Timeline for Work on "Churning Polygons"
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 25, 2017 at 17:58 | comment | added | j.c. | This is 6 variables satisfying 5 equations so you can set one more condition freely, e.g. tweak the angle at vertex 2 or change the distance between vertices 1 and 3. Hopefully that is sufficiently concrete that you can test this out with your favorite polynomial system solver. | |
| Jun 25, 2017 at 17:55 | comment | added | j.c. | For a concrete example when $n=5$, consider a polygon with all side lengths equal to 1 but not in the regular configuration (as that maximizes the area and hence cannot be "churned"). Suppose vertex 1 is at the origin and vertex 2 is at $(1,0)$. Then we have 6 variables $(x_i,y_i)$ for $i=3,\dots,5$ which must satisfy 4 more equations preserving unit lengths of sides 2 through 5. The area of the polygon can be written in terms of the vertex coordinates using e.g. en.wikipedia.org/wiki/Shoelace_formula and this gives one more equation. | |
| Jun 25, 2017 at 17:39 | comment | added | Manfred Weis | The provided pointers to the resources answer my question regarding previous/related work sufficiently; than you very much! | |
| Jun 25, 2017 at 17:37 | vote | accept | Manfred Weis | ||
| Jun 25, 2017 at 17:35 | comment | added | Manfred Weis | A concrete example for $n=5$ would be very desirable to me. | |
| Jun 25, 2017 at 16:10 | history | answered | j.c. | CC BY-SA 3.0 |