Editing Talk:2121: Light Pollution
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[[User:AlanKilian|AlanKilian]] ([[User talk:AlanKilian|talk]]) 16:03, 8 March 2019 (UTC) | [[User:AlanKilian|AlanKilian]] ([[User talk:AlanKilian|talk]]) 16:03, 8 March 2019 (UTC) | ||
:Six triangles form a hexagon - just an explanation for people with less mathematical or geometric knowledge. --[[User:Dgbrt|Dgbrt]] ([[User talk:Dgbrt|talk]]) 16:17, 8 March 2019 (UTC) | :Six triangles form a hexagon - just an explanation for people with less mathematical or geometric knowledge. --[[User:Dgbrt|Dgbrt]] ([[User talk:Dgbrt|talk]]) 16:17, 8 March 2019 (UTC) | ||
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::but a indefinite large group of triangles doesn't automatically transform to hexagons, since it could be overlapping hexagons, or hexagons with their interim spaces filled up by triangles?--[[User:Lupo|Lupo]] ([[User talk:Lupo|talk]]) 16:29, 8 March 2019 (UTC) | ::but a indefinite large group of triangles doesn't automatically transform to hexagons, since it could be overlapping hexagons, or hexagons with their interim spaces filled up by triangles?--[[User:Lupo|Lupo]] ([[User talk:Lupo|talk]]) 16:29, 8 March 2019 (UTC) | ||
:::Look at that hexagons (consisting of six triangles), each fitting to the next, and you will understand that this is only possible in a plane but not in a sphere. --[[User:Dgbrt|Dgbrt]] ([[User talk:Dgbrt|talk]]) 16:37, 8 March 2019 (UTC) | :::Look at that hexagons (consisting of six triangles), each fitting to the next, and you will understand that this is only possible in a plane but not in a sphere. --[[User:Dgbrt|Dgbrt]] ([[User talk:Dgbrt|talk]]) 16:37, 8 March 2019 (UTC) | ||
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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) | ||
− | :Y'all need to stop arguing about the geometry and look at this picture of a (approximation of a) sphere made out of triangular pyramids: | + | :Y'all need to stop arguing about the geometry and look at this picture of a (approximation of a) sphere made out of triangular pyramids: https://www.google.com/url?sa=i&source=images&cd=&cad=rja&uact=8&ved=2ahUKEwjvhZHLoPTgAhXmhVQKHRLnDSwQjRx6BAgBEAU&url=http%3A%2F%2Fblog.zacharyabel.com%2Ftag%2Fspheres%2F&psig=AOvVaw2-zrroG1RBFI-t2GHyHt-9&ust=1552193238617042 [[User:Tplaza64|Tplaza64]] ([[User talk:Tplaza64|talk]]) 04:50, 9 March 2019 (UTC) |
::Also note that we see just small part of sky there, so it's fully possible the few deformed/missing triangles are outside of what we see. -- [[User:Hkmaly|Hkmaly]] ([[User talk:Hkmaly|talk]]) 23:49, 8 March 2019 (UTC) | ::Also note that we see just small part of sky there, so it's fully possible the few deformed/missing triangles are outside of what we see. -- [[User:Hkmaly|Hkmaly]] ([[User talk:Hkmaly|talk]]) 23:49, 8 March 2019 (UTC) | ||
: An interactive sphere divided into hexagonals - where is the trick? [http://pub.ist.ac.at/~edels/hexasphere/ Hexagonal tiling of the two-dimensional sphere] Sebastian --[[Special:Contributions/172.68.110.64|172.68.110.64]] 16:11, 12 March 2019 (UTC) | : An interactive sphere divided into hexagonals - where is the trick? [http://pub.ist.ac.at/~edels/hexasphere/ Hexagonal tiling of the two-dimensional sphere] Sebastian --[[Special:Contributions/172.68.110.64|172.68.110.64]] 16:11, 12 March 2019 (UTC) | ||
