Projections of the sphere refer to the various methodologies and mathematical transformations used to represent a three-dimensional sphere onto a two-dimensional surface. The purpose of these projections is to accurately depict the geometry and attributes of the sphere in a flat format, enabling easy visualization and measurements.
Since the Earth is a sphere, representing its surface on a flat map requires the use of projections. Numerous projection techniques have been developed over the centuries, each with its own advantages and disadvantages. The projections aim to preserve certain properties or aspects of the original surface, such as distance, direction, shape, or area, while inevitably distorting others.
Common types of projections include the cylindrical, conic, and azimuthal projections. The cylindrical projection, derived from wrapping a cylinder around the sphere, typically results in straight meridians and parallel lines of latitude. Conic projections involve wrapping a cone around the sphere, yielding a map with curved meridians and parallel lines that intersect at a central point. Azimuthal projections, on the other hand, project from a central point or tangent plane, and typically produce accurate directions from that point but distort the shapes and distances of other regions.
Each projection introduces some level of distortion due to the intrinsic properties of the sphere. Consequently, choosing an appropriate projection requires consideration of the purpose, area of interest, and trade-offs between distortions in different attributes. Projections of the sphere are vital tools in cartography, geography, navigation, and various fields involving the representation and analysis of the Earth's surface.
