# How square is a square

I've recently heard the follwing sentence in a text for children learning English:

The blackboard is square.

It got translated to the German equivalent of “the blackboard is quadrilateral”. The English version felt plain wrong to me, since to me a square has to have four right angles and four edges of equal length, while blackboards tend to be wider than they are high. But since my professional interest lies with geometry, I might be overly picky when it comes to using correct terms for geometric objects.

I've seen an online dictionary use the term “square” as a possible translation for the German term for quadrilateral. The Merriam-Webster online dictionary, on the other hand, only gives the precise mathematical meaning, with no leeway for rectangles or other quads.

So I wonder, what's the common man-on-the-street interpretation of the word “square”? If presented with a definitely non-sequare rectangle (in the mathematical sense), would people call this a square by themselves, or accept square as a correct term if used by someone else? How about a quadrilateral which is not even rectangular?

The accepted answer at In daily conversation, can I call an object (eg a button) square to emphasize it's not round even though it's rectangular? suggests reserving the word “square” for things which are actually square in the mathematical sense. While I agree with that preference in active use, I'd like to gain some intuition whether diverging from this is plain wrong, or just imprecise everyday language.

Square can refer to a 90˚ angle, which is why a carpenter's square looks like an uppercase "L".

Merriam-Webster does give this definition, it's just really far down:

forming a right angle

They also give this example (even further down):

The room has four square corners.

The interesting thing here is you're right that square, as a noun at least, will generally refer to something with equal sides and angles.

Square is an adjective in your example; and the quoted definition above is from the adjective sense.

The verb definition also supports the idea that making something square doesn't necessarily mean equal side length:

to make (something) square : to give (something) straight edges, flat surfaces, or sharp, even corners

Also, in my opinion, "quadrilateral" is a poor translation ;) since they may not have square corners. It would be more accurate to say the blackboard is rectangular.

• I agree, without the article and absent other context I would read this sentence to mean "the blackboard's angles are each 90°". This would be an unremarkable sentence if you were, say, building or hanging a blackboard. However, it's a remarkably odd sentence to use in a book meant to teach English to children; there I would much more expect to see the blackboard is a rectangle and some other example for a square. – 1006a Nov 15 '16 at 10:26

In my understanding, "square" in terms of a 90-degree angle is more commonly used in phrases such as "square up" or "squared against". This can refer to people (metaphorically or literally) as well as objects (usually literally).

When talking about a square as a four-sided entity, it normally denotes something with four equal sides. Eg. "Madison Square Garden" or "Union Square". The term "quadrilateral" is not not normally used in day-to-day English, except "quadrangle" which tends to denote a physical space eg. in the middle of a school or university campus.

If talking about a specific object, eg. a blackboard or any other non-equal four-sided object, the term rectangular is normally used. That is, "the blackboard is a rectangle" or "most smartphones are rectangular". Keep in mind that this implies two pairs of equal sides (the definition of a rectangle).

As for "quadrilateral", certain objects that are quadrilateral are not necessarily rectangular nor square. A rectangle implies having a pair of opposite and equal sides. Whereas "quadrilateral" specifically denotes a four-sided plane (not three-dimensional object) which may have unequal lenghts of all four sides.

In summary, in day-to-day usage since most objects which are four-sided are rectangular in two and three dimensions, calling it a rectangle or rectangular is adequate. In more specific situations especially where the object is not equal in a pair of sides or any of the sides, then quadrilateral is more accurate.

To mathematicians, a square is a regular right quadrilateral. Rectangle and oblong are useful description words for blackboard-shaped objects. The question is, which is the easiest word for young children to learn? Oblong seems to be little used in (UK) English these days. Quadrilateral is rather long, and in any case, means any four-sided figure. That leaves rectangle and square. Three syllables versus one. Which to use?

Here is the result of a Google Ngram search on square, oblong, rectangle and quadrilateral: I know which word I'd choose, even if it means stretching the definition a bit.

• This isn't a useful n-gram, as the query does not restrict the use of these terms to refer to shapes. There is a Poe story and a film called The Oblong Box which will inflate the number of oblongs, not to mention square as in hip to be square, three squares a day, square on the mark, in the town square, the Square Deal, etc. – choster Nov 14 '16 at 23:48