The Euclidean plane is with its standard Euclidean norm and the resulting distance, angles, and Riemannian metric.
A connected open subset of the Euclidean plane. For a bounded polygonal example, the Dirichlet Laplacian is the self-adjoint operator associated with the Dirichlet energy on ; its eigenfunctions are smooth in the interior but need not be smooth at reentrant boundary corners.
Articles by others on the same topic
The Euclidean plane is a two-dimensional geometric space that adheres to the principles of Euclidean geometry, named after the ancient Greek mathematician Euclid. It is characterized by several key features: 1. **Points and Lines**: The Euclidean plane consists of points, which have no dimensions, and straight lines, which extend infinitely in both directions, defined by two distinct points.