Invariant (mathematics)
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In mathematics, an invariant is a property of a mathematical object which remains unchanged after operations or transformations of a certain type are applied to the objects. The particular class of ob
A wallpaper is invariant under some transformations. This one is invariant under horizontal and vertical translation, as well as rotation by 180° (but not under reflection).
Symmetry
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In everyday life, Symmetry refers to a sense of harmonious and beautiful proportion and balance. In mathematics, the term has a more precise definition and is usually used to refer to an object that i
Invariant (mathematics)
…points of a transformation are the elements in the domain that are invariant under the transformation. They may, depending on the application, be called symmetric with respect to that transformation. For example, objects with translational symmetry are invariant under certain translations. The integral ∫ M K d μ…
Many animals are approximately mirror-symmetric, though internal organs are often arranged asymmetrically.
Seen from the side, the Taj Mahal has bilateral symmetry; from the top (in plan), it has fourfold symmetry.
Clay pots thrown on a pottery wheel acquire rotational symmetry.
FWF Samuel Monnier