Surface (geometry): Difference between revisions
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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>. | ||
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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 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 22:36, 14 November 2007
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.