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)