symmetry (simetri)

[Formerly also sym metrie, metrie, simmetrie; pecially, pecially, the proper commensurability of the parts of the human body, according to a canon: hence, congruity; beauty of form. The Greek word συμμετρία was probably first applied to the commensurability of numbers, thence to that of the parts of a statue, and soon to elegance of form in general. 2. The metrical correspondence of parts with reference to a median plane, each element of geometrical form having its counterpart upon the opposite side of that plane, in the same continued perpendicular to the plane, and at the same distance from it, so that the two halves are geometrically related as a body and its im symmetry age in a plane mirror: so, usually, in geometry. Especially, in arch., the exact or geometrical repetition of one half of any structure or composition by the other half, only with the parts arranged in reverse order, as notably in much Renai ance and modern architecture for instance, in the placing of two spires, exact duplicates of each other, on the front of a church. Such practice is very seldom followed in the best architecture, which in general seeks in its designs to exhibit harmony (see har mony, 3), but avoids symmetry in this sense. We have an Idea of Symmetry ; and an axiom involved in this Idea is that in a symmetrical natural body, if there be a tendency to modify any member in any manner, there is a tendency to modify all the corresponding members in the same manner. Whewell, Philos. of Inductive Sciences, I. p. xxx. John and Jeremiah sat in symmetry on opposite sides of the fireplace; the very smiles on their honest faces seemed drawn to a line of exactitude. Mrs. Gaskell , Sylvia's Lovers, xiv. 3. The composition of like and equably distributed parts to form a unitary whole; a balance between different parts, otherwise than in reference to a medial plane: but the mere repetition of parts, as in a pattern, is not properly called symmetry.-4. Consistency; congruity; keeping; proper subordination of a part to the whole. It is in exact symmetry with Western usage that this great compilation was not received as a code until the year 1369. Stubbs , Medieval and Modern Hist., p. 167. 5. In biol .: (a) In botany, specifically, agreement in number of parts among the cycles of organs which compose a flower. See symmetrical , 3. ( b ) In zoölogy and anatomy, the symmetrical disposition or reversed repetition of parts around an axis or on opposite sides of any plane of the body. Symmetry in this sense is something more and other than that due proportion of parts noted in def. 1, since it implies a geometrical representation approximately as in def. 2 (see pro morphology ); it is also to be distinguished from mere metamerism, or the serial repetition of like parts conceived to face one way and not in opposite directions; but it coincides in some cases with actinome rism, and in others with antimerism or platetropy (see antimere, plate trope ). Several sorts of symmetry are recognized. One is radial or act i nom eric, in which like parts are arranged about an axis, from which they radiate like the parts of a flower, as in many zoöphytes and echinoderms; but such symmetry is unusual in the animal king dom, being mainly confined to some of the lower cla es of invertebrates, and even in these the departures from it are frequently obvious. (See bivium, trivium, and cuts under echinopædium and Spa tango idea.) The tendency of animal form on the whole being to grow along one main axis (the longitudinal), with symmetrical duplication of parts on each side of the vertical plane (the meson) pa ing through that axis, it follows that the usual symmetry is bilateral (see below). This is exhibited only obscurely, however, by some cylindrical organisms, as worms, whose right and left "sides," though existent, are not well marked; and to such symmetry of ringed or annulose forms the term zonal is sometimes applied. When the ordinary metameric divisions of any animal, as a vertebrate or an arthropod, are conceived as not simply serial but also as anti tropic, such disposition of parts is regarded as constituting anteroposterior symmetry, in which parts are supposed to be reversed repetitions of each other on opposite sides of an imaginary plane dividing the body transversely to its axis, in the same sense that right and left parts are reversed repetitions of each other in bilateral symmetry. The existence of the last is denied or ignored by those who consider the segments of an articulate or vertebrate body as simply serially homologous; but in the view of those who recognize it the back of the arm corresponds to the front of the thigh, the convexity of the elbow (backward) to the convexity of the knee (forward), the extensor brachii to the extensor cruris, etc. Anteroposterior symmetry is also recognized by some naturalists in certain arthropods from the arrangements of the legs (in amphipods, for example), the correspondences observed between anal and oral parts, etc. Since any body is a solid, and therefore may be intersected by three mutually perpendicular planes, two of which are concerned in bilateral and anteroposterior symmetry respectively, a kind of symmetry called dors abdominal symmetry is recognized by some, being that of parts lying upon opposite sides of a longitudinal horizontal plane pa ing through the axis of the body, as that between the neural and hemal arches of a vertebra; but it is generally obscure, and probably never perfect. Bilateral symmetry (see end i pleural ) is the nearly universal rule in vertebrates and articulates. The chief departures from it in vertebrates are in the family of flatfishes or flounders (as the plaice, turbot, halibut), in parts of the cranium of various cetaceans and the single great tusk of the narwhal, in the skulls (especially the ear-parts) of sundry owls, in the beak of a plover ( Anarhynchus ) which is bent sidewise, in the atrophy of one of the ovaries and oviducts in most birds, and in the position finally a umed by the heart and great ve els and most of the digestive organs of vertebrates at large. (See cuts under asymmetry, narwhal, plaice, and plover.) In articulates notable exceptions to it are seen in the difference between the great claws or chelæ of a lobster, etc. In Mollusca asymmetry is the rule rather than the exception. (See An i so pleura, I so pleura.) A certain symmetry, apart from that exhibited by an animal body as a whole, may be also predicated of the several components of any part in their respective selves: as, the symmetry of a carpus or of a tarsus whose several bones are regularly disposed on each side of its axial plane, or around a central bone. (See cuts under carpus and tarsus.) -Axis of symmetry. See axis1. - Center of symmetry. See center1. Kinetical symmetry, the equality of the principal axes of a body through its center of ma . -Plane of symmetry, a symmetral or median plane.Quartic symmetry. See quartic. Quintic symmetry, 6127 regularity of form depending on a pentagon being regular. See quintic. - Radial symmetry. See det. 5 (b). - Rectangular or right symmetry, symmetry depending on that of the right angle, or consisting in some angle being a right angle. - Skew symmetry. See skewl. - Uniform symmetry, in arch., such disposition of parts that the same ordonnance reigns throughout the whole. =Syn. Symmetry, Proportion. Proportion is the more general word, being applicable to numbers, etc.; it is also the more abstract. Symmetry is limited to the relation of the parts of bodies, especially living bodies: as, symmetry in the legs of a horse; it is thus sometimes more external. Symmetry sometimes is more expre ive of the pleasure of the behold "Symmetry is the opposition of equal quantities to er. each other. Proportion the connection of unequal quantities with each other. The property of a tree in sending out equal boughs on opposite sides is symmetrical. Its sending out shorter and smaller toward the top, prop or tional. In the human face its balance of opposite sides is symmetry, its division upwards, proportion." ( Ruskin.) sympalmograph (sim-pal'mo-graf), n. [ ple harmonic motions. A convenient form employs a double pendulum, the rate of oscillation of whose parts can be varied at will, while a suitable style traces out upon a lampblack surface the curves resulting from the combined motions.