page_title: Symmetry
section_title: In carpets and rugs
hierarchical_section_title: Symmetry / In the arts / In carpets and rugs
caption_attribution_description: English: Image of a Persian rug. Used for background in a template. The image is real. But I, Zereshk, created it with photoshop (fading, and everything else)
context_page_description: Symmetry in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definition, and is usually used to refer to an object that is invariant under some transformations; including translation, reflection, rotation or scaling. Although these two meanings of "symmetry" can sometimes be told apart, they are intricately related, and hence are discussed together in this article.
  Mathematical symmetry may be observed with respect to the passage of time; as a spatial relationship; through geometric transformations; through other kinds of functional transformations; and as an aspect of abstract objects, including theoretic models, language, and music.
  The opposite of symmetry is asymmetry, which refers to the absence or a violation of symmetry.
context_section_description: A long tradition of the use of symmetry in carpet and rug patterns spans a variety of cultures. American Navajo Indians used bold diagonals and rectangular motifs. Many Oriental rugs have intricate reflected centers and borders that translate a pattern. Not surprisingly, rectangular rugs have typically the symmetries of a rectangle—that is, motifs that are reflected across both the horizontal and vertical axes (see Klein four-group § Geometry).
caption: Persian rug with rectangular symmetry
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