# What do you call a pair of diagonally-opposite points on a square or rectangle, relative to the other pair of points?

Suppose there is a rectangle with corners `N,E,S,W`, names assigned in a clockwise fashion, as you might expect. `N` and `S` are diametrically opposite, as are `E` and `W`.

Is there a term that describes points `E,W`, relative to `N,S`?

I am told diametrically opposite is not totally correct, perpendicular describes the line connecting the points rather than the pairs of points themselves, and other diagonally-opposite pair is clumsy and dissatisfying. This question is related, but I'm hoping for a term which may be applied arbitrarily (without knowing the orientation of the rectangle, needed for diagonal sinister and dexter) and without referring directly to the cardinal points ("NS-EW," etc.).

Mathematics, like medicine, has nomenclature for every trivial thing (usually in Latin). Surely there must be a term for this, too?

(For clarity's sake, I am looking for a term describing the relationship between the two pairs of points, rather than between the individual points in the remaining pair.)

• What's wrong with opposite? Jun 16, 2016 at 22:45
• @Silenus Opposite is okay, but the problem with it is that the term is more at home describing the points themselves, rather than the relationship between the two pairs of diagonally-opposite points. That the points (collectively or individually) are not properly opposite from either in the other pair is a problem for it, as well. :/ Jun 16, 2016 at 22:47
• I would say they're opposite corners. Jun 17, 2016 at 2:02
• What about catercorner? Jun 17, 2016 at 6:22
• @BruceWayne It looks like catercorner also refers to the relationship between the remaining points ("diagonal"), rather than the relationship between the two pairs of points. I've never heard the term before, so I could be wrong? Jun 18, 2016 at 19:37

Consider main and transverse pairs: the 'transverse' pair lying across the diagonal axis described by the 'main' pair. In geometry, 'transverse' seems to apply more to curves and waves than to points on a plane, though, so it may not be fully appropriate.

I am not sure there is any such term. All I recall from my mathematics days (up through and including college—I'm now a Computer Scientist, we do no real math :-) ) is labeling each vertex A, B, C, and D, for instance.

This Wolfram page on quadrilaterals gives a bunch of useful mathematics jargon terms. The two diagonals, specifically, are the polygon diagonals. You could speak of the "vertices of a polygon diagonal" and then simply say "the other vertices" or "the vertices of the other diagonal" to refer to either pair.

(Note that a rectangle is simply a special case of a parallelogram, which is a special case of a quadrilateral. That, plus one Wolfram link, is hardly proof that there is no special term, of course.)

• I'm an amateur programmer and city planner. What I know of math I know from 'Overflow. ;) (And first year calculus which passed by the atoms of my fingernails, but eh.) Jun 17, 2016 at 16:54

The pairs are symmetric to each other.

That's the type of rotational symmetry.

• That's true for remaining points relative to each other, but does it describe the pair properly? The two of them together are not symmetrically opposite from the first two. Also, this doesn't work on a rectangle... Jun 16, 2016 at 22:58
• There are different types of symmetry Jun 16, 2016 at 22:59
• Aa, I see. It does have rotational symmetry. But does it describe one pair's relationship to the other, or the relationship between the remaining two points themselves? Jun 16, 2016 at 23:02
• The edit (1) removed 'A "normal" car' which looked strange = improvement, (2) changed wording staying within OP's intention. Result: improvement. Edit accepted. Jul 9, 2016 at 10:24
• @Rathony In short: I uphold my decision to accept this edit. You can call me a moron, because I have different opinion than yours; but don't rebuke me for a lack of attention. Jul 9, 2016 at 10:28