# Words for diagonal directions

I'm a mathematician currently working on a problem involving splitting a square into two triangles, either by a line connecting top-left and bottom-right, or top-right and bottom left. I'm trying to think of natural names for these, but the only thing I could think of was acute and grave (after the directions of accents, originally Greek I believe). Are there other options?

• If you are looking to simply identify them in text, you could refer to the forward slash(/) and the back slash (\), but note that many people don’t intuitively grasp which is which. Jun 13 at 9:12
• NW - SE and SW - NE seem fairly clear. Jun 13 at 10:35
• Duplicate of Terminology for diagonal line that also indicates orientation, but the answers there aren't so great.
– Laurel
Jun 13 at 12:44
• The heraldic terms for those lines are bend (for the top left to bottom right, as seen full-on), and the bend sinister in the opposite orientation. As the shield was worn, the bend went from the holder's right shoulder to his left hip. Jun 13 at 17:05
• There is also "up to right" and "up to left." Do you have a sample sentence with an underline so we know what to put in it? Jun 13 at 20:19

I have seen them being referred to as positive diagonal (forward slash, / ) and negative diagonal (backslash, \ ), basically in reference to their slope as seen in a standard euclidean axial system.

In a mathematical setting, I feel those terms might be more intuitive than names of accents most speakers of English are not directly familiar with.

As mentioned in a comment, I probably picked up this usage from sodoku. It is used regularly on the cracking the cryptic Youtube channel. Logic masters Germany uses this terminology as well:

Digits cannot repeat along the positive diagonal.

• Without supporting references, this comes across as anecdotal or at best niche usage. The string 'positive diagonal' seems to appear most often when discussing matrices, and refers to the values of elements, not orientation. Jun 13 at 10:33
• The terms "positive diagonal" and "negative diagonal" are used in this way in sudoku, for example here Simon, in explaining a rule, uses these terms. Jun 13 at 11:22
• For matrices, the NW-SE diagonal is the main or principal diagonal, the NE-SW the minor or anti- diagonal (see math.stackexchange.com/questions/227345), so in a sense contrary the positive/negative Jun 13 at 11:39
• Ah, another CTC devotee. Jun 13 at 19:47
• @PhilSweet Yup, I need the daily double dose :) Jun 14 at 9:01

One idea is to call them according to their attitude from left to right, that is, an inclining diagonal when going from bottom to top and a declining diagonal when going from top to bottom.

For example, these quilting directions by Linda Ambrosini ("Pixie Sticks," Hoffman Fabrics) make use of the inclining cut and inclining diagonal to describe a cut going from bottom left to top right and the declining cut and diagonal for the other case. Then an explanation of Hanidoku, a hexagonal Sudoku variant, uses inclining diagonal and descending diagonal to describe lines of hexagons.

You could also use rising and falling diagonal, which are the names of the Unicode characters ⟋ and ⟍, respectively (Compart 1, 2). In both cases, you rely on an English reader's tendency to read from left to right and thus to perceive a line as rising or falling based on its behavior going from left to right.

• "Rising" and "falling" seem intuitive, based on the shape of line graphs and similar. "Inclining" and "declining" less so, as "incline" typically means to lean or tilt regardless of direction, and can mean to bow down. Jun 13 at 13:20

It's a bit off the wall, but could you possibly rotate your problem to dividing a diamond into two triangles? Then you can refer to the lines as vertical and horizontal, and avoid any confusion.

• That's very true! (and out of the box thinking), but rather putting the cart before the horse :-) Jun 15 at 16:00

Given the standard (and very widespread) road signs for hills such as that below which is for an uphill gradient.

I would suggest that either Ascending/Descending or Up/down slant.

Of course in a formal paper you could always mention, or illustrate, the words that you decide to use either in an introductory section or at the first usage.