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Adams World in a Square I Projection is a conformal map projection developed by American mathematician and astronomer Oscar Sherman Adams in 1925. Adams, who worked at the U.S. Coast and Geodetic Survey, was a prolific contributor to theoretical cartography, known for his work on conformal projections and his adaptation of the Peirce quincuncial concept. The "World in a Square I" (often referred to as simply the Adams Square I projection) represents the Earth within a perfect square, with the poles located at two opposite corners. It is a member of the same conformal family as the Guyou and Peirce quincuncial projections, and like them, it relies on elliptical functions for its mathematical construction. The projection is notable for its ability to be tiled seamlessly in both directions, allowing the entire sphere to be represented without interruption in a compact, aesthetically striking square format.

Guyou projection is a conformal map projection proposed by French mathematician and naval captain Émile Guyou in 1886. As a member of the French Academy of Sciences (elected 1894) and a recipient of the Légion d'Honneur, Guyou developed this projection as an elegant solution for displaying the world in a rectangular form while preserving local angles. The projection belongs to the same family as the Peirce quincuncial projection—in fact, the Guyou and Peirce projections are transverse cases of each other: Guyou represents the equatorial aspect, while Peirce represents the polar aspect. Though mathematically complex, relying on elliptical integrals for its computation, the Guyou projection offers the unique ability to be tiled infinitely, allowing any point on Earth to be connected to any other by a straight line.

Littrow Projection is a unique conformal retroazimuthal map projection proposed by Austrian astronomer and cartographer Joseph Johann von Littrow in 1833. It stands out as the only map projection that combines both conformal and retroazimuthal properties, a rare dual characteristic that distinguishes it from all other projection designs. Later independently reinvented by British Merchant Navy’s Patrick Weir in 1890, it is also occasionally referred to as the Weir Azimuth Diagram. Unlike global projections designed for world maps, the Littrow Projection is specialized for directional measurement, presenting a limited geographic scope with hyperbolic meridians and elliptical parallels. It cannot display the entire globe, focusing instead on preserving local angles and accurate azimuths toward a predefined central point.

Eckert VI Projection is a pseudocylindrical equal-area map projection proposed by German cartographer Max Eckert in 1906. As the sixth and most widely recognized projection in the Eckert series, it represents a significant departure from the earlier Eckert I–V designs. Unlike its predecessors, Eckert VI features equally spaced straight parallels and curved meridians that are elliptical arcs, with the central meridian appearing as a straight line half the length of the equator. The poles are represented as points (rather than lines), creating a more conventional and visually appealing world map while maintaining strict equal-area properties. This projection is often compared favorably to the Robinson projection in terms of aesthetic balance.

Eckert II Projection is a pseudocylindrical equal-area map projection proposed by German cartographer Max Eckert in 1906. As the second projection in the Eckert series, it shares the same geometric framework as Eckert I—equally spaced straight meridians interrupted at the equator, a central meridian half the length of the equator, and uniformly distributed straight parallels—but introduces a critical mathematical modification to achieve equal-area property. The poles are represented as straight lines half the length of the equator, and the projection maintains zero area distortion globally, making it a rare example of a simple pseudocylindrical equal-area projection.

Eckert I Projection is a pseudocylindrical compromise map projection proposed by German cartographer Max Eckert in 1906. As the first of six projections in the Eckert series, it features a highly distinctive geometric structure: meridians are equally spaced straight lines that are interrupted at the equator, while the central meridian is a straight line only half the length of the projected equator. Parallels are uniformly distributed straight lines perpendicular to the central meridian, and the poles are represented as straight lines half the length of the equator. The projection is neither conformal nor equal-area, with scale correct only along the 47°10′ north and south parallels.

Putnins P6 Projection is a pseudoconic equal-area projection proposed by Soviet geographer A. Putnins in the mid-20th century. Designed specifically for world maps, it aims to accurately preserve the area relationships between land and ocean. In this projection, the Earth’s graticule is projected onto a conical surface and then unfolded into a plane, resulting in meridians represented by straight lines radiating from a common vertex and parallels as concentric circular arcs centered at that vertex. Distortion is minimized near the standard parallels and increases with distance from them, yet area distortion remains zero throughout.

Putnins P5 Projection is a mathematical method in map projections, belonging to the pseudocylindrical projection category. It is primarily used to transform the Earth's three-dimensional surface into a two-dimensional plane in a specific manner, balancing distortions in area, shape, or angle. It is suitable for thematic mapmaking and the visualization of geographic information for specific regions.

Putnins P4 Projection is a pseudocylindrical projection that maintains approximate accuracy in area proportions to balance map distortion, making it suitable for mapping mid-scale regions. This projection compresses distortion in polar areas while generally achieving a compromise between shape and area representation, positioning it as a balanced solution among pseudocylindrical projections.

Putnins P2 Projection is a pseudocylindrical equal-area map projection proposed by R. V. Putnins in 1934, primarily used for creating thematic world maps. This projection employs a specific mathematical method to transform the curved geometric features of the Earth onto a plane. It is characterized by a central meridian that is a straight line with a length half that of the equator, and parallels that are straight lines parallel to the equator, with spacing decreasing as latitude increases. There is no distortion along the central meridian or at latitudes 36°46′ N/S, but distortion gradually increases farther away from these areas.