Timeline for Constructing a polygon from another with collinearity constraints
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 29, 2023 at 16:36 | vote | accept | Manfred Weis | ||
| Jan 29, 2023 at 11:26 | answer | added | Ivan Izmestiev | timeline score: 2 | |
| Jan 28, 2023 at 10:12 | comment | added | Manfred Weis | @ChristopheLeuridan its a line orthogonal to $p_{i+1}-p_i$ through $\left(p_i+p_{i+1}\right)/2$ | |
| Jan 28, 2023 at 10:09 | comment | added | Manfred Weis | @IosifPinelis in the case of regular $2n$-gons the solution is not unique; would be another interesting problem to characterise the polygons with ambiguous solution - I suspect that periodicity of angles and sidelengths plays a role. The existence seems however to be granted - if one starts with $q_0$ arbitrarily chosen and proceed on the repeated sequence of polygon points to get $q_{i+1}$ from $q_i$ and $p_{i+1}$ one will observe a kind of spiraling behavior where $q_0'\ne q_0$ in general. Using $\left(q_0'+q_0\right)/2$ as the starting point for the next iteration will solve the problem. | |
| Jan 27, 2023 at 19:40 | comment | added | Christophe Leuridan | What is the bisector of two points? | |
| Jan 27, 2023 at 19:36 | comment | added | Iosif Pinelis | I see. Do you know anything about the existence and uniqueness of the $q_i$'s? About their expressions in terms of the $p_i$'s? | |
| Jan 27, 2023 at 16:04 | comment | added | Manfred Weis | @IosifPinelis my apologies; I mixed up the $p$ and $q$; it should now be correct. | |
| Jan 27, 2023 at 16:02 | history | edited | Manfred Weis | CC BY-SA 4.0 |
fixed an error
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| Jan 27, 2023 at 15:37 | comment | added | Iosif Pinelis | Do I understand it correctly that $q_i$ is just the midpoint between $p_i$ and $p_{i+1}$? If so, what is the difficulty? Or, perhaps, I don't understand what you mean by the bisector of points. | |
| Jan 27, 2023 at 14:55 | history | asked | Manfred Weis | CC BY-SA 4.0 |