Jordan Curve (Noun)
Meaning
A closed curve that does not intersect itself.
Classification
Nouns denoting two and three dimensional shapes.
Examples
- The mathematician proved that any simple closed curve in the plane can be continuously transformed into a circle without changing its topological properties, a famous example of a jordan_curve.
- In topology, the Schoenflies theorem states that a jordan_curve in the plane divides it into two distinct regions.
- One way to construct a fractal is to iteratively replace each line segment of a jordan_curve with a sequence of smaller segments that connect the same endpoints.
- According to the Jordan-Schoenflies theorem, any jordan_curve can be transformed into a circle through a continuous deformation without self-intersections.
- Every polygon can be represented as a jordan_curve in the plane, consisting of a sequence of connected line segments that form a closed loop.