Wikipedia:Reference desk/Archives/Mathematics/2020 September 20

= September 20 =

Who is this quote from?
Hi, I am searching for a Quote somewhere arround the lines of: "One of the strangest facts about Numbers is that they stay the same no matter the order of counting". Does anyone know whom it is from? Thanks in advance TheFibonacciEffect (talk • contribs) 11:02, 20 September 2020 (UTC)

Is there any 3d planet shape that you can project into 2d without distortion?
Is there any 3d shape that you can project into 2d without distortion?

When talking about earth shape, you can't make a map of it that wont have distortion, is there any 3d shape that you can make a map out of it without distortion?2804:7F2:594:E83B:102D:4EF4:250E:874F (talk) 21:08, 20 September 2020 (UTC)


 * It depends a bit what you mean by "distortion". A conformal map preserves angles but not relative sizes. If missing out on one or two points is not a big deal, then the Mercator projection and the stereographic projection are two examples that map the sphere conformally to the plane. If relative sizes also need to be preserved, it is impossible for any shape that is plausible for a planet. A cylinder can be unrolled without distortion into the plane, and so can a cone. Any shape that is topologically a sphere or a torus (see Homeomorphism) cannot be mapped completely distortion-free to a plane. --Lambiam 22:12, 20 September 2020 (UTC)


 * This planet can be mapped in 2D with minimal distortion. catslash (talk) 22:15, 20 September 2020 (UTC)


 * See Developable surface, the examples in the Particulars section. Any polyhedral planet would count, assuming you don't mind edges or corners. There is an embedding of the the torus in 4d which maps to the plane with no local distortion, and I suppose that could be a planet shape. Some old-school video games used this plan, see Wraparound (video games). --RDBury (talk) 01:14, 21 September 2020 (UTC)
 * We of course have an article on such a planet: Bizarro World or Htrae - from our article: "Htrae is a cube-shaped planet"John Z (talk) 01:22, 21 September 2020 (UTC)
 * To map the surface of a cube to a plane, you have to cut it open, so that points that were extremely close on the cube are far apart in the plane, which I consider a distortion. --Lambiam 07:30, 21 September 2020 (UTC)