타일링과 테셀레이션

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사전 형태의 자료


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관련논문

  • Nelson, Roice, and Henry Segerman. “Visualizing Hyperbolic Honeycombs.” arXiv:1511.02851 [math], November 7, 2015. http://arxiv.org/abs/1511.02851.
  • Gao, Honghao, Nan Shi, and Min Yan. 2013. “Spherical Tiling by 12 Congruent Pentagons.” Journal of Combinatorial Theory, Series A 120 (4): 744–76. doi:10.1016/j.jcta.2012.12.006.
  • Mendelsohn, N. S. 2004. “Tiling with Dominoes”. The College Mathematics Journal 35 (2) (3월 1): 115-120. doi:10.2307/4146865.

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노트

  1. A semi-regular tessellation is made of two or more regular polygons.[1]
  2. To name a tessellation, go around a vertex and write down how many sides each polygon has, in order ... like "3.12.12".[1]
  3. 1953 ROTATION - A Tessellation which the shape repeats by rotating or turning.[2]
  4. A Tessellation which the shape repeats by reflecting or flipping.[2]
  5. A real physical tessellation is a tiling made of materials such as cemented ceramic squares or hexagons.[3]
  6. Historically, tessellations were used in Ancient Rome and in Islamic art such as in the decorative geometric tiling of the Alhambra palace.[3]
  7. Tessellations are sometimes employed for decorative effect in quilting.[3]
  8. In 1619 Johannes Kepler made an early documented study of tessellations.[3]
  9. Tessellations are a fun, hands-on way to explore STEAM, whether you are in art class, math class, or in a STEM or STEAM classroom.[4]
  10. Tessellations are patterns resulting from arranging, or tiling, shapes without any gaps.[4]
  11. This is the type of tessellation you can make easily with a sticky note (as shown below).[4]
  12. Rotation tessellations are accomplished by (you guessed it!) rotating the tessellated shape.[4]
  13. A tiling of regular polygons (in two dimensions), polyhedra (three dimensions), or polytopes ( dimensions) is called a tessellation.[5]
  14. In the plane, there are eight such tessellations, illustrated above (Ghyka 1977, pp. 76-78; Williams 1979, pp.[5]
  15. A tessellation of -dimensional polytopes is called a honeycomb.[5]
  16. The tessellation process is divided into three stages which form an optional part of Vertex Processing in the rendering pipeline.[6]
  17. The amount of tessellation done in this case is taken from default values set into the context.[6]
  18. This stage is only executed if a tessellation evaluation shader (TES) is active in the current program or program pipeline.[6]
  19. The TES can also force the generation of the tessellation as a series of points rather than triangles or lines by providing the primitive.[6]
  20. But tessellations can be formed from multiple shapes.[7]
  21. The word tessellation can also refer to the act of tessellating—forming such a pattern.[7]
  22. Example: The building was designed to look like a tessellation in the form of a honeycomb pattern.[7]
  23. There are three regular shapes that make up regular tessellations: the equilateral triangle, the square and the regular hexagon.[8]
  24. Equilateral triangles, squares and regular hexagons make up regular tessellations.[8]
  25. Semi-regular tessellations are made of more than one kind of regular polygon.[8]
  26. Within the limit of the same shapes surrounding each vertex (the points where the corners meet), there are eight such tessellations.[8]
  27. : Create a tessellation by deforming a triangle, rectangle or hexagon to form a polygon that tiles the plane.[9]
  28. Tessellation is when shapes fit together in a pattern with no gaps or overlaps.[10]
  29. Alain Nicolas, the great French tessellation artist, has posted a gallery of new original tessellations that are quite amazing.[11]
  30. Try coloring our new "Angry Birds" tessellation.[11]
  31. Brick walls, tiled floors, and the honeycomb in bee hives are all tessellations.[11]
  32. Yes, we'd be happy to post your class's tessellations in a "school gallery" on www.Tessellations.org.[11]
  33. We can study the way regular polygons interact with each other, and one way they can do so is through tessellations.[12]
  34. A regular tessellation is one made using only one regular polygon.[12]
  35. A semi-regular tessellation uses two or more regular polygons.[12]
  36. A tessellation is a repeated series of geometric shapes that covers a surface with no gaps or overlapping of the shapes.[13]
  37. Tessellations are used in works of art, fabric patterns or to teach abstract mathematical concepts, such as symmetry.[13]
  38. All regular tessellations must be made of regular polygons.[13]
  39. However, not all regular polygons can be used to create a tessellation because their sides do not line up evenly.[13]
  40. The words tessellate and tessellation come from a Latin word which means "small stones" and "to pave with small stones".[14]
  41. We will now look at different types of tessellations that deal with regular polygons.[14]
  42. A tessellation is a pattern of shapes repeated to fill a plane.[15]
  43. Tessellations are something we often see in quilts, carpets, floors, and more.[15]
  44. For the tessellation above composed of squares to the left, the sum of the angles at a vertex are 90°+90°+90°+90°=360°.[15]
  45. A regular tessellation is made up of regular congruent polygons.[15]
  46. That function computes triangle edge and inside tessellation factors.[16]
  47. This next example shows a surface shader that does some displacement mapping without using tessellation.[16]
  48. This is not needed yet, but it’s more efficient for tessellation to use as small structure as possible.[16]
  49. Purely distance based tessellation is effective only when triangle sizes are quite similar.[16]
  50. As one journey — the classification of all convex polygon tessellations — ends, another is just beginning.[17]
  51. The squinting eyes, the jut of the chin, the precise tessellation of the lower lip and upper lip stay the same.[17]
  52. Start with creating a tessellation shape using the "translation pattern" ( see the steps below ).[18]
  53. There are few patterns that you can follow to construct a tessellation.[18]
  54. This tessellation was based on a hexagon.[18]
  55. Do you know what is the definition of tessellation and what does it take to create one?[19]
  56. A fundamental region is a shape that is repeated in order to form a tessellation.[19]
  57. One shape of a tile in a tessellation is called a prototile.[19]
  58. Based on the types of polygons, tessellations are classified as regular, semi-regular and non-regular or irregular.[19]
  59. Therefore, these complex structures can be interpreted as interwoven tessellations of the α and β phases.[20]
  60. 4e–g) reveal the detailed structures around the tessellation vertices.[20]
  61. The angular sum of the polygons involved is therefore 360°, resulting in perfect tessellation.[20]
  62. These complex tessellations can be regarded as two different phases interweaving in multiple ways.[20]
  63. Here you can create your own tessellations using regular polygons.[21]
  64. At every vertex in the tessellation, the internal angles of multiple different polygons meet.[21]
  65. Tessellations in Art Many artists, architects and designers use tessellations in their work.[21]
  66. All the tessellations we saw so far have one thing in common: they are periodic.[21]
  67. A tessellation of the plane is an arrangement of polygons which cover the plane without gaps or overlapping.[22]
  68. The goal of the task is to use algebra in order to understand which tessellations of the plane with regular polygons are possible.[22]
  69. In particular, students, perhaps in groups, should be encouraged to produce their own (non-regular) tessellations of the plane.[22]
  70. Tessellations and Fractals are two different art techniques that often get mistaken for one another despite being nothing alike.[23]
  71. Regular tessellations are tile coverings made up of only one shape.[23]
  72. Semi-regular tessellations: When two or three different polygonal shapes share a common vortex, it is called a semi-regular tessellation.[23]
  73. C. Escher used tessellation patterns extensively in his work, often to great effect.[23]
  74. Tessellation is a system of shapes which are fitted together to cover a plane, without any gaps or overlapping.[24]
  75. The word tessellation itself derives from the Greek tessera, which is associated with four, square and tile.[24]
  76. Tessellations are a common feature of decorative art and occur in the natural world all around us.[24]
  77. Traditionally, the pattern formed by a tessellation is repetitive.[24]
  78. Tessellations run the gamut from basic to boggling.[25]
  79. All tessellations, even shapely and complex ones like M.C. Escher's, begin with a shape that repeats without gaps.[25]
  80. No tessellation talent outshines Dutch graphic artist M.C. Escher.[25]
  81. In the context of quilting, tessellation refers to regular and semiregular of tessellation of either patch shapes or the overall design.[26]
  82. Then make your own tessellations inspired by artist M.C. Escher .[27]
  83. To our knowledge, this is a genuine molecular-level realization of a 2D superstructure exhibiting this kind of surface tessellation.[28]

