Port563
Posts:
721
Registered:
12/15/13


A tensided polygon has the following property ...
Posted:
Jun 8, 2014 3:25 PM


Draw a tensided 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 nsided polygon (or "ngon") may be defined as the union of n > 2 distinct line segments ("sides") of nonzero 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 10gon is not also a kgon where k<10.

