Polygons – Is a Line Segment Considered a Polygon?

polygons

per wiki, a polygon is

a plane figure that is described by a finite number of straight line
segments connected to form a closed polygonal chain or polygonal
circuit.

"is a line segment a polygon"? i searched this question on math.stackexchange, and didn't get a related post though, this post on gamedev.stackexchange is discussing this question.

I guess the answer is yes, I just need a double confirmation.

a well-recognized textbook claim this would be appreciated.

Best Answer

Instead of the definition on wiki, a more authoritative reference is Hilbert's The foundations of geometry. In $\S 4$, a polygon is defined as follows

A system of segments $AB, BC, CD, \ldots, KL$ is called a broken line joining $A$ with $L$ ...... The points lying within the segments $AB, BC, CD, \ldots, KL$, as also the points $A,B,C,D,\ldots,K,L$, are called the points of the broken line. In particular, if the point $A$ coincides with $L$, the broken line is called a polygon...

The key part is the starting point $A$ coincides with the ending point $L$. This is the same as the requirement of closed polygon chain on wiki.

By this definition, a single line segment cannot be a chain (unless it reduces to a single point).

A polygon isn't just a collection of its points. In addition to its points, it also contain the geometrical/combinatorial information like where are the vertices and how are the vertices connected.

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