소스

  1. ↑ 1.0 1.1 Tessellation
  2. ↑ 2.0 2.1 Kinds of Tessellations
  3. ↑ 3.0 3.1 3.2 3.3 Tessellation
  4. ↑ 4.0 4.1 4.2 4.3 Create a Simple Tessellation
  5. ↑ 5.0 5.1 5.2 Tessellation -- from Wolfram MathWorld
  6. ↑ 6.0 6.1 6.2 6.3 Tessellation
  7. ↑ 7.0 7.1 7.2 Definition of Tessellation at Dictionary.com
  8. ↑ 8.0 8.1 8.2 8.3 Tessellation: The Geometry of Tiles, Honeycombs and M.C. Escher
  9. ↑ Interactivate: Tessellate!
  10. ↑ What is tessellation?
  11. ↑ 11.0 11.1 11.2 11.3 M. C. Escher and how to make your own Tessellation Art
  12. ↑ 12.0 12.1 12.2 At-Home STEM Activities: Tessellations—Exploration and M.C. Escher-Inspired Drawing — McAuliffe-Shepard Discovery Center
  13. ↑ 13.0 13.1 13.2 13.3 Rules for Creating Tessellations
  14. ↑ 14.0 14.1 The words tessellate and tessellation come from a Latin word which means “small
  15. ↑ 15.0 15.1 15.2 15.3 Tessellation
  16. ↑ 16.0 16.1 16.2 16.3 Manual: Surface Shaders with DX11 / OpenGL Core Tessellation
  17. ↑ 17.0 17.1 Definition of Tessellation by Merriam-Webster
  18. ↑ 18.0 18.1 18.2 Tessellations. Art lesson.
  19. ↑ 19.0 19.1 19.2 19.3 Tessellation Patterns - From Mathematics to Art
  20. ↑ 20.0 20.1 20.2 20.3 Two-dimensional tessellation by molecular tiles constructed from halogen–halogen and halogen–metal networks
  21. ↑ 21.0 21.1 21.2 21.3 Tessellations – Polygons and Polyhedra – Mathigon
  22. ↑ 22.0 22.1 22.2 Illustrative Mathematics
  23. ↑ 23.0 23.1 23.2 23.3 Tessellations and fractals? What's the difference between the two?
  24. ↑ 24.0 24.1 24.2 24.3 Shaping up with Tessellations
  25. ↑ 25.0 25.1 25.2 How Tessellations Work
  26. ↑ meaning in the Cambridge English Dictionary
  27. ↑ Tessellations
  28. ↑ Five-vertex Archimedean surface tessellation by lanthanide-directed molecular self-assembly

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