Timeline for Number of polytopes formed by connecting points on a hypercube
Current License: CC BY-SA 4.0
16 events
| when toggle format | what | by | license | comment | |
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| Apr 24, 2020 at 22:40 | comment | added | Joseph O'Rourke | @GerhardPaseman: Beautiful! Same diagram, colored. | |
| Apr 24, 2020 at 22:34 | comment | added | Gerhard Paseman | You should check out the pictures behind the OEIS link. Gerhard "Step Up Your Game Time" Paseman, 2020.04.24. | |
| Apr 24, 2020 at 20:35 | comment | added | Joseph O'Rourke | @GerhardPaseman: Thanks for your several corrections. I confirm your count of $340$. | |
| Apr 24, 2020 at 20:34 | history | undeleted | Joseph O'Rourke | ||
| Apr 24, 2020 at 20:34 | history | edited | Joseph O'Rourke | CC BY-SA 4.0 |
deleted 81 characters in body
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| Apr 24, 2020 at 19:25 | history | deleted | Joseph O'Rourke | via Vote | |
| Apr 24, 2020 at 19:08 | comment | added | Gerhard Paseman | OK, as long as you caption the picture as having to do with something other than a(3,2), it should be OK. Remember the problem speaks of boundary points. Gerhard "Likes Getting A Good Picture" Paseman, 2020.04.24. | |
| Apr 24, 2020 at 18:44 | history | edited | Joseph O'Rourke | CC BY-SA 4.0 |
added 44 characters in body
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| Apr 24, 2020 at 18:43 | history | undeleted | Joseph O'Rourke | ||
| Apr 24, 2020 at 16:40 | history | deleted | Joseph O'Rourke | via Vote | |
| Apr 24, 2020 at 14:49 | comment | added | Gerhard Paseman | I just noticed there are sixteen extra lines in the picture above, creating extra regions. (Dividing lines need to not stop at internal points.) Using symmetry, we see one line has ten segments and another has fourteen. Taking into account the (up to symmetry) two kinds of intersections involving only internal lines, we get 8*(10+14 - 1) - 4 .= 180 fewer regions, for a new total of 340. Gerhard "Surely That's Easier To Count?" Paseman, 2020.04.24. | |
| Apr 23, 2020 at 23:48 | comment | added | Gerhard Paseman | I think the pixellation makes a one pixel high contrast which suggests part of a horizontal line segment, and having several them at the same y ordinate reinforces the idea that there is a horizontal"ground line" occurring. I'm not seeing the vertical as much, possibly be sure of astigmatism. Gerhard "We Should Ask Scott Kim" Paseman, 2020.04.23. | |
| Apr 23, 2020 at 23:43 | comment | added | alesia | yes, I'm seeing them as well | |
| Apr 23, 2020 at 23:25 | comment | added | Joseph O'Rourke | Does anyone else experience the optical illusion of thin, white horizontal and vertical lines passing through the center of the square? For me they come and go depending on my visual focus... | |
| Apr 23, 2020 at 22:22 | comment | added | Gerhard Paseman | Didn't your mother teach you to use symmetry? Really, I had higher hopes. Starting with half of the lower right square ( (3,3) in my indexing) I count 20 regions (more than half triangular) which gives 160 for all four corner squares. Picking half of an edge square ((1,2), say) I count 31 non central and four central regions, giving 264 for the edge squares. Take a triangular fourth of the central square and use symmetry to get 24 for the quarter and 96 for the square. 520 in all. Gerhard "Taught Himself Symmetry When Younger" Paseman, 2020.04.23. | |
| Apr 23, 2020 at 21:21 | history | answered | Joseph O'Rourke | CC BY-SA 4.0 |
