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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: 918 Registered: 12/15/13
A ten-sided polygon has the following property ...
Posted: Jun 8, 2014 3:25 PM

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
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 Port563
6/8/14 James Waldby
6/9/14 Port563
6/9/14 William Elliot
6/9/14 Robin Chapman
6/9/14 Port563
6/9/14 Peter Percival
6/10/14 William Elliot
6/9/14 Peter Percival
6/9/14 Robin Chapman
6/9/14 Phil Carmody
6/9/14 Brian Q. Hutchings
6/10/14 Port563
6/10/14 Leon Aigret
6/10/14 Port563
6/10/14 Leon Aigret
6/10/14 Port563
6/10/14 Leon Aigret
6/10/14 Port563
6/10/14 Phil Carmody
6/10/14 Phil Carmody
6/10/14 Port563
6/10/14 Phil Carmody
6/10/14 Port563
6/10/14 thenewcalculus@gmail.com
6/10/14 Brian Q. Hutchings
6/10/14 Brian Q. Hutchings
6/11/14 Port563
6/10/14 Waldek Hebisch
6/11/14 quasi
6/11/14 quasi
6/11/14 quasi
6/11/14 quasi
6/12/14 quasi
6/12/14 quasi
6/11/14 Phil Carmody
6/11/14 quasi
6/11/14 Phil Carmody
6/11/14 Port563
6/11/14 Leon Aigret
6/11/14 quasi