Editing Talk:2121: Light Pollution

Jump to: navigation, search
Ambox notice.png Please sign your posts with ~~~~

Warning: You are not logged in. Your IP address will be publicly visible if you make any edits. If you log in or create an account, your edits will be attributed to your username, along with other benefits.

The edit can be undone. Please check the comparison below to verify that this is what you want to do, and then save the changes below to finish undoing the edit.
Latest revision Your text
Line 18: Line 18:
  
 
: 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, but isosceles triangles instead, since the hexagons appear to be uniform).  Once you realize that the angles on the hexagons' vertices 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)  
+
::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)

Please note that all contributions to explain xkcd may be edited, altered, or removed by other contributors. If you do not want your writing to be edited mercilessly, then do not submit it here.
You are also promising us that you wrote this yourself, or copied it from a public domain or similar free resource (see explain xkcd:Copyrights for details). Do not submit copyrighted work without permission!

To protect the wiki against automated edit spam, we kindly ask you to solve the following CAPTCHA:

Cancel | Editing help (opens in new window)

Templates used on this page: