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What are the four main types of Map projections?

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Hint: Map projection is the method of transmitting the graticule of longitude and latitude on a plane surface. It can also be defined as the transformation of a spherical network of parallels and meridians on a plane surface.

Complete step-by-step answer: Map projections take developable surfaces like cones, cylinders, and planes. The aim of a developable surface is to flatten the world in a two-dimensional plane. Every single surface is statistically rendered based on those geometric shapes.
Types of Map Projections: Many different kinds of map projections are being used for map making. They are divided into four categories in accordance with the Map Projection Theory or the kinds of surfaces that are tangent with the globe. The four categories are Planar, Azimuthal or Zenithal projection, Conic projection, cylindrical projection, and Mathematical or Conventional projection obtained from mathematical calculation.
Planar, Azimuthal or Zenithal projection: This kind of map projection lets a flat sheet touch with the globe, with the light being cast from some positions, including the centre of the Earth, opposite to the tangent area, and from an infinite distance. This group of map projections can be classified into three categories as Gnomonic projection, Stereographic projection, and Orthographic projection.
Conic projection: This kind of projection uses a conic surface to touch the globe once the light is cast. When the cone is unrolled, the meridians will be in semicircles similar to the ribs of a fan. The tangent areas of conic projection can be categorised as central conical projection or tangent cone, secant conical projection, and polyconic projection.
Cylindrical projection: This kind of projection uses a cylinder as a tangent surface that encloses a globe or intersects the globe at specific positions. If the cylinder is unrolled into a flat sheet, the parallels and meridians will be straight lines that create the right angles in which they intersect each other. The projection shows the directions and shapes properly.
Conventional projections: These kinds of projections are pure-mathematical constructions designed in order to map the whole sphere with minimum distortion. The Euler angles for constructing oblique forms of these projections are indicated just like cylindrical projections.

Note: A map projection is used to portray all or part of the round Earth on a flat surface. This cannot be done without some distortion. It is done by an orderly and systematic representation of the parallels of latitude and the meridians of longitude of the spherical earth or part of it on a plane surface on a conveniently selected scale.