− | ::The "trick" is that you are making the unwarranted assumption that every hexagon in the matrix is composed from six identical equilateral triangles. Which can't possible be the case for it to form a non-flat surface. A hexagon composed of six equilateral triangles will have each vertex at exactly 120 degrees. Three of them joined at a corner ''must'' add up to 360 degrees and therefore must lie flat and therefore can't curve into 3-space. The fact that the surface does curve means that the sum of the angles at those vertices adds up to something less than 360 degrees, which means at least some of the hexagons have vertices that are less than 120 degrees (and they are therefore not composed of equilateral triangles | + | ::The "trick" is that you are making the unwarranted assumption that every hexagon in the matrix is composed from six identical equilateral triangles. Which can't possible be the case for it to form a non-flat surface. A hexagon composed of six equilateral triangles will have each vertex at exactly 120 degrees. Three of them joined at a corner ''must'' add up to 360 degrees and therefore must lie flat and therefore can't curve into 3-space. The fact that the surface does curve means that the sum of the angles at those vertices adds up to something less than 360 degrees, which means at least some of the hexagons have vertices that are less than 120 degrees (and they are therefore not composed of equilateral triangles). Once you realize that the angles on the hexagons are less than 120 degrees, the solution to the problem is figuring out exactly what angles are needed to form a sphere of a given size. This may be a hard problem to solve, but definitely not impossible. [[User:Shamino|Shamino]] ([[User talk:Shamino|talk]]) 16:37, 12 March 2019 (UTC) |
Oh man where are the conspiracy nuts from a few weeks ago ;-) [[User:Cgrimes85|Cgrimes85]] ([[User talk:Cgrimes85|talk]]) 17:03, 8 March 2019 (UTC) | Oh man where are the conspiracy nuts from a few weeks ago ;-) [[User:Cgrimes85|Cgrimes85]] ([[User talk:Cgrimes85|talk]]) 17:03, 8 March 2019 (UTC) | ||
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: Only if you restrict yourself to using equilateral triangles. If you're allowed to vary the lengths of the edges, then the sum of angles at the center of each "hexagon" will be less than 360 degrees, causing the "hexagon" to flex into a non-planar shape. If you're using these to construct cosmic structures, the difference needed would be minuscule and undetectable to the naked eye. [[User:Shamino|Shamino]] ([[User talk:Shamino|talk]]) 13:03, 12 March 2019 (UTC) | : Only if you restrict yourself to using equilateral triangles. If you're allowed to vary the lengths of the edges, then the sum of angles at the center of each "hexagon" will be less than 360 degrees, causing the "hexagon" to flex into a non-planar shape. If you're using these to construct cosmic structures, the difference needed would be minuscule and undetectable to the naked eye. [[User:Shamino|Shamino]] ([[User talk:Shamino|talk]]) 13:03, 12 March 2019 (UTC) | ||
− | Note that you *would* see regular patterns in the cosmic Big Bang remnant radiation in some cosmological models (think of Arcade scrollers, just in 3D). Citation needed no longer: https:// | + | Note that you *would* see regular patterns in the cosmic Big Bang remnant radiation in some cosmological models (think of Arcade scrollers, just in 3D). Citation needed no longer: https://www.nature.com/articles/nature01944 [[Special:Contributions/198.41.242.46|198.41.242.46]] 10:29, 11 March 2019 (UTC) |
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Has anyone noticed that the Earth Temperature Timeline is in the list of the classic comics at the bottom? I looked on the wayback machine and it looks like it appeared on March 1, but i didnt see anybody mention it on the other talk pages since. Maybe I just missed it though. [[User:Choochoobob123|Choochoobob123]] ([[User talk:Choochoobob123|talk]]) 13:59, 11 March 2019 (UTC) | Has anyone noticed that the Earth Temperature Timeline is in the list of the classic comics at the bottom? I looked on the wayback machine and it looks like it appeared on March 1, but i didnt see anybody mention it on the other talk pages since. Maybe I just missed it though. [[User:Choochoobob123|Choochoobob123]] ([[User talk:Choochoobob123|talk]]) 13:59, 11 March 2019 (UTC) | ||
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