Editing Talk:2121: Light Pollution
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:::::But can it form a [https://www.explainxkcd.com/wiki/index.php/1365:_Inflation basketball?] [[User:Netherin5|Netherin5]] ([[User talk:Netherin5|talk]]) 17:24, 8 March 2019 (UTC) | :::::But can it form a [https://www.explainxkcd.com/wiki/index.php/1365:_Inflation basketball?] [[User:Netherin5|Netherin5]] ([[User talk:Netherin5|talk]]) 17:24, 8 March 2019 (UTC) | ||
:Your eyes are making the hexagons up. Some triangles would be left over if you tried to make every group of 6 triangles a hexagon. Triangle arrays like this are commonly used in computer graphics, as they are the closest approximation to a sphere: https://mft-dev.dk/wp-content/uploads/2014/05/icosahedron_frame_sub3.gif [[Special:Contributions/162.158.79.185|162.158.79.185]] 17:25, 8 March 2019 (UTC) | :Your eyes are making the hexagons up. Some triangles would be left over if you tried to make every group of 6 triangles a hexagon. Triangle arrays like this are commonly used in computer graphics, as they are the closest approximation to a sphere: https://mft-dev.dk/wp-content/uploads/2014/05/icosahedron_frame_sub3.gif [[Special:Contributions/162.158.79.185|162.158.79.185]] 17:25, 8 March 2019 (UTC) | ||
| − | ::Not really. On a plane, there are only three {{W|tesselation|tesselations}} made only of identical regular polygons: {{W|triangular tiling}}, {{W|square tiling}} or {{W|hexagonal tiling}}. But since a regular hexagon can be divided into six equilateral triangles, the tiling in the picture can be seen as both triangular and hexagonal. The leaving out you write about may have come from another tesselation which uses hexagons and triangles, the {{W|trihexagonal tiling}}. On a sphere, there's a completely different discussion as there's no tesselations, only approximations of them. {{unsigned|Malgond}} | + | ::Not really. On a plane, there are only three {{W|tesselation|tesselations}} made only of identical regular polygons: {{W|triangular tiling}}, {{W|square tiling}} or {{W|hexagonal tiling}}. But since a regular hexagon can be divided into six equilateral triangles, the tiling in the picture can be seen as both triangular and hexagonal. The leaving out you write about may have come from another tesselation which uses hexagons and triangles, the {{W|trihexagonal tiling}}. On a sphere, there's a completely different discussion as there's no tesselations, only approximations of them. {{unsigned|Malgond}} |
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There is no way to know that the triangles shown are equilateral (in fact, as drawn here they're quite ''un''even). All 3D renderings are in fact assembled from uneven-sided triangles, including renderings attempting to approximate rounded surfaces. And yes, you can buy a ball tiled only with triangles; they're not even-sided, but you can't tell with the naked eye. Also, there ''is'' one roughly spherical shape tiled only with equilateral triangles: It's the shape found on a 20-sided die. Skyboxes intended to minimize viewing angle distortions use triangles that are very nearly, but not quite equilateral. In fact, ''all shapes'' that use flat planes to tile a sphere can be broken down into triangles of one degree of asymmetry or another. Your argument is invalid. | There is no way to know that the triangles shown are equilateral (in fact, as drawn here they're quite ''un''even). All 3D renderings are in fact assembled from uneven-sided triangles, including renderings attempting to approximate rounded surfaces. And yes, you can buy a ball tiled only with triangles; they're not even-sided, but you can't tell with the naked eye. Also, there ''is'' one roughly spherical shape tiled only with equilateral triangles: It's the shape found on a 20-sided die. Skyboxes intended to minimize viewing angle distortions use triangles that are very nearly, but not quite equilateral. In fact, ''all shapes'' that use flat planes to tile a sphere can be broken down into triangles of one degree of asymmetry or another. Your argument is invalid. | ||
[[User:ProphetZarquon|ProphetZarquon]] ([[User talk:ProphetZarquon|talk]]) 22:51, 8 March 2019 (UTC) | [[User:ProphetZarquon|ProphetZarquon]] ([[User talk:ProphetZarquon|talk]]) 22:51, 8 March 2019 (UTC) | ||
