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My favorite unusual map is probably AuthaGraph: > This rectangular world map called AuthaGraph World Map is made by equally dividing a spherical surface into 9

by hezag 6y ago

My favorite unusual map is probably AuthaGraph: > This rectangular world map called AuthaGraph World Map is made by equally dividing a spherical surface into 96 triangles, transferring it to a tetrahedron while maintaining areas proportions and unfolding it to be a rectangle. > The world map can be tiled in any directions without visible seams. From this map-tiling, a new world map with triangular, rectangular or parallelogram’s outline can be framed out with various regions at its center. http://www.authagraph.com/projects/description/%e3%80%90%e4%bd%9c%e5%93%81%e8%a7%a3%e8%aa%ac%e3%80%91%e8%a8%98%e4%ba%8b01/?lang=en http://www.authagraph.com/projects/description/%e3%80%90%e4%... > It shows there are no "four corners of the earth" by arranging several world maps without visible seams around a world map with color. You can see Antarctica at the right bottom is close to not only South America but also Africa and Australia. http://www.authagraph.com/products/map/product-article-01/?lang=en http://www.authagraph.com/products/map/product-article-01/?l...

DiogenesKynikos 6y ago
The Peirce Quincuncial Map can also be seamlessly tiled: [1]. It's a conformal map, meaning that it preserves shapes. But strange things happen at the four corners of each diamond-shaped tile. If you go around one of those points on the map, you've actually gone around the real point on Earth twice. Also at those points, opposite directions on the map are actually the same direction on the Earth. The technical description of those four points is that they're singularities of the map projection (derivatives of the form d(location on Earth)/d(map coordinate) are undefined). The map looks fine because the four singularities on each tile are in the middle of the ocean. But if you play around with the projection to put any of the singularities inside a landmass, your head will explode. Looking at the AuthaGraph may you linked, it has at least two singularities on each tile. 1. https://en.wikipedia.org/wiki/Peirce_quincuncial_projection#/media/File%3APeirce_quincuncial_projection_SW_20W_tiles.JPG https://en.wikipedia.org/wiki/Peirce_quincuncial_projection#...

by hezag 6y ago

DiogenesKynikos 6y ago

The Peirce Quincuncial Map can also be seamlessly tiled: [1]. It's a conformal map, meaning that it preserves shapes. But strange things happen at the four corners of each diamond-shaped tile. If you go around one of those points on the map, you've actually gone around the real point on Earth twice. Also at those points, opposite directions on the map are actually the same direction on the Earth. The technical description of those four points is that they're singularities of the map projection (derivatives of the form d(location on Earth)/d(map coordinate) are undefined). The map looks fine because the four singularities on each tile are in the middle of the ocean. But if you play around with the projection to put any of the singularities inside a landmass, your head will explode. Looking at the AuthaGraph may you linked, it has at least two singularities on each tile. 1. https://en.wikipedia.org/wiki/Peirce_quincuncial_projection#/media/File%3APeirce_quincuncial_projection_SW_20W_tiles.JPG https://en.wikipedia.org/wiki/Peirce_quincuncial_projection#...