Definition talk:Polygon/Chord

Definition
Sorry for the confusion. My source, the Joseph O'Rourke book has:


 * p. 12:  [the chord] is completely interior to $P$ (i.e., does not intersect $\partial P$)

It was the last part that confused me, so I believed it was enough to require that the chord should not intersect any other sides of $P$, but that obviously does not work. Have changed it now.
 * "should not intersect any other sides of $P$" could be made more rigorous by wording it as "does not intersect $\partial P$ except at the endpoints."

O'Rourke also uses the word internal diagonal, but he does not formally define it. Maybe we could do that. --Anghel (talk) 17:02, 18 November 2022 (UTC)


 * If it's in there, it's worth defining. I have always found it a mistake to gloss over or ignore a definition given in a source work, as it is often the case that it is used later on when you are not expecting it. --prime mover (talk) 17:40, 18 November 2022 (UTC)


 * I also wonder whether O'Rourke's constraint that it should lie entirely internal to $P$ may not be so much an "also defined as" as the main canonical definition. Can we find sources which allow $AF$ to be a chord? --prime mover (talk) 17:43, 18 November 2022 (UTC)


 * Most sources use the word diagonal of polygonal instead of chord of polygon. The standard definition of diagonal does not require it to be entirely internal, so $AF$, and $AE$ as well, are diagonals. I have not found any hard-copy sources that uses chord. There are a few questions on StackExchange and a few papers that use the term chord, most of them use it without the internal requirement. So no, I don't believe we should change our canonical definition.


 * Maybe we should define internal chord, and make a rigorous definition like:


 * ...expect for the two vertices, which are the endpoints of the chord, the chord lies entirely in the interior of the polygon.


 * Any sources or opinions on whether we should use internal chord or internal diagonal, whether chords and diagonals should have the same definition, or different definitions? --Anghel (talk) 19:34, 18 November 2022 (UTC)


 * More examples, maybe: "$GE$ is an internal chord, $AF$ is a ..., $AE$ is a ...(more complicated thing) etc. --prime mover (talk) 00:25, 19 November 2022 (UTC)