Symmetry
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9/1/2026, 10:28:32 AM · Catalpa
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A symmetry is a transformation of an object or system that leaves some of its essential structure unchanged. In geometry, for example, a figure may have rotational, reflective, or translational symmetry if it coincides with itself after being rotated, reflected, or shifted. More generally, symmetry expresses the idea that certain changes do not affect the properties considered important: a physical law may remain unchanged under a change of position or orientation, while an algebraic structure may be preserved by particular transformations of its elements. Mathematically, symmetries are often studied through [[Group theory|group theory]], which describe how symmetry transformations can be combined and inverted.1
A symmetry is a transformation of an object or system that leaves some of its essential structure unchanged. In geometry, for example, a figure may have rotational, reflective, or translational symmetry if it coincides with itself after being rotated, reflected, or shifted. More generally, symmetry expresses the idea that certain changes do not affect the properties considered important: a physical law may remain unchanged under a change of position or orientation, while an algebraic structure may be preserved by particular transformations of its elements. 2
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##### Remarks4
Mathematically, symmetries are often studied through [[Group theory|group theory]], which describe how symmetry transformations can be combined and inverted.Revision 3394
9/1/2026, 10:28:16 AM · Catalpa
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Revision 1264
8/13/2026, 1:03:26 PM · Ancient Tree
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A symmetry is an intuitive notion that something is something...1
A symmetry is a transformation of an object or system that leaves some of its essential structure unchanged. In geometry, for example, a figure may have rotational, reflective, or translational symmetry if it coincides with itself after being rotated, reflected, or shifted. More generally, symmetry expresses the idea that certain changes do not affect the properties considered important: a physical law may remain unchanged under a change of position or orientation, while an algebraic structure may be preserved by particular transformations of its elements. Mathematically, symmetries are often studied through [[Group theory|group theory]], which describe how symmetry transformations can be combined and inverted.2
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In mathematics, symmetries are formalized with [[Group theory|Group theory]].Revision 1263
8/13/2026, 1:01:45 PM · Ancient Tree
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Revision 873
8/3/2026, 7:14:03 PM · Ancient Tree
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A symmetry is an intuitive notion that something is something... In mathematics, symmetries are formalized with [[Group theory|Group theory]].