Timeline for Gauss-Bonnet Theorem: Neither Gauss nor Bonnet [closed]
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 1, 2021 at 16:16 | history | left closed in review |
Johannes Hahn Joonas Ilmavirta Dag Oskar Madsen |
Original close reason(s) were not resolved | |
| Nov 23, 2021 at 21:23 | review | Reopen votes | |||
| Dec 1, 2021 at 16:16 | |||||
| Nov 23, 2021 at 20:09 | history | closed |
Wojowu LSpice Daniele Tampieri Alexandre Eremenko Ben McKay |
Not suitable for this site | |
| Nov 23, 2021 at 0:32 | comment | added | Joseph O'Rourke | A belated addition to explain what Needham means by "the Gauss-Bonnet theorem." | |
| Nov 23, 2021 at 0:21 | history | edited | Joseph O'Rourke | CC BY-SA 4.0 |
added 264 characters in body
|
| Nov 22, 2021 at 0:25 | vote | accept | Joseph O'Rourke | ||
| Nov 21, 2021 at 22:21 | comment | added | Ryan Budney | Perhaps Needham's statement stems from a relatively narrow reading of what the Gauss-Bonnet theorem is stating. At its most broad, you could view Gauss-Bonnet as a statement of what the integral of the curvature over a 2-dimensional manifold (perhaps with corners) is, in terms of the curvature of the boundary curves (including jump angles) and the euler characteristic of the 2-dimensional manifold. Gauss's version assuming the region is a geodesic triangle is one instance of the theorem, but it of course can be stated in greater generality. | |
| Nov 21, 2021 at 17:45 | history | became hot network question | |||
| Nov 21, 2021 at 14:58 | answer | added | Carlo Beenakker | timeline score: 14 | |
| Nov 21, 2021 at 6:41 | comment | added | Kapil | The "classical" form of the Gauss-Bonnet theorem talks about the sum of angles of a geodesic triangle in terms of the integral of the curvature over it; this is a statement in differential geometry. However, in modern differential topology books it is usually stated as a relation between the Euler characteristic of a compact surface and the integral of the curvature over it. Perhaps this distinction is at play. | |
| Nov 21, 2021 at 2:25 | review | Close votes | |||
| Nov 23, 2021 at 20:09 | |||||
| Nov 21, 2021 at 1:11 | comment | added | Gerald Edgar | Surely better for hsm.stackexchange.com | |
| Nov 21, 2021 at 1:05 | history | edited | Carl-Fredrik Nyberg Brodda | CC BY-SA 4.0 |
added 4 characters in body
|
| Nov 21, 2021 at 0:28 | history | asked | Joseph O'Rourke | CC BY-SA 4.0 |