Society is a system of social interaction that includes both culture and social organization. Society includes social institutions, or established organized social behavior, and exists for a recognized purpose; social structure is the patterned relationships within a society. Two other forms of social organization also contribute to the cohesion of a society: What are the Types of Societies?
For example, translational symmetry is present when the pattern can be translated shifted some finite distance and appear unchanged. Think of shifting a set of vertical stripes horizontally by one stripe. The pattern is unchanged. Strictly speaking, a true symmetry only exists in patterns that repeat exactly and continue indefinitely.
A set of only, say, five stripes does not have translational symmetry—when shifted, the stripe on one end "disappears" and a new stripe is "added" at the other end. In practice, however, classification is applied to finite patterns, and small imperfections may be ignored.
Sometimes two categorizations are meaningful, one based on shapes alone and one also including colors. When colors are ignored there may be more symmetry. In black and white there are also 17 wallpaper groups; e. The types of transformations that are relevant here are called Euclidean plane isometries.
If we shift example B one unit to the right, so that each square covers the square that was originally adjacent to it, then the resulting pattern is exactly the same as the pattern we started with.
This type of symmetry is called a translation. Examples A and C are similar, except that the smallest possible shifts are in diagonal directions.
This is called a rotation. We can also flip example B across a horizontal axis that runs across the middle of the image. This is called a reflection. Example B also has reflections across a vertical axis, and across two diagonal axes.
The same can be said for A. However, example C is different. It only has reflections in horizontal and vertical directions, not across diagonal axes. If we flip across a diagonal line, we do not get the same pattern back; what we do get is the original pattern shifted across by a certain distance.
This is part of the reason that the wallpaper group of A and B is different from the wallpaper group of C. Another transformation is "Glide", a combination of reflection and translation parallel to the line of reflection.
A glide reflection will map a set of left and right footprints into each other Formal definition and discussion[ edit ] Mathematically, a wallpaper group or plane crystallographic group is a type of topologically discrete group of isometries of the Euclidean plane that contains two linearly independent translations.
Two such isometry groups are of the same type of the same wallpaper group if they are the same up to an affine transformation of the plane.
The same applies for a change of angle between translation vectors, provided that it does not add or remove any symmetry this is only the case if there are no mirrors and no glide reflectionsand rotational symmetry is at most of order 2.
Unlike in the three-dimensional casewe can equivalently restrict the affine transformations to those that preserve orientation. It follows from the Bieberbach theorem that all wallpaper groups are different even as abstract groups as opposed to e. Isometries of the Euclidean plane[ edit ] Isometries of the Euclidean plane fall into four categories see the article Euclidean plane isometry for more information.
Translationsdenoted by Tv, where v is a vector in R2. This has the effect of shifting the plane applying displacement vector v.
Reflectionsor mirror isometries, denoted by FL, where L is a line in R2.2 Your Communication in Groups GROUP SKILLS PREVIEW In this chapter, you will learn to do the following: to their role in society or their impact on culture. Thus viewing group interaction from a communication perspective is a distinct and unique approach.
Sociologists have identified five different patterns of social interaction. (1) Cooperation - occurs when two or more people or groups work together to achieve a common goal -- . A wallpaper group (or plane symmetry group or plane crystallographic group) is a mathematical classification of a two-dimensional repetitive pattern, based on the symmetries in the pattern.
Such patterns occur frequently in architecture and decorative art, especially in textiles and tiles as well as wallpaper.. A proof that there were only 17 distinct groups of possible patterns was first.
Human society is best defined as: a. A system of social interaction that includes norms and values. b. A system of social organization that is characterized by a distinct social structure.
c. A system of social organization that includes ordered social interaction. d. A system of social interaction that includes culture and social organization.
The Islamic arabesque is a form of artistic decoration consisting of "surface decorations based on rhythmic linear patterns of scrolling and interlacing foliage, tendrils" or plain lines, often combined with other elements.
It usually consists of a single design which can be 'tiled' or seamlessly repeated as many times as desired. Temperament is a configuration of observable personality traits, such as habits of communication, patterns of action, and sets of characteristic attitudes, values, and talents.