Timeline for Intersection of pencils in $\mathcal{R}^2$
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Aug 28, 2011 at 11:13 | comment | added | Sukhada Fadnavis | Sure, $n$ would also be good. There are examples of $n$ pencils each with $n$ lines such that $|S| = 2n$. One way to see this example is as follows: Consider the regular 2n-gon. Let the pencils be centred at points at infinity in the directions joining the midpoints of opposite edges. This is not in the euclidean plane as described but can be modified to fit in it. But in general I don't know if $|S| = O(n)$. I think $9n$ should further restrict the configuration and wonder if there are examples with $|S| \geq cn$ in this case for any constant $c >1$. | |
| Aug 28, 2011 at 10:00 | comment | added | domotorp | Why 9n and not n? | |
| Aug 26, 2011 at 11:03 | comment | added | Gjergji Zaimi | As you pointed out my answer was incomplete. I will think about it some more and then un-delete it if I can make it work. | |
| Aug 26, 2011 at 7:45 | comment | added | Gjergji Zaimi | I hope you don't mind, I added the arxiv tags. | |
| Aug 26, 2011 at 7:43 | history | edited | Gjergji Zaimi |
edited tags
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| Aug 26, 2011 at 6:16 | history | asked | Sukhada Fadnavis | CC BY-SA 3.0 |