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symmetrical, a.|sɪˈmɛtrɪkəl|
[f. symmetry + -ical, after geometrical. Cf. prec. and next.]
Characterized by or exhibiting symmetry.
1. Having the parts or elements regularly and harmoniously arranged; regular in form; well-proportioned; balanced. (Said of natural or artificial bodies or structures, or of abstract or immaterial things; cf. symmetry 2.)
1751Johnson Rambler No. 94 ⁋4 Some of the lines of this description are..defective in harmony, and therefore by no means correspondent with that symmetrical elegance..which they are intended to exhibit. 1833Lyell Princ. Geol. III. 319 The oldest lavas of Etna were poured out many thousand..years before the newest, and yet they have produced a symmetrical mountain. 1841Dickens Barn. Rudge viii, That I had but eyes!..to behold my captain's symmetrical proportions. 1870Rolleston Anim. Life p. xxiii, An increase in our knowledge..may..overthrow the most perfectly symmetrical of systems. 1886Ruskin Præterita I. 272 The symmetrical clauses of Pope's logical metre.
2. a. Geom., etc. Said of a figure or body whose points or parts are equably distributed about a dividing line, plane, or point, i.e. arranged in pairs or sets so that those of each pair or set are at equal distances on opposite sides of such line, plane, or point; consisting of, or capable of being divided into, two or more exactly similar and equal parts. Also said of the form of such a figure or object, of its parts or their arrangement, or of any part in relation to the corresponding part.
1794R. J. Sulivan View Nature xxix. I. 423 In the passing of a substance from a fluid into a solid state, it almost universally appears..to have its parts arranged in a symmetrical order. 1805–17R. Jameson Char. Min. (ed. 3) 146 When the nucleus has not what is called a symmetrical form, as when it is a parallelopiped, whose faces differ in the respective inclinations of their faces, or in the measure of their angles. 1850Grove Corr. Phys. Forces (ed. 2) 88 Those crystals which have one axis of figure, or a line around which the figure is symmetrical. 1885C. Leudesdorf Cremona's Proj. Geom. 267 The point M (and the symmetrical point in which the parabolas intersect again) can then be constructed. 1889Cockshott & Walters Geometr. Conics 40 The ellipse is symmetrical with respect to the minor axis. 1894C. Smith Geometr. Conics 4 When..corresponding to any point of the curve there is another point such that the chord joining the two points is bisected perpendicularly by [a] straight line, then the curve is said to be symmetrical about the straight line, and the straight line is called an axis of the curve.
b. Alg. and Higher Math. Applied to an expression, function, or equation whose value is never altered by interchanging the values of any two of the variables or unknown quantities. In Physics also applied to a state represented by such a wave function. Also in Logic, = symmetric a. 2.
symmetrical or symmetric determinant: a determinant in which the constituents in each row are the same respectively, and in the same order, as those in the corresponding column, and which is therefore symmetrical about its principal diagonal.
1816tr. Lacroix' Diff. & Int. Calc. 536 On the supposition that f (α, β, γ, &c.) is symmetrical with respect to all the roots, except α. 1854Orr's Circ. Sci., Math. 217 Thus x + y = a; x2 + 3xy + y2 = b;..are..symmetrical equations; because for every x you may put y, and for every y, x, without altering either of the equations. 1863Frost & Wolstenholme Solid Geom. 29 To find the symmetrical equations of a straight line. 1878W. K. Clifford Math. Papers (1882) 317 If n is odd,..the determinant is skew symmetrical, and being of odd order it necessarily vanishes. 1903,1937[see reflexive a. 7]. 1930P. A. M. Dirac Princ. Quantum Mech. xi. 201 It is quite possible for only symmetrical or antisymmetrical states to occur in nature... One assumes the symmetrical states for photons. 1954I. M. Copi Symbolic Logic v. 141 Various symmetrical relations are designated by the phrases: ‘is next to’, ‘is married to’, and ‘has the same weight as’. A symmetrical relation is one such that if one individual has that relation to a second individual, then the second individual must have that relation to the first. 1963R. P. Feynman et al. Feynman Lect. Physics I. xi. 2 The laws of physics are symmetrical for translational displacements,..in the sense that the laws do not change when we make a translation of our coordinates. 1973B. H. Bransden et al. Fundamental Particles iv. 79 The triplet spin state is symmetrical. 1979Georgacarakos & Smith Elementary Formal Logic ix. 329 When a relational expression has this property, we say that it is symmetrical.
c. Photogr. Applied to a lens of symmetrical form; also ellipt. as n. = symmetrical lens.
1890Anthony's Photogr. Bull. III. 326 Rapid, and portable symmetrical lenses, and a whole plate rapid symmetrical for long distance work. 1892Photogr. Ann. II. 355 The lens is a rapid symmetrical with revolving diaphragms.
d. Math. and Logic. symmetrical difference = symmetric difference s.v. symmetric a. 1 b.
1978C. H. Greenstein Dict. Logical Terms & Symbols 172 Symmetrical difference. 1979Kandel & Lee Fuzzy Switching & Automata ii. 53 The symmetrical difference (or Boolean sum) of two fuzzy sets.
3. a. Bot. Of a flower: Having the same number of parts in each whorl: = isomerous 1.
1849Balfour Man. Bot. §644 In speaking of flowers, it is usual to call them symmetrical when the sepals, petals, and stamens follow the law mentioned, even although the pistil may be abnormal. Thus, many Solanaceæ are pentamerous, and have a dimerous ovary, yet they are called symmetrical... In Papilionaceous flowers, the parts are usually symmetrical, there being five divisions of the calyx, five petals, and ten stamens in two rows.
b. (a) Anat. and Zool. Having similar or corresponding parts or organs on opposite sides of a dividing plane, or regularly arranged around an axis or centre; consisting of two or more similar or corresponding divisions. Also said of the parts. (b) Path. Of a disease: Affecting such corresponding parts or organs simultaneously. (Cf. symmetry 3 c.)
1851Richardson Geol. viii. (1855) 230 Some have internal symmetrical bones, as the Sepia and Loligo. 1851Woodward Mollusca i. (1856) 62 Unlike most of the mollusca, they are symmetrical animals, having their right and left sides equally developed. a1883Fagge Princ. Pract. Med. (1886) II. 669 Remarkable cases of symmetrical gangrene of the extremities. 1892H. Lane Differ. Rheum. Dis. (ed. 2) 46 Rheumatoid Arthritis..affection of joints often symmetrical.
Hence symmetriˈcality = symmetricalness.
1893Chamb. Jrnl. 21 Jan. 44/2 With regard to symmetricality, Nature, when she has a purpose to serve, is nowise loth to depart from it. |