AuthaGraph is an approximately equal-area

world map A world map is a map of most or all of the surface of Earth. World maps, because of their scale, must deal with the problem of map projection, projection. Maps rendered in two dimensions by necessity distort the display of the three-dimensiona ...

projection invented by Japanese architect

Hajime Narukawa is a Japanese architect. He was born in 1971 in Kawasaki-City, Kanagawa and lives and practices in Tokyo. Biography Narukawa graduated in 1994 from the Shibaura Institute of Technology, Tokyo National University of Fine Arts with a master's ...

in 1999. The map is made by equally dividing a spherical surface into 96 triangles, transferring it to a

tetrahedron In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. The tetrahedron is the simplest of all the ...

while maintaining area proportions, and unfolding it onto a rectangle: it is a

polyhedral map projection A polyhedral map projection is a map projection based on a spherical polyhedron. Typically, the polyhedron is overlaid on the globe, and each face of the polyhedron is transformed to a polygon or other shape in the plane. The best-known polyhedral ...

. The map substantially preserves sizes and shapes of all continents and oceans while it reduces distortions of their shapes, as inspired by the

Dymaxion map The Dymaxion map or Fuller map is a projection of a world map onto the surface of an icosahedron, which can be unfolded and flattened to two dimensions. The flat map is heavily interrupted in order to preserve shapes and sizes. The projection w ...

. The projection does not have some of the major distortions of the

Mercator projection The Mercator projection () is a cylindrical map projection presented by Flemish geographer and cartographer Gerardus Mercator in 1569. It became the standard map projection for navigation because it is unique in representing north as up and so ...

, like the expansion of countries in far northern latitudes, and allows for Antarctica to be displayed accurately and in whole. Triangular world maps are also possible using the same method. The name is derived from " authalic" and "graph". The method used to construct the projection ensures that the 96 regions of the sphere that are used to define the projection each have the correct area, but the projection does not qualify as equal-area because the method does not control area at infinitesimal scales or even within those regions. The AuthaGraph world map can be tiled in any direction without visible seams. From this map-tiling, a new world map with

triangular A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices ''A'', ''B'', and ''C'' is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, ...

rectangular In Euclidean plane geometry, a rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal (360°/4 = 90°); or a parallelogram containin ...

or a

parallelogram In Euclidean geometry, a parallelogram is a simple (non- self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of eq ...

's outline can be framed with various regions at its center. This

tessellation A tessellation or tiling is the covering of a surface, often a plane, using one or more geometric shapes, called ''tiles'', with no overlaps and no gaps. In mathematics, tessellation can be generalized to higher dimensions and a variety of ge ...

allows for depicting temporal themes, such as a satellite's long-term movement around the earth in a continuous line. In 2011 the AuthaGraph mapping projection was selected by the Japanese National Museum of Emerging Science and Innovation (Miraikan) as its official mapping tool. In October 2016, the AuthaGraph mapping projection won the 2016 Good Design Grand Award from the Japan Institute of Design Promotion.

References

External links

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Good Design Award
1999 introductions Map projections Japanese inventions {{Cartography-stub

See also

References

External links