We are writing a mathematical article. We are describing objects (unit squares) rotated only 0° and 45°.

For easier use we call 0° rotated "axial".

What should we call 45° rotated? Using just "rotated" can be misleading, as it could mean arbitrarily rotated.

"Oblique" seems best to me. "Diagonal" is something else.

Edit: Sure, we are going to define it. But imagine a casual reader who looks in the middle of the article and see "rotated square". It is neither obvious that this square is 45° rotated nor that there is some definition. "mitred square" does not sounds familiar and reader will see the definition.

  • 2
    As long as you define how you are describing it, you can use any such word. "When the square is rotated 45°, which we shall call oblique, ..."
    – Andrew Leach
    Commented Apr 19, 2013 at 11:15
  • I don't think there's a word or phrase (beyond 'rotated 45 degrees') that captures exactly (no more, no less) that concept. 'Oblique', 'askew', 'at an angle' all capture a general angle, just not exactly 45 degrees.
    – Mitch
    Commented Apr 19, 2013 at 12:20
  • Sometimes you have to define acronyms and abbreviations. It doesn't take a sophisticated reader to know (or expect) that an unfamiliar term is defined somewhere in a paper. Use whatever term you want, define it, and go from there. If you are really concerned that readers need to know something in order to understand the rest of your document, you should organize it so they can easily find the introductory material. Maybe in a section called "Introduction" or something... Commented Apr 19, 2013 at 18:32

2 Answers 2


Also consider calling the rotated square a biased square or a square on the bias, where bias imparts the sense of diagonal, oblique, slanting.

For example, on the bias ordinarily refers to a 45° slope (or more precisely, the slope of a series of intersections of warp and weft) in sewing. From Merriam Webster:

a line diagonal to the grain of a fabric; especially: a line at a 45 degree angle to the selvage often utilized in the cutting of garments for smoother fit.

From OED1, sense A.1. of bias:

Slanting, oblique. Bias line : (in early geometry) a diagonal or hypotenuse. [eg] 1551 RECORDE Pathw. Knowl. II. xxxii, By the Bias line, I meane that lyne, whiche in any square figure dooth runne from corner to corner.

You might also refer to an indexed square. Like rotated square, the phrase indexed square does not imply a certain angle, such as 45°; but on the other hand, indexing is not free rotation. It frequently is to cardinal angles or to multiples of 15, 30, or 45°. In short, indexing an item means rotating or moving it to a preset location:

Usually when the word indexing is used, it refers specifically to rotation. ... For example, Machinery’s Handbook, 25th edition, in its section on milling machine indexing, says, “Positioning a workpiece at a precise angle or interval of rotation for a machining operation is called indexing.”


The OED has:

mid-angle n. (a) an angle of 45 degrees (rare—0); (b) an intermediate or mean angle.

The newer version of mid-angle is cited in the 1980s in the Journal of the Royal Statistical Society and Journal of the American Statistical Association.


  1. Mil. The action or position of facing half-way to the right or left, i.e. at an angle of 45 degrees.

mitre | miter:

  1. A usually right-angled joint in wood or other material in which the angle made by the joined pieces is bisected by the line or plane of junction; more fully mitre joint. Also: the shaped end or edge of a piece of wood, etc., intended to form one side of such a joint; the angle (usually of 45 degrees) into which such an end or edge is shaped.

And adjectives mitred | mitered:

  1. Of a surface: having an end or edge shaped to an angle of 45 degrees. Also: designating a mitre joint; connected or united by such a joint.

If you do use any of these, I agree with Andrew Leach that you should define it first.

  • +1 for mid-angle. Until today, I considered (subconsciously) it as a 'Maths word' from the elementary geometry classes and didn't even use it all this while as an actual English word!
    – camelbrush
    Commented Apr 20, 2013 at 1:04

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