Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math

Topic: polygons thrugh a given set of points
Replies: 63   Last Post: Jun 14, 2014 4:29 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Marnie Northington

Posts: 712
Registered: 12/13/04
Re: polygons thrugh a given set of points
Posted: Jun 12, 2014 1:51 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

quasi <quasi@null.set> wrote:
> Let n be an integer, n >= 3. For a set of n points in the plane,
> no 3 collinear, is there always at least one n-gon having those
> points as vertices?


Yes. For n = 3 this certainly holds.

For n > 3, choose two points p, q in the set such that the line between
them divides the remaining n - 2 points into two non-empty sets. For
both such sets, build a smaller polygon out of {that set's elements} U
{p, q} by induction, then join the two such polygons by equating the
mutual pq edge. Since no three points are collinear, no two remaining
edges are collinear, so it is easily seen that there are, in fact, n
edges.

This seems too straight-forward. Have I missed a catch?


Date Subject Author
6/12/14
Read polygons thrugh a given set of points
quasi
6/12/14
Read Re: polygons thrugh a given set of points
Marnie Northington
6/12/14
Read Re: polygons through a given set of points
quasi
6/12/14
Read Re: polygons through a given set of points
William Elliot
6/12/14
Read Re: polygons through a given set of points
quasi
6/12/14
Read Re: polygons through a given set of points
Marnie Northington
6/12/14
Read Re: polygons through a given set of points
quasi
6/12/14
Read Re: polygons through a given set of points
Marnie Northington
6/12/14
Read Re: polygons through a given set of points
quasi
6/12/14
Read Re: polygons through a given set of points
Marnie Northington
6/12/14
Read Re: polygons through a given set of points
quasi
6/12/14
Read Re: polygons thrugh a given set of points
Timothy Murphy
6/12/14
Read Re: polygons thrugh a given set of points
quasi
6/12/14
Read Re: polygons thrugh a given set of points
Peter Percival
6/12/14
Read Re: polygons thrugh a given set of points
quasi
6/13/14
Read Re: polygons thrugh a given set of points
Peter Percival
6/13/14
Read Re: polygons thrugh a given set of points
Port563
6/13/14
Read Re: polygons thrugh a given set of points
Peter Percival
6/13/14
Read Re: polygons thrugh a given set of points
Port563
6/12/14
Read Re: polygons thrugh a given set of points
Port563
6/12/14
Read Re: polygons thrugh a given set of points
quasi
6/12/14
Read Re: polygons thrugh a given set of points
Port563
6/12/14
Read Re: polygons thrugh a given set of points
quasi
6/12/14
Read Re: polygons thrugh a given set of points
quasi
6/13/14
Read Re: polygons thrugh a given set of points
Port563
6/13/14
Read Re: polygons thrugh a given set of points
quasi
6/13/14
Read Re: polygons thrugh a given set of points
Port563
6/13/14
Read Re: polygons thrugh a given set of points
quasi
6/13/14
Read Re: polygons thrugh a given set of points
Port563
6/13/14
Read Re: polygons thrugh a given set of points
scattered
6/12/14
Read Re: polygons thrugh a given set of points
quasi
6/13/14
Read Re: polygons thrugh a given set of points
Port563
6/12/14
Read Re: polygons thrugh a given set of points
David Hartley
6/12/14
Read Re: polygons thrugh a given set of points
quasi
6/12/14
Read Re: polygons thrugh a given set of points
quasi
6/13/14
Read Re: polygons thrugh a given set of points
Port563
6/13/14
Read Re: polygons thrugh a given set of points
David Hartley
6/13/14
Read Re: polygons thrugh a given set of points
Peter Percival
6/13/14
Read Re: polygons thrugh a given set of points
Port563
6/13/14
Read Re: polygons thrugh a given set of points
quasi
6/13/14
Read Re: polygons thrugh a given set of points
Port563
6/13/14
Read Re: polygons thrugh a given set of points
quasi
6/13/14
Read Re: polygons thrugh a given set of points
quasi
6/13/14
Read Re: polygons thrugh a given set of points
Port563
6/13/14
Read Re: polygons thrugh a given set of points
Peter Percival
6/13/14
Read Re: polygons thrugh a given set of points
quasi
6/12/14
Read Re: polygons thrugh a given set of points
Bart Goddard
6/12/14
Read Re: polygons thrugh a given set of points
scattered
6/12/14
Read Re: polygons thrugh a given set of points
scattered
6/12/14
Read Re: polygons thrugh a given set of points
quasi
6/12/14
Read Re: polygons thrugh a given set of points
David Hartley
6/12/14
Read Re: polygons thrugh a given set of points
quasi
6/12/14
Read Re: polygons thrugh a given set of points
Richard Tobin
6/12/14
Read Re: polygons thrugh a given set of points
quasi
6/13/14
Read Re: polygons thrugh a given set of points
William Elliot
6/13/14
Read Re: polygons thrugh a given set of points
quasi
6/13/14
Read Re: polygons thrugh a given set of points
William Elliot
6/13/14
Read Re: polygons thrugh a given set of points
quasi
6/13/14
Read Re: polygons thrugh a given set of points
David Hartley
6/13/14
Read Re: polygons thrugh a given set of points
quasi
6/13/14
Read Re: polygons thrugh a given set of points
Phil Carmody
6/13/14
Read Re: polygons thrugh a given set of points
Phil Carmody
6/14/14
Read Re: polygons thrugh a given set of points
quasi
6/14/14
Read Re: polygons thrugh a given set of points
quasi

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.