Surface (geometry): Difference between revisions
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imported>Michael Lee Schwartz m (include hyper-link to Topological_space (for "topologically")) |
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A '''surface''' in mathematics has many different uses, the most common referring to a two-dimensional submanifold of three-dimensional Euclidean space, <math>\scriptstyle \mathbb{R}^2</math>. | A '''surface''' in mathematics has many different uses, the most common referring to a two-dimensional submanifold of three-dimensional Euclidean space, <math>\scriptstyle \mathbb{R}^2</math>. | ||
Any set of points composed of pieces topologically equivalent to a subset of a plane is a surface: this includes curved surfaces such as a paraboloid, infinite surfaces such as a plane, surfaces of limited extent such as the interior of a polygon, and surfaces with strange topology such as an infinitely long row of squares each separated by some distance, or the set of all points with rational coordinates in a plane. | Any set of points composed of pieces [[Topological_space|topologically]] equivalent to a subset of a plane is a surface: this includes curved surfaces such as a paraboloid, infinite surfaces such as a plane, surfaces of limited extent such as the interior of a polygon, and surfaces with strange topology such as an infinitely long row of squares each separated by some distance, or the set of all points with rational coordinates in a plane. | ||
The extremities of a [[solid (geometry)|solid]] are made up of surfaces. | The extremities of a [[solid (geometry)|solid]] are made up of surfaces. | ||
Revision as of 18:10, 9 April 2008
A surface in mathematics has many different uses, the most common referring to a two-dimensional submanifold of three-dimensional Euclidean space, .
Any set of points composed of pieces topologically equivalent to a subset of a plane is a surface: this includes curved surfaces such as a paraboloid, infinite surfaces such as a plane, surfaces of limited extent such as the interior of a polygon, and surfaces with strange topology such as an infinitely long row of squares each separated by some distance, or the set of all points with rational coordinates in a plane. The extremities of a solid are made up of surfaces.