Surface (geometry): Difference between revisions
Jump to navigation
Jump to search
imported>Natalie Watson No edit summary |
imported>Subpagination Bot m (Add {{subpages}} and remove any categories (details)) |
||
| Line 1: | Line 1: | ||
{{subpages}} | |||
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>. | ||
| Line 4: | Line 6: | ||
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 23:36, 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.