فسيفساء (رياضيات)
A tessellated plane seen in street pavement.
A Honeycomb is an example of a tessellated natural structure
في الرياضيات، الفسيفساء tessellation أوالتبليط tiling لمستوى هومجموعة أشكال مستوية تملأ المستوى المعني بدون ثغرات ودون تداخلات. الفسيفساء أيضا يمكن اعتبارها أجزاء من مستوى أوسطوح أخرى. يقوم بعض الرياضيين بتعميم قضايا التبليط والفسيفساء الرياضية إلى أبعاد أعلى. قضايا التبليط كثيرا ما تظهر في فن إيشر. لكنها تاريخيا يمكن حتى تظهر في تاريخ الفنون من العمارة القديمة إلى الفنون الحديثة.
باللغة اللاتينية : tessella تعبر عن بترة مكعبة صغيرة من الغضار clay، حجار أوبتر زجاجية. تسيلا أساسا تعني "البتر الصغيرة". ترتبط دوما بمصطلح التبليط tiling وهوتطبيق وملأ مساحة معينة ببلاطات أوفسيفساء صغيرة أوكبيرة.
الفسيفساء والألوان
If this parallelogram pattern is colored before tiling it over a plane, seven colors are required to ensure each complete parallelogram has a consistent color that is distinct from that of adjacent areas. (This tiling can be compared to the surface of a torus.) Tiling before coloring, only four colors are needed.
الفسيفساء ونماذج الحاسوب
A tessellation of a disk used to solve a finite element problem.
These rectangular bricks are connected in a tessellation which, considered as an edge-to-edge tiling, is topologically identical to a hexagonal tiling; each hexagon is flattened into a rectangle whose long edges are divided in two by the neighboring bricks.
This basketweave tiling is topologically identical to the Cairo pentagonal tiling, with one side of each rectangle counted as two edges, divided by a vertex on the two neighboring rectangles.
فسيفساء الفراغات الأخرى
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An example tessellation of the surface of a sphere by a truncated icosidodecahedron. |
A torus can be tiled by a repeating matrix of isogonal quadrilaterals. |
M.C.Escher, Circle Limit III (1959) |
انظر أيضاً
- Convex uniform honeycomb - The 28 uniform 3-dimensional tessellations, a parallel construction to this plane set
- Coxeter groups - algebraeic groups that can be used to find tesselations
- Four color theorem
- Girih tiles
- Honeycomb (geometry)
- Jig-saw puzzle
- List of regular polytopes
- List of uniform tilings
- Mathematics and fiber arts
- Mosaic
- Nikolas Schiller - Artist using tessellations of aerial photographs
- Penrose tilings
- Pinwheel tiling
- Polyiamond - tilings with equilateral triangles
- Polyomino
- Quilting
- Self-replication
- Tile
- Tiling puzzle
- Tiling, Aperiodic
- Tilings of regular polygons
- Trianglepoint - needlepoint with polyiamonds (equilateral triangles)
- Triangulation
- Uniform tessellation
- Uniform tiling
- Uniform tilings in hyperbolic plane
- Voronoi tessellation
- Wallpaper group - seventeen types of two-dimensional repetitive patterns
- Wang tiles
الهامش
المراجع
- Grunbaum, Branko and G. C. Shephard. Tilings and Patterns. New York: W. H. Freeman & Co., 1987. ISBN 0-7167-1193-1.
- Coxeter, H.S.M.. Regular Polytopes, Section IV : Tessellations and Honeycombs. Dover, 1973. ISBN 0-486-61480-8.
- Magnus, Wilhelm (1974), Noneuclidean tesselations and their groups, Academic Press, ISBN 978-0-12465450-1
وصلات خارجية
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مشاع الفهم فيه ميديا متعلقة بموضوع Tessellation. |
- Interactive Girih Tiles - Tessellation
- K-12 Tessellation Lesson
- Tilings Encyclopedia - Reference for Substitution Tilings
- Math Forum Tessellation Tutorials - make your own
- Mathematical Art of M. C. Escher - tessellations in art
- The 14 Different Types of Convex Pentagons that Tile the Plane
- at Southern Polytechnic State University
- , Andrew Crompton
- - many examples and do it yourself tutorials from the artistic, not mathematical, point of view
- A database with over 500 tessellations categorized by artist and depicted subjects
- Tiles and Tessellations
- Semiregular pattern - This pattern can describe a collapsing cylinder
- , David E. Joyce, Clark University
- Some Special Radial and Spiral Tilings
