I'm looking for an example that illustrates the concept of a manifold. Preferably, something that's easy to understand and visualize, helping me grasp this complex mathematical idea.
6 answers
Martina
Tue Nov 05 2024
Manifolds exist in various dimensions.
CryptoChieftain
Tue Nov 05 2024
One example of a one-dimensional manifold is the circle, denoted as S1.
GwanghwamunGuardianAngelWingsBlessing
Tue Nov 05 2024
Another one-dimensional manifold is the long line, which is an infinite line without a specific endpoint.
Thunderbolt
Mon Nov 04 2024
The real line, denoted as R, is also a one-dimensional manifold, representing the set of all real numbers.
WhisperInfinity
Mon Nov 04 2024
The real projective line, RP1, is a one-dimensional manifold that is topologically equivalent to the circle, S1.