Is there a good word for a square-rectangle relationship?
Any given square is always a rectangle, but a rectangle isn't necessarily a square, so squares and rectangles have a _ relationship. I've been noticing this sort of thing everywhere ever since I noticed that I didn't know a good word for it. I've been calling it a container relationship because one class of things is contained within a larger class of things. However, a "container" relationship doesn't sound very good and doesn't really convey the meaning on its own. A more elegant word would be helpful.
Edit: A specific definition would be something like: a is always b. b is sometimes a.
Solution 1:
You can utilize the word "subset" for this usage.
Squares are a "subset" of Rectangles.
Meaning, they are within the "set" of Rectangles, but not all rectangles are squares.
Taken from Google Define:
sub·set
ˈsəbˌset
noun
noun: subset;
plural noun: subsets;
noun: sub-set;
plural noun: sub-sets
DEFINTION
a part of a larger group of related things.
synonyms: subcategory, branch, subdivision, subsection, subsidiary
Examples:
"the quartet is a subset of our orchestral group"
Usage in MATHEMATICS
a set of which all the elements are contained in another set.
Solution 2:
Square is a hyponym of rectangle, which is a hypernym of square. The wikipedia article Hyponymy and hypernymy says
In linguistics, a hyponym is a word or phrase whose semantic field is included within that of another word, its hypernym (sometimes spelled hyperonym outside of the natural language processing community). In simpler terms, a hyponym shares a type-of relationship with its hypernym. For example, "pigeon", "crow", "eagle" and "seagull" are all hyponyms of "bird" (their hypernym); which, in turn, is a hyponym of "animal".
Edit: For more precision, one should add qualifying phrases like “the word” or “the set”:
- the word square is a hyponym of the word rectangle
- the set of squares is a subset of the set of rectangles
However, I think subclass [a term mentioned in Joshua Taylor's comments] can be used without added qualifiers.Wiktionary gives the following definition of subclass relevant within computing: “In object-oriented programming, an object class derived from another class (its superclass) from which it inherits a base set of properties and methods”.
- squares are a subclass of rectangles
Speaking mathematically, a class is a less-determinate category or collection of things than is a set. From en.wiktionary, class means “A group, collection, category or set sharing characteristics or attributes”, and subclass means “A rank directly below class”.
Solution 3:
A square is a special type, or a specialisation of rectangle.
A rectangle is a more general type, a generalisation of a square.
They are in a hierarchical relationship. They are in a specialisation relationship.
Solution 4:
The relationship between a square and a rectangle is "type of". A square is a type of rectangle, but a rectangle is not a type of square.
I'm not aware of a single word that means "type of".
In engineering and programming circles, this relationship is also described as "is a". Another similar relationship in this context is are "has a".
A rectangle definitely does not "contain" a square, in the sense of the original question: that would be the wrong thing to say to mean that a square is a type of rectangle. When you say "a rectangle contains a square" you mean "has a" not "is a".
It's also "obscure" to think of a "square" as a subset of a "rectangle". The set of squares might be a subset of the set of rectangles, but "square" and "rectangle" in this context are types (of shapes), not sets.
Solution 5:
There are different ways to think about this:
You can consider the set of all squares and the set of all rectangles and how they overlap with one another. In mathematical jargon we would say Squares are a proper subset of rectangles. or Rectangles are a proper superset of squares.
In normal, non-technical English, Squares are a subset of rectangles. will generally be understood to mean this.
You can also consider the meanings of square and rectangle and how they relate to one another. The meaning of square can be expressed in terms of being a rectangle with additional restriction: A square is an equilateral rectangle. So the relationship could be expressed as: A square is a kind of rectangle. There are a wide range of other ways of expressing kind of. Depending on the direction, the relationship itself is called specialization or generalization.
Most people are more comfortable expressing things in terms of subsets or specialization than they are in terms of supersets or generalization. So unless you are in a technical context, or the direction is very important to your meaning, it's best to stick to expressing these relationships in terms of specialization.