The Jordan curve theorem states that a simple closed curve divides the plane into two regions: an interior and an exterior. This theorem has both educational and academic significance in geometry and graph theory.
6 answers
Margherita
Mon Dec 16 2024
This division is crucial in understanding the properties of closed curves in the plane.
MountFujiView
Mon Dec 16 2024
The Jordan curve theorem is a fundamental theorem in topology.
Raffaele
Mon Dec 16 2024
It was initially proposed by the French mathematician Camille Jordan in 1881.
AzurePulseStar
Mon Dec 16 2024
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Daniela
Mon Dec 16 2024
The theorem states that any simple closed curve, which is a continuous closed curve that does not intersect itself, divides the plane into exactly two distinct regions.