symmetricadj.

/sɪˈmɛtrɪk/

Etymology: < symmetry n. + -ic suffix, after geometric. Compare French symétrique, †symmetrique (1529).

a. = symmetrical adj.

ΘΚΠ

the world > space > shape > symmetry or regularity > [adjective]

well-proportioneda1398

regularc1450

proportionable1576

formly1577

symmetriated1592

symmetrial1612

well-proportionated1612

well-balanceda1616

symmetrical1751

symmetric1796

eurhythmic1831

eumorphous1859

the world > relative properties > number > algebra > [adjective] > relating to expressions

interscendent1796

symmetrical1816

zeta-ic1840

associative1844

discriminantal1852

symmetric1853

discriminant1870

idempotent1870

interscendental1873

bilinear1886

non-trivial1901

left1926

right1930

the world > relative properties > number > geometry > [adjective] > of geometrical relation

reciprocal1570

regular1570

projectivea1652

semi-conjugate axis1743

homographic1859

symmetric1860

confocal1867

correlative1881

involutorial1885

conjugate1902

antisymmetrical1913

homoeomorphic1918

homotopic1918

isometric1952

1796 C. Burney Mem. Life Metastasio II. 332 The air should be phrased and symmetric.

1816 J. K. Tuckey Narr. Exped. River Zaire (1818) iii. 108 The faces of many of the women were by no means unprepossessing, and their forms extremely symmetric.

1853 Sylvester in Philos. Trans. (Royal Soc.) 143 434 Calculating the symmetric functions as a function only of x [etc.].

1854 A. Cayley Coll. Math. Papers II. 233 The covariant may in the former case be called a symmetric covariant, and in the latter case a skew covariant.

1860 J. Tyndall Glaciers of Alps ii. xxix. 403 The ripples from the two sides form a pair of symmetric curves.

1871 R. Browning Balaustion 102 While still one's heart, in time and tune, Paced after that symmetric step of Death.

1885 R. F. Burton tr. Arabian Nights' Entertainm. (1887) III. 12 Perfect in beauty and loveliness and stature and symmetric grace.

b. Physics. = symmetrical adj. 2b.

ΘΚΠ

the world > matter > physics > quantum theory > quantum mechanics > symmetry, conserved properly > [adjective]

symmetrical1930

symmetric1935

1935 E. U. Condon & G. H. Shortley Theory Atomic Spectra iii. 165 If the atom is at a certain moment in a symmetric state it will always remain in a symmetric state.

1965 H. Muirhead Physics Elem. Particles ix. 369 It is apparent from this equation that parallel spin states..are symmetric.

1979 Nature 29 Mar. 404/2 Certain baryons..contain three identical quarks with parallel spins in a state which is symmetric (the wave function does not change sign) to the interchange of a pair of quarks.

2. Logic. Of a binary relation: such that when two terms for which it is true are interchanged, it remains true.

ΘΚΠ

the mind > mental capacity > philosophy > logic > predicate or propositional logic > [adjective] > terms expressing types of relation

transitive1856

intransitive1870

irreflexive1890

dyadic1897

symmetrical1903

non-reflexive1905

polyadic1905

symmetric1933

mereological1957

1933 Mind 42 34 Not even God himself can make men into women by shifting words, or make what we call ‘implies’ symmetric by changing names.

1968 New Scientist 16 May 339/1 Equality is symmetric as well as being reflexive.

1979 K. J. Devlin Fund. Contemp. Set Theory i. 14 A binary relation on a set is an equivalence relation just in case it is reflective, symmetric, and transitive.

Compounds

Mathematics and Logic.

symmetric difference n. see quot. 1936.

ΘΚΠ

the mind > mental capacity > philosophy > logic > predicate or propositional logic > [noun] > set theory or extension > symmetric group or difference

symmetric group1897

symmetric difference1936

symmetrical difference1978

the world > relative properties > number > mathematical number or quantity > numerical arrangement > [noun] > set > elements in or parts of > relation between

well-ordering1914

symmetric difference1936

partial ordering1938

equivalence relation1940

symmetrical difference1978

1936 Trans. Amer. Math. Soc. 40 38 The Union (modulo 2), or symmetric difference, of two classes is the class of objects belonging to one or the other, but not to both, of those classes.

1971 J. H. Conway in Powell & Higman Finite Simple Groups vii. 225 If some non-empty -set has fewer than five elements, every set of the same cardinal would be a -set,..and by taking symmetric differences we should obtain every two-element set..as a -set, which cannot be.

symmetric group n. the group of all the permutations of a set of unlike entities.

ΘΚΠ

the mind > mental capacity > philosophy > logic > predicate or propositional logic > [noun] > set theory or extension > symmetric group or difference

symmetric group1897

symmetric difference1936

symmetrical difference1978

the world > relative properties > number > mathematical number or quantity > numerical arrangement > [noun] > set > in abstract algebra > groups

syntheme1844

group1854

substitution group1861

quaternion group1881

subgroup1881

Abelian group1892

permutation group1893

quotient group1893

factor group1895

order1897

symmetric group1897

point group1903

Sylow subgroup1905

module1927

Lie group1939

symmetry group1956

Weyl group1961

stabilizer1965

1897 W. Burnside Theory Groups of Finite Order viii. 139 The group of order n! which consists of all the substitutions that can be performed on n symbols is called the symmetric group of degree n.

1955 L. Mirsky Introd. Linear Algebra ix. 257 In addition to the symmetric group..there are other groups of permutations, all of them naturally subgroups of the symmetric group.

This entry has not yet been fully updated (first published 1919; most recently modified version published online June 2021).

