Here is the challenge: Representing a three-dimensional object in two-dimensions. It is impossible to do without distortions. Those distortions can reflect cultural biases as well as the function of the map, such as for navigation purposes.
The Mercator Projection, which generates the map that may be most familiar, dates back to the 16th century. It projects the image on to a cylinder, where parallels of latitude are as long as the equator. It is especially useful for navigating the waters and some climatological purposes.
The Peters Projection seems to present the land masses in proportion to each other. Over the last couple of years, it has become the preferred map in many US and British schools. Still, all maps distort and the Peter Projection, for example, preserves the middle latitudes (where Peters lived) while diminishing the lower latitudes.
Last year, a Japanese architect and artist, Hajime Narukawa, of Keio University’s Graduate School of Media and Governance in Tokyo offered a new projection, the AuthaGraph World Map, which won Japan’s Good Design Grand Award. He did not offer simply a new projection but a new approach. Rather than abstract the globe on a cylinder and then a plane, Narukawa’s innovation was to project it on a tetrahedron, which can be unfolded numerous way. The innovation is that rather than one focal point, any place can be the center.