Polygon or not?

  • #1
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Can someone please tell is this (ibb.co/stGFSKs) figure a polygon. If yes then is the middle line would count as an edge?

15487814949745525543992389032260.jpg
 

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  • #2
.Scott
Homework Helper
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Yes, it could be described as a polygon - but not a "simple polygon".
https://en.wikipedia.org/wiki/Polygon

If the left edge from top to bottom is A, B, D and the right edge from top to bottom is A, C, E:
Then this could be described as polygon ABCBDECA or ABCEDCDA.

Thus, it would be a polygon that intersects itself.
polygons that do not intersect themselves are called "simple polygons".

Oh, and to answer your follow-on question: The middle line segment would be two edges.
 
  • #3
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Yes, it could be described as a polygon - but not a "simple polygon".
https://en.wikipedia.org/wiki/Polygon

If the left edge from top to bottom is A, B, D and the right edge from top to bottom is A, C, E:
Then this could be described as polygon ABCBDECA or ABCEDCDA.

Thus, it would be a polygon that intersects itself.
polygons that do not intersect themselves are called "simple polygons".

Oh, and to answer your follow-on question: The middle line segment would be two edges.
let be name the points as,(https://ibb.co/2srLjB1) if AC would be an edge then A and C are vertices and segments BC, AC, AD, CE became edges. Is this justified Also for a simple polygon there should be no self intersecting edge, the line AC just touches the lines BD and BE, is this sufficient to fulfill the intersecting condition?
 
  • #4
.Scott
Homework Helper
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.With your new point labels, the polygon would be either BACADECB or BADECACB.
In order for it to be a polygon, you need to close the loop - end at the same place you started.
I am not sure I am interpreting your statements correctly, but it doesn't sound as though you are following that rule.
 
  • #5
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Can someone please tell is this (ibb.co/stGFSKs) figure a polygon. If yes then is the middle line would count as an edge?
To me, the question isn't answerable: either you define a polygon one way or the other, either allow straight angles or don't.
 
  • #6
14
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.With your new point labels, the polygon would be either BACADECB or BADECACB.
In order for it to be a polygon, you need to close the loop - end at the same place you started.
I am not sure I am interpreting your statements correctly, but it doesn't sound as though you are following that rule.
thanks for correcting
 

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