Difference between revisions of "Sierpiński triangle"
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| − | The '''Sierpiński triangle''' (also known as '''Sierpiński gasket''') is a [[fractal]] [[geometry]] constructed from [[triangle]]s. It was first created by [[Wacław Sierpiński]] to triangulate the one-dimensional [[Cantor set]] into a two-dimensional fractal geometry. Sierpiński later generalized his technique to create fractal geometries from other [[polygon]]s, including the square (creating the [[Sierpiński carpet]]) and the circle (Sierpiński circle). [[Topology|Topologically]], the Sierpiński triangle is everywhere [[Dense_subset|dense]], so its closure is the full triangle. | + | The '''Sierpiński triangle''' (also known as '''Sierpiński gasket''') is a [[fractal]] [[geometry]] constructed from [[triangle]]s. It was first created by [[Wacław Sierpiński]] to triangulate the one-dimensional [[Cantor set]] into a two-dimensional fractal geometry. Sierpiński later generalized his technique to create fractal geometries from other [[polygon]]s, including the square (creating the [[Sierpiński carpet]]) and the circle (Sierpiński circle). [[Topology|Topologically]], the Sierpiński triangle is everywhere [[Dense_subset|dense]], so its closure is the full triangle.{{fact}} |
[[Category:Geometry]] | [[Category:Geometry]] | ||
Revision as of 02:35, June 4, 2011
The Sierpiński triangle (also known as Sierpiński gasket) is a fractal geometry constructed from triangles. It was first created by Wacław Sierpiński to triangulate the one-dimensional Cantor set into a two-dimensional fractal geometry. Sierpiński later generalized his technique to create fractal geometries from other polygons, including the square (creating the Sierpiński carpet) and the circle (Sierpiński circle). Topologically, the Sierpiński triangle is everywhere dense, so its closure is the full triangle.[Citation Needed]