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Wednesday, August 4, 2010

2-D and 3-D


a)2-Dimension

First of all, we must know the definition of dimension first before talk about 2-Dimension. In common usage, a dimension which is Latin word, give the meaning "measured out" is a parameter or measurement required to define the characteristics of an object which is consists of length, width, and height or size and shape.

In mathematics, dimensions are the parameters required to describe the position and relevant characteristics of any object within a conceptual space, where the dimension of a space is the total number of different parameters used for all possible objects considered in the model. Generalizations of this concept are possible and different fields of study will define their spaces by their own relevant dimensions, and use these spaces as frameworks upon which all other study (in that area) is based.Hence, the corresponding space has therefore two dimensions, its dimension is two, and this space is said to be 2-dimensional (2D).

b)Tesellation

The definition of tesellation comes from the Latin word.In Latin, tessella was a small cubical piece of clay, stone or glass used to make mosaics. The word "tessella" means "small square" which is from the word "tessera", square, which in its turn is from the Greek word for "four. It corresponds with the everyday term tiling which refers to applications of tessellation, often made of glazed clay.

A tessellation or tiling of the plane is a collection of plane figures that fills the plane with no overlaps and no gaps. One may also speak of tessellations of the parts of the plane or of other surfaces. Generalizations to higher dimensions are also possible. Tessellations are seen throughout art history, from ancient architecture to modern art. Tesellation can be grouped into a few groups. 2 of them were regular tessellation and semiregular tessellation.

A regular tessellation is a highly symmetric tessellation made up of congruent regular polygons. Only three regular tessellations exist: those made up of equilateral triangles, squares, or hexagons. A semiregular tessellation uses a variety of regular polygons; there are eight of these. The arrangement of polygons at every vertex point is identical. An edge-to-edge tessellation is even less regular: the only requirement is that adjacent tiles only share full sides, i.e. no tile shares a partial side with any other tile. Other types of tessellations exist, depending on types of figures and types of pattern. There are regular versus irregular, periodic versus aperiodic, symmetric versus asymmetric, and fractal tesselations, as well as other classifications.

c) 3-Dimension

3Dimension can be defined as something having three dimensions e.g. width, lengthand depth.The body is bounded by the faces, and is usually the volume inside them. As an example, there is three-dimensional space, the physical universe we live in. A vector space or coordinate space with three dimensions and Volume, is a measurement of space.

d) Explain the design that you create, consists the combination of what shape.
I had created a tessellation from the triangle and hexagon shape under a fer process of repetation. As we all already know, a tessellation is created when a shape is repeated over and over again covering a plane without any gaps or overlaps. Basically, a tessellation is a way to tile a floor that goes on forever with shapes so that there is no overlapping and no gaps. These tessellations are made by using two or more different regular polygons. The rules are still the same.

Every vertex must have the exact same configuration. Normally, triangle's angle is 60 while hexagon's angle is 120. However, the hexagon’s angle I my tessellation is different. Here I would like to describe my tessellation.

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