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Topic: A ten-sided polygon has the following property ...
Replies: 40   Last Post: Jun 12, 2014 12:44 AM

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Port563

Posts: 721
Registered: 12/15/13
A ten-sided polygon has the following property ...
Posted: Jun 8, 2014 3:25 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

Draw a ten-sided polygon* with the property that each of its sides is
collinear with at least one other side.

If this is impossible, prove why.

Otherwise, briefly describe its shape and prove an insightful necessary and
sufficient condition (other than the above collinearity property itself,
naturally) for it to have that property.

(-:



* For the avoidance of doubt (as there are many here whose mathematical
abilities exist only in their own imaginations):
A n-sided polygon (or "n-gon") may be defined as the union of n > 2 distinct
line segments ("sides") of non-zero length, arranged in a plane such that
each end of each side is coincident with an end of exactly one other side,
with no side touching or intersecting any other side except as above, and
with no adjacent sides collinear.
It follows from this definition that there are no gaps, intersections,
retracings/overlaps, multiple distinct internal areas, etc., and the 10-gon
is not also a k-gon where k<10.




Date Subject Author
6/8/14
Read A ten-sided polygon has the following property ...
Port563
6/8/14
Read Re: A ten-sided polygon has the following property ...
James Waldby
6/9/14
Read Re: A ten-sided polygon has the following property ...
Port563
6/9/14
Read Re: A ten-sided polygon has the following property ...
William Elliot
6/9/14
Read Re: A ten-sided polygon has the following property ...
Robin Chapman
6/9/14
Read Re: A ten-sided polygon has the following property ...
Port563
6/9/14
Read Re: A ten-sided polygon has the following property ...
Peter Percival
6/10/14
Read Re: A ten-sided polygon has the following property ...
William Elliot
6/9/14
Read Re: A ten-sided polygon has the following property ...
Peter Percival
6/9/14
Read Re: A ten-sided polygon has the following property ...
Robin Chapman
6/9/14
Read Re: A ten-sided polygon has the following property ...
Phil Carmody
6/9/14
Read Re: A ten-sided polygon has the following property ...
Brian Q. Hutchings
6/10/14
Read Re: A ten-sided polygon has the following property ...
Port563
6/10/14
Read Re: A ten-sided polygon has the following property ...
Leon Aigret
6/10/14
Read Re: A ten-sided polygon has the following property ...
Port563
6/10/14
Read Re: A ten-sided polygon has the following property ...
Leon Aigret
6/10/14
Read Re: A ten-sided polygon has the following property ...
Port563
6/10/14
Read Re: A ten-sided polygon has the following property ...
Leon Aigret
6/10/14
Read Re: A ten-sided polygon has the following property ...
Port563
6/10/14
Read Re: A ten-sided polygon has the following property ...
Phil Carmody
6/10/14
Read Re: A ten-sided polygon has the following property ...
Phil Carmody
6/10/14
Read Re: A ten-sided polygon has the following property ...
Port563
6/10/14
Read Re: A ten-sided polygon has the following property ...
Phil Carmody
6/10/14
Read Re: A ten-sided polygon has the following property ...
Port563
6/10/14
Read Re: A ten-sided polygon has the following property ...
thenewcalculus@gmail.com
6/10/14
Read Re: A ten-sided polygon has the following property ...
Brian Q. Hutchings
6/10/14
Read Re: A ten-sided polygon has the following property ...
Brian Q. Hutchings
6/11/14
Read Re: A ten-sided polygon has the following property ...
Port563
6/10/14
Read Re: A ten-sided polygon has the following property ...
Waldek Hebisch
6/11/14
Read Re: A ten-sided polygon has the following property ...
quasi
6/11/14
Read Re: A ten-sided polygon has the following property ...
quasi
6/11/14
Read Re: A ten-sided polygon has the following property ...
quasi
6/11/14
Read Re: A ten-sided polygon has the following property ...
quasi
6/12/14
Read Re: A ten-sided polygon has the following property ...
quasi
6/12/14
Read Re: A ten-sided polygon has the following property ...
quasi
6/11/14
Read Re: A ten-sided polygon has the following property ...
Phil Carmody
6/11/14
Read Re: A ten-sided polygon has the following property ...
quasi
6/11/14
Read Re: A ten-sided polygon has the following property ...
Phil Carmody
6/11/14
Read Re: A ten-sided polygon has the following property ...
Port563
6/11/14
Read Re: A ten-sided polygon has the following property ...
Leon Aigret
6/11/14
Read Re: A ten-sided polygon has the following property ...
quasi

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