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  2. Knot density - Wikipedia

    en.wikipedia.org/wiki/Knot_density

    A carpet with a lesser knot density is better adapted to bold, geometric designs and can utilize a long pile for softer, more reflective surface that appeals to the sense of touch." [9] Hand-tying of knots is a very labour-intensive task. An average weaver can tie almost 10,000 knots per day. More difficult patterns with an above-average knot ...

  3. Aperiodic tiling - Wikipedia

    en.wikipedia.org/wiki/Aperiodic_tiling

    [8] [9] This first such set, used by Berger in his proof of undecidability, required 20,426 Wang tiles. Berger later reduced his set to 104, and Hans Läuchli subsequently found an aperiodic set requiring only 40 Wang tiles. [10] A smaller set, of six aperiodic tiles (based on Wang tiles), was discovered by Raphael M. Robinson in 1971. [11]

  4. Einstein problem - Wikipedia

    en.wikipedia.org/wiki/Einstein_problem

    The Socolar–Taylor tile was proposed in 2010 as a solution to the einstein problem, but this tile is not a connected set. In 1996, Petra Gummelt constructed a decorated decagonal tile and showed that when two kinds of overlaps between pairs of tiles are allowed, the tiles can cover the plane, but only non-periodically. [6]

  5. Tessellation - Wikipedia

    en.wikipedia.org/wiki/Tessellation

    The elaborate and colourful zellige tessellations of glazed tiles at the Alhambra in Spain that attracted the attention of M. C. Escher. More formally, a tessellation or tiling is a cover of the Euclidean plane by a countable number of closed sets, called tiles, such that the tiles intersect only on their boundaries. These tiles may be polygons ...

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    Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!

  7. Tile - Wikipedia

    en.wikipedia.org/wiki/Tile

    Tiles are often used to form wall and floor coverings, and can range from simple square tiles to complex or mosaics. Tiles are most often made of ceramic, typically glazed for internal uses and unglazed for roofing, but other materials are also commonly used, such as glass, cork, concrete and other composite materials, and stone. Tiling stone ...