JORDAN CURVE Meaning and
Definition
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A Jordan curve is a term used in mathematics to describe a simple closed curve in the Euclidean plane. It is named after the French mathematician Camille Jordan.
More specifically, a Jordan curve is a continuous, closed curve that does not intersect itself except at its endpoints. This means that the curve is smooth and does not have any sharp corners or self-intersections. Furthermore, the curve divides the plane into two distinct regions: one that lies inside the curve and one that lies outside.
An important characteristic of a Jordan curve is that it has an orientation or direction associated with it. This means that as one travels along the curve, the interior of the curve is always on the same side. This orientation can be either clockwise or counterclockwise.
Jordan curves have several important properties in mathematics. One key property is that they are homeomorphic to a circle, which means that they have the same topological structure. This property allows mathematicians to study a Jordan curve by examining the properties of a circle.
Another important property is that Jordan curves divide the plane into connected components. These components are regions of the plane that are completely surrounded by the curve. By understanding the structure of these regions, mathematicians can analyze the behavior and properties of Jordan curves in greater detail.
Common Misspellings for JORDAN CURVE
- hordan curve
- nordan curve
- mordan curve
- kordan curve
- iordan curve
- uordan curve
- jirdan curve
- jkrdan curve
- jlrdan curve
- jprdan curve
- j0rdan curve
- j9rdan curve
- joedan curve
- joddan curve
- jofdan curve
- jotdan curve
- jo5dan curve
- jo4dan curve
- jorsan curve
- jorxan curve
Etymology of JORDAN CURVE
The term "Jordan curve" is named after the French mathematician Camille Jordan, who introduced the concept in the late 19th century. The term refers to a simple closed curve, which means a non-self-intersecting closed curve in the plane. Camille Jordan made significant contributions to the field of topology, and his work on the topological properties of curves and surfaces led to the concept of the Jordan curve theorem, which states that the points in the plane are divided into two disjoint regions: the inside and the outside of the curve.
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