In abstract algebra, the symmetry group of an object (image, signal, etc.) is the group of all isometries under which the object is invariant with composition as the operation. It is a subgroup of the isometry group of the space concerned. If not stated otherwise, this article considers symmetry groups in Euclidean geometry, but the concept may also be studied in wider contexts; see below.
Famous quotes containing the words symmetry and/or group:
“What makes a regiment of soldiers a more noble object of view than the same mass of mob? Their arms, their dresses, their banners, and the art and artificial symmetry of their position and movements.”
—George Gordon Noel Byron (17881824)
“Its important to remember that feminism is no longer a group of organizations or leaders. Its the expectations that parents have for their daughters, and their sons, too. Its the way we talk about and treat one another. Its who makes the money and who makes the compromises and who makes the dinner. Its a state of mind. Its the way we live now.”
—Anna Quindlen (20th century)