单词	symmetric
释义	symmetricadj. /sɪˈmɛtrɪk/ Etymology: < symmetry n. + -ic suffix, after geometric. Compare French symétrique, †symmetrique (1529). 1. a. = symmetrical adj. ΘΚΠ the world > space > shape > symmetry or regularity > [adjective] well-proportioneda1398 regularc1450 proportionable1576 formly1577 symmetriated1592 symmetrial1612 well-proportionated1612 well-balanceda1616 symmetrical1751 symmetric1796 eurhythmic1831 eumorphous1859 the world > relative properties > number > algebra > [adjective] > relating to expressions interscendent1796 symmetrical1816 zeta-ic1840 associative1844 discriminantal1852 symmetric1853 discriminant1870 idempotent1870 interscendental1873 bilinear1886 non-trivial1901 left1926 right1930 the world > relative properties > number > geometry > [adjective] > of geometrical relation reciprocal1570 regular1570 projectivea1652 semi-conjugate axis1743 homographic1859 symmetric1860 confocal1867 correlative1881 involutorial1885 conjugate1902 antisymmetrical1913 homoeomorphic1918 homotopic1918 isometric1952 1796 C. Burney Mem. Life Metastasio II. 332 The air should be phrased and symmetric. 1816 J. K. Tuckey Narr. Exped. River Zaire (1818) iii. 108 The faces of many of the women were by no means unprepossessing, and their forms extremely symmetric. 1853 Sylvester in Philos. Trans. (Royal Soc.) 143 434 Calculating the symmetric functions as a function only of x [etc.]. 1854 A. Cayley Coll. Math. Papers II. 233 The covariant may in the former case be called a symmetric covariant, and in the latter case a skew covariant. 1860 J. Tyndall Glaciers of Alps ii. xxix. 403 The ripples from the two sides form a pair of symmetric curves. 1871 R. Browning Balaustion 102 While still one's heart, in time and tune, Paced after that symmetric step of Death. 1885 R. F. Burton tr. Arabian Nights' Entertainm. (1887) III. 12 Perfect in beauty and loveliness and stature and symmetric grace. b. Physics. = symmetrical adj. 2b. ΘΚΠ the world > matter > physics > quantum theory > quantum mechanics > symmetry, conserved properly > [adjective] symmetrical1930 symmetric1935 1935 E. U. Condon & G. H. Shortley Theory Atomic Spectra iii. 165 If the atom is at a certain moment in a symmetric state it will always remain in a symmetric state. 1965 H. Muirhead Physics Elem. Particles ix. 369 It is apparent from this equation that parallel spin states..are symmetric. 1979 Nature 29 Mar. 404/2 Certain baryons..contain three identical quarks with parallel spins in a state which is symmetric (the wave function does not change sign) to the interchange of a pair of quarks. 2. Logic. Of a binary relation: such that when two terms for which it is true are interchanged, it remains true. ΘΚΠ the mind > mental capacity > philosophy > logic > predicate or propositional logic > [adjective] > terms expressing types of relation transitive1856 intransitive1870 irreflexive1890 dyadic1897 symmetrical1903 non-reflexive1905 polyadic1905 symmetric1933 mereological1957 1933 Mind 42 34 Not even God himself can make men into women by shifting words, or make what we call ‘implies’ symmetric by changing names. 1968 New Scientist 16 May 339/1 Equality is symmetric as well as being reflexive. 1979 K. J. Devlin Fund. Contemp. Set Theory i. 14 A binary relation on a set is an equivalence relation just in case it is reflective, symmetric, and transitive. Compounds Mathematics and Logic. symmetric difference n. see quot. 1936. ΘΚΠ the mind > mental capacity > philosophy > logic > predicate or propositional logic > [noun] > set theory or extension > symmetric group or difference symmetric group1897 symmetric difference1936 symmetrical difference1978 the world > relative properties > number > mathematical number or quantity > numerical arrangement > [noun] > set > elements in or parts of > relation between well-ordering1914 symmetric difference1936 partial ordering1938 equivalence relation1940 symmetrical difference1978 1936 Trans. Amer. Math. Soc. 40 38 The Union (modulo 2), or symmetric difference, of two classes is the class of objects belonging to one or the other, but not to both, of those classes. 1971 J. H. Conway in Powell & Higman Finite Simple Groups vii. 225 If some non-empty -set has fewer than five elements, every set of the same cardinal would be a -set,..and by taking symmetric differences we should obtain every two-element set..as a -set, which cannot be. symmetric group n. the group of all the permutations of a set of unlike entities. ΘΚΠ the mind > mental capacity > philosophy > logic > predicate or propositional logic > [noun] > set theory or extension > symmetric group or difference symmetric group1897 symmetric difference1936 symmetrical difference1978 the world > relative properties > number > mathematical number or quantity > numerical arrangement > [noun] > set > in abstract algebra > groups syntheme1844 group1854 substitution group1861 quaternion group1881 subgroup1881 Abelian group1892 permutation group1893 quotient group1893 factor group1895 order1897 symmetric group1897 point group1903 Sylow subgroup1905 module1927 Lie group1939 symmetry group1956 Weyl group1961 stabilizer1965 1897 W. Burnside Theory Groups of Finite Order viii. 139 The group of order n! which consists of all the substitutions that can be performed on n symbols is called the symmetric group of degree n. 1955 L. Mirsky Introd. Linear Algebra ix. 257 In addition to the symmetric group..there are other groups of permutations, all of them naturally subgroups of the symmetric group. This entry has not yet been fully updated (first published 1919; most recently modified version published online June 2021). < adj.1796
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