Sorry about a typo in my previous question on: common intersection of
circles
Jie Lin
jie.lin at yale.edu
Tue Mar 11 22:21:46 PST 2003
I am reall sorry for sending this msg again. But I discovered a typo in my
previous msg.
The set of point should be "Within" radius R from the origin, not "With".
Best Regards,
Jie
----- Original Message -----
From: "Jie Lin" <jie.lin at yale.edu>
To: <compgeom-discuss at research.bell-labs.com>
Sent: Tuesday, March 11, 2003 9:21 PM
Subject: common intersection of circles
> Hello computational geometry people,
>
> I have n points {z_1, z_2, ... z_n} in the plane, located with radius R
from
> the origin. Denote H the convex hull of these n points plus the origin.
> Denote C_i the circle with radius R centered at each point z_i. Denote S
the
> intersection of C_i.
>
> Now, it can be shown that if the origin 0 is a corner of the convex hull
H,
> then S has non-empty interior (contains more than point 0).
>
> My question is that whether or not the centroid (center of mass) of
S ---the
> common intersection of circles, is located in the convex hull H. If not,
> does the line segment from 0 to the centroid of S has a positive
> intersection with H?
>
> My feeling is yes, but I had trouble showing it. I hope someone in this
> group can help me out here. Thanks in advance.
>
> Sincerely,
>
> Jie
>
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