Symmetry

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Brunswick School Department

Technologie Divertissement et humour

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Symmetry (from Greek συμμετρία symmetria "agreement in dimensions, due proportion, arrangement")[1] in everyday language refers to a sense of harmonious and beautiful proportion and balance.[2][3][a] In mathematics, "symmetry" has a more precise definition, that an object is invariant to any of various transformations; including reflection, rotation or scaling. Although these two meanings of "symmetry" can sometimes be told apart, they are related, so they are here discussed together. 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, theoretic models, language, music and even knowledge itself.[4][b] This article describes symmetry from three perspectives: in mathematics, including geometry, the most familiar type of symmetry for many people; in science and nature; and in the arts, covering architecture, art and music. The opposite of symmetry is asymmetry. In geometry[edit] Main article: Symmetry (geometry) The triskelion has 3-fold rotational symmetry. A geometric shape or object is symmetric if it can be divided into two or more identical pieces that are arranged in an organized fashion.[5] This means that an object is symmetric if there is a transformation that moves individual pieces of the object but doesn't change the overall shape. The type of symmetry is determined by the way the pieces are organized, or by the type of transformation: An object has reflectional symmetry (line or mirror symmetry) if there is a line going through it which divides it into two pieces which are mirror images of each other.[6] An object has rotational symmetry if the object can be rotated about a fixed point without changing the overall shape.[7] An object has translational symmetry if it can be translated without changing its overall shape.[8] An object has helical symmetry if it can be simultaneously translated and rotated in three-dimensional space along a line known as a screw axis.[9] An object has scale symmetry if it does not change shape when it is expanded or contracted.[10] Fractals also exhibit a form of scale symmetry, where small portions of the fractal are similar in shape to large portions.[11]

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Symmetry

1. Line Symmetry 3 rd Grade

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Notes de l'éditeur

How would you define the term 'line symmetry'? Why might some people see line symmetry as a thing of beauty?

Symmetry

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