# Is there a specific mathematical term for a shape whose dimensions are defined?

When I say the word "circle", I know that I have described a "shape". Specifically, a "circle" is the shape formed by the set of all points in a plane that are at a given distance from a given point. I don't need to provide any more information about the circle in order for it to qualify as a shape.

However, if I describe more specifically, a "circle with a radius of 5 meters", I do not quite know what I am describing, in terms of a generic mathematical definition. Now that I've added the dimension of the circle to my description, what is it called? Is there an official word or phrase for this, other than "shape plus dimensions"?

• 'Manifolds' are a subset of all such spaces. Commented Jul 25, 2015 at 1:32
• No. What you can say is that you are describing a specific (or particular) circle instead of a generic circle. Also, note that the term shape itself is somewhat fuzzy and, as far as I know, not really used mathematically (outside of informal speaking).
– A.P.
Commented Jul 25, 2015 at 9:36

I would use computer science and the concept of classes and objects. Let Shape be a class, say:

class Shape(shape) [Array pts];

Then define Circle as a subclass of Shape:

Then your circle is an object:

myCircle = new Circle({0,0},15);

Object

Class

• "Instance" may be better than "object" as the upshot of your analogy.
– Blue
Commented Jul 25, 2015 at 2:25
• – JMP
Commented Jul 25, 2015 at 3:33
• I like this quote from one of the answers in that link: "Objects are the definitions of something, instances are the physical things." Insofar as a circle is "a thing with radius and center", it's a "definitional" object; but once I've specified that radius and center, it's a "physical" instance. The latter situation seems to be what the OP wants to describe. In any case, something like "the Unit Circle is the particular instance of a circle that has its center at the origin and radius of length one" is natural-sounding English; "object" doesn't seem to lend itself to such natural prose.
– Blue
Commented Jul 25, 2015 at 3:46
• @Blue; but 'instance-oriented programming' doesn't ring the same bells.
– JMP
Commented Jul 25, 2015 at 3:57
• @blue, if i add a draw() function, is the object the abstract circle and the instance the graphic circle?
– JMP
Commented Jul 25, 2015 at 4:16