Timeline for Classification of spherical polygons
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 14, 2014 at 9:35 | vote | accept | asd | ||
| Dec 13, 2014 at 14:07 | answer | added | Alexandre Eremenko | timeline score: 5 | |
| Dec 13, 2014 at 13:51 | comment | added | asd | @Alex: In Euclidean plane this problem (from the comment above) would mean to construct two n-gons with same interior angles, area and perimeter. This problem is easily solved. In spherical case this is less obvious to me. | |
| Dec 13, 2014 at 13:42 | comment | added | asd | Thank you for your comments, I will be more precise. First, it would help me to know if there are non isometric n-gons with $n\geq 4$ with same interior angles $\alpha_1,…,\alpha_n$ and same perimeter (i.e. sum of the side lengths) $a_1+…+a_n$. E.g. for n=4 I could construct a one parameter family of non isometric 4-gons with same interior angles, but which all have different perimeter. Are there two 4-gone which not only have the same interior angles but also the same perimeter? | |
| Dec 13, 2014 at 12:27 | comment | added | Joonas Ilmavirta | You can triangulate any polygon with more than three vertices. This helps reduce some problems for general polygons (like the sum of angles as a function of area) to those with triangles, but it's hard to say more before you specify your question. | |
| Dec 13, 2014 at 11:50 | comment | added | Alex Degtyarev | In the case of more than three vertices you have more than $0$ degrees of freedom. What kind of classification are you looking for? E.g., what would the Euclidean counterpart be? | |
| Dec 13, 2014 at 11:41 | review | First posts | |||
| Dec 13, 2014 at 11:50 | |||||
| Dec 13, 2014 at 11:41 | history | asked | asd | CC BY-SA 3.0 |