinces.

It preserves local angles, thereby ensuring a faithful rendering of shapes on a regional scale, while limiting distortions.

Parallels and meridians: a grid for understanding

Meridians are lines running north-south, perpendicular to the equator.

Parallels are the imaginary horizontal circles that run parallel to the equator, corresponding to the latitudes.

Together, these lines form the fundamental geographical grid that underpins any projection.

Standard parallels: at the heart of accuracy

The Lambert conformal projection defines one or two standard (or reference) parallels on which the projection is tangent or secant to the terrestrial orb.

There is no distortion along these lines
Between these lines, distortion is weak
Beyond this, distortion increases gradually

For example, for a large latitudinal strip running from southern to central Canada, 49°N and 60°N may be selected as standard parallels. This makes it possible to achieve great accuracy within this strip, hence its use in geomatics, urban planning and environmental management.

A projection is never neutral

Each projection represents a choice. Behind the geometry lies an intent, be it to facilitate navigation, accurately render the size of geographic areas, produce an esthetically balanced map, or other aim.

Sometimes, though, these choices serve to buttress a geopolitical perspective. For instance, Mercator has long dominated schoolbooks, positioning Europe in the centre and exaggerating the size of the northern countries. Inversely, the Peters projection, which represents the size of areas more accurately, has been promoted to counter inequalities in representation.

Conclusion: To choose is to orientate

No cartographic projection is perfect. All are compromises between geometric accuracy, visual clarity and political intent. Today, GIS software makes it possible to dynamically select the projection best suited for each type of use.

Yet, the impacts of each use still need to be understood, for behind a well-drawn map… always lies a vision of the world.

Cartographic projections: representing the impossible

The major types of projections

Types of distortion