[{"data":1,"prerenderedAt":36},["ShallowReactive",2],{"history-quilt-sierpinski":3,"history-setting-sierpinski":35},{"designer":4,"related":7,"sources":10,"da":15,"en":25},{"name":5,"url":6},"Wacław Sierpiński (1915)","https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FSierpi%C5%84ski_triangle",[8,9],"quilt:thousand-pyramids","quilt:triangle-in-triangle",[11,12,13,14],"wiki-sierpinski","smg-mathematical-quilt","venters-ellison","bridges-sierpinski",{"lead":16,"period":17,"firstKnown":18,"history":19,"use":22},"En trekant delt i fire, hvor den midterste står tom, og det samme igen i hver af de tre hjørner: en fraktal syet af stof.","Matematikken fra 1915; quilts fra 1990'erne","Den polske matematiker Wacław Sierpiński beskrev trekanten i tidsskriftet Comptes Rendus i 1915.",[20,21],"Trekanten er opkaldt efter Sierpiński, men mønsteret er ældre end matematikken: lignende trekanter i trekanter findes i Cosmati-mosaikkerne i italienske kirkegulve fra 1200-tallet. Den er et af de mest kendte eksempler på en fraktal, en figur der ligner sig selv, uanset hvor tæt man ser.","Det er et moderne quiltmotiv, ikke et traditionelt mønster. Science Museum Group i London har \"A mathematical quilt\" fra 1991 af Elaine Krajenke Ellison fra Indiana, inspireret af Benoit Mandelbrot, og hun og Diana Venters udgav bogen Mathematical Quilts i 1999. På matematik- og kunstkonferencen Bridges i 2011 viste Andreia Hall og Prudência Leite quilten \"Sierpinski's Triangle Revisited\".",[23,24],"I QuiltCrafter er den en 60°-blok på trekantgitteret: en trekant med fire små trekanter pr. side, hvor de små trekanter med spidsen op er farvede, hvor Pascals trekant har et ulige tal. Det giver to trin af fraktalen; hvert nyt trin fordobler siden.","Blokkene gentages over hele quilten som trekanter i rækker, skiftevis op og ned, ligesom [[quilt:thousand-pyramids]].",{"lead":26,"period":27,"firstKnown":28,"history":29,"use":32},"A triangle divided into four with the middle one left empty, and the same again in each of the three corners: a fractal sewn in fabric.","The mathematics from 1915; quilts from the 1990s","The Polish mathematician Wacław Sierpiński described the triangle in the journal Comptes Rendus in 1915.",[30,31],"The triangle is named after Sierpiński, but the pattern is older than the mathematics: similar triangles in triangles are in the Cosmati mosaics of Italian church floors from the 1200s. It is one of the best-known examples of a fractal, a figure that looks like itself however closely you look.","It is a modern quilt motif, not a traditional pattern. The Science Museum Group in London has \"A mathematical quilt\" of 1991 by Elaine Krajenke Ellison of Indiana, inspired by Benoit Mandelbrot, and she and Diana Venters published the book Mathematical Quilts in 1999. At the Bridges conference on mathematics and art in 2011, Andreia Hall and Prudência Leite showed the quilt \"Sierpinski's Triangle Revisited\".",[33,34],"In QuiltCrafter it is a 60° block on the triangle lattice: a triangle with four small triangles to a side, the small ones pointing up coloured where Pascal's triangle has an odd number. That gives two steps of the fractal; each new step doubles the side.","The blocks repeat over the whole quilt as triangles in rows, alternately up and down, like [[quilt:thousand-pyramids]].",null,1794245553583]