Many years ago Earth-bound observers could only view a small section of the globe at a time and it was difficult to tell from direct observation whether the Earth was a disk or a sphere. The Greeks were the first to theorize that the Earth was round. Scholars like Pythagoras (500 BC) based their theories on observations of how the altitudes of stars varied at different places on Earth and how ships appeared on the horizon. As a ship returned to port, first its mast tops, then the sails, and finally its hull gradually came into view. Aristotle, who lived 300 years before Christ, observed that the Earth cast a round shadow on the moon. When a light is shined on a sphere, it casts a round shadow.
The Greeks calculated the general size and shape of the Earth. They also created the grid system of latitude and longitude, so that with just two coordinates one can locate any point on the Earth. Greek philosophers also concluded that the Earth could only be a sphere because that, in their opinion, was the "most perfect" shape.
Today, Earth is recognized as an oblate spheroid since it bulges a bit at the equator. Represention of a round Earth onto a flat surface is still a challenge for cartographers and for people studying the Earth from space using satellite imagery.
Since information about the Earth from satellites is descending on us in vast amounts, it is impractical to make a globe from each image or set of images. Thus scientists choose the flat representation of the Earth that best allows them to answer the question they are asking.
Cartographers primarily use three types of projections to represent the earth on a flat surface: planar projections, cylindrical projections, and conical projections. Each has advantages and disadvantages in transfering a sphere to a flat plane.
Planar projections show half of the world at a time from a vantage point often centered on the north or south pole, areas that are distorted on other maps. The advantage of a planar projection is that directions can be determined simply by examining the map. However, the map only depicts half of the Earth at a time.
Cylindrical projections, such as a Mercator projection, project the earth onto a map with lines of latitude and longitude that intersect at right angles. These maps enable pilots and sailors to plot courses without difficulty and are often used for navigation. However, the maps are distorted near the poles causing areas such as Greenland to appear far larger than they actually are. Antarctica is transformed from a circular "island" to a long, thin strip of borderland.
Conical projections use a cone-shaped piece of paper to depict the globe. They are a compromise between cylindrical projections and planar projections because size discrepancies between the poles and equator are smaller.
The basis of the Fuller Dymaxion Projection is an icosahedron. Essentially this is a polyhedron with twenty equilateral triangles that form a planar representation of earth. A few of the equilateral triangles are sub-divided for a more effective presentation, but this modification does not distort the relative size or shape of the continents. The beauty in the Fuller Dymaxion Projection lies in its ability to depict planet Earth on one flat surface without gross distortions of other map projections. Like a globe, it is difficult to use as a navigation tool because of the rectilinear nature of conventional navigation systems.