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 projection. Maps rendered in two dimensions by necessity distort the display of the three-dimensional surface of t ...

projection Projection or projections may refer to: Physics * Projection (physics), the action/process of light, heat, or sound reflecting from a surface to another in a different direction * The display of images by a projector Optics, graphics, and carto ...

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

tetrahedron In geometry, a tetrahedron (: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular Face (geometry), faces, six straight Edge (geometry), edges, and four vertex (geometry), vertices. The tet ...

while maintaining area proportions, and unfolding it in the form of a rectangle: it is a polyhedral map projection. 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 projection does not have some of the major distortions of the Mercator projection, 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, rectangular or a

parallelogram In Euclidean geometry, a parallelogram is a simple polygon, simple (non-list of self-intersecting polygons, self-intersecting) quadrilateral with two pairs of Parallel (geometry), parallel sides. The opposite or facing sides of a parallelogram a ...

'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 ...

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. On April 16, 2024,

Nebraska Nebraska ( ) is a landlocked U.S. state, state in the Midwestern United States, Midwestern region of the United States. It borders South Dakota to the north; Iowa to the east and Missouri to the southeast, both across the Missouri River; Ka ...

Governor Jim Pillen signed a law that requires public schools to use only maps based on the

Gall–Peters projection The Gall–Peters projection is a rectangular, Equal-area projection, equal-area map projection. Like all equal-area projections, it distorts most shapes. It is a cylindrical equal-area projection with latitudes 45° north and south as the regions ...

, a similar

cylindrical equal-area projection In cartography, the normal cylindrical equal-area projection is a family of Map projection#Normal cylindrical, normal cylindrical, equal-area projection, equal-area map projections. History The invention of the Lambert cylindrical equal-area pr ...

, or the AuthaGraph projection, beginning in the 2024–2025 school year.

References

External links

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

See also

References

External links