A characterization of a mathematical object is a collection of properties that collectively distinguish that object from other similar objects. The object is said to be characterized by (or "determined by") the properties.
Some examples from Euclidean geometry:
- A line in two dimensions is characterized by two points it passes through.
- A circle is characterized by a point called its center and a distance called its radius.
- A plane in three dimensions is characterized by three points it passes through, or by one point and a line it is perpendicular to.
Note that while the characterization itself is not unique (an infinite number of pairs of points can characterize the same straight line, for example), a given characterization must uniquely specify the intended object (two different straight lines cannot pass through the same two points).