binomialadj.n.

/bʌɪˈnəʊmɪəl/

Etymology: < late Latin binōmius (see binomy n.) + -al suffix¹; compare French binôme.

A. adj.

1. Mathematics. Consisting of two terms; see B. Also, relating to or derived from the binomial theorem or the binomial distribution; binomial coefficient: a coefficient of a term in a binomial expansion; binomial distribution: a frequency distribution of the possible number of successful outcomes in a given number of trials in each of which there is the same probability of success; binomial equation: an equation reducible to the form xⁿ − A = 0; binomial expansion: an expansion of a power of a binomial; binomial series: an infinite series obtained by expanding (x + y)ⁿ, where n is not a positive integer or zero; also, a binomial expansion; binomial theorem: the general algebraic formula, discovered by Newton, by which any power of a binomial quantity may be found without performing the progressive multiplications.

ΘΚΠ

the world > relative properties > number > algebra > [adjective] > relating to expressions > involving specific number of terms

binomial1570

multinomial1608

quadrinomial1673

solinomial1690

polynomial1704

trinomial1704

infinitinomial1706

monomial1801

tetranomial1817

unipartite1819

monome1829

mononomial1861

polynomic1868

tripartite1869

multinominal1940

the world > relative properties > number > algebra > [noun] > expression > formula

binomial theorem1755

formula1794

Rankine's formula1868

proportionality1882

Hero's formula1886

Rutherford's law1913

Mellin transform1927

Langevin equation1943

the world > relative properties > number > algebra > [noun] > expression > equation

equation1570

cardanic equation1684

binomial equation1814

simultaneous equation1816

characteristic equation1828

characteristic equation1841

characteristic equation1849

intrinsic equation of a curve1849

complete primitive1859

primitive1862

Poisson's equation1873

Jacobi equation1882

formulaic equation1884

adjoint1889

recursion formula1895

characteristic equation1899

characteristic equation1900

Pell equation1910

Lotka–Volterra equations1937

Langevin equation1943

the world > relative properties > number > algebra > [noun] > expression > consisting of specific number of terms > method relating to

Horner's method1842

binomial expansion1848

the world > relative properties > number > algebra > [noun] > expression > consisting of specific number of terms > method relating to > coefficient of

binomial coefficient1889

the world > relative properties > number > probability or statistics > [noun] > distribution

distribution1854

random distribution1882

frequency distribution1895

probability distribution1895

Poisson distribution1898

binomial distribution1911

Student's t-distribution1925

sampling distribution1928

probability density1931

Poisson1940

beta distribution1941

Cauchy distribution1948

geometric distribution1950

the world > relative properties > number > mathematical number or quantity > numerical arrangement > [noun] > set > sequence > series > infinite

secundan1685

infinite series1706

Taylor('s) series1816

Maclaurin's series1881

power series1884

Fibonacci('s) series1891

Laurent's expansion1893

Fibonacci('s) numbers1914

majorant1925

tetrahedral numbers1939

Fibonacci('s) sequence1964

binomial series1966

1570 H. Billingsley tr. Euclid Elements Geom. x. f. 258 If two rationall lines commensurable in power onely be added together: the whole line is irrationall, and is called a binomium, or a binomiall line.

1673 J. Kersey Elem. Algebra I. ii. i. 137 (heading) Production of Powers, from Roots Binomial, Trinomial, &c.

1706 Phillips's New World of Words (new ed.) (at cited word) A binomial Quantity or Root, i.e. a Quantity or Root that consists of two Names or Parts joyn'd together by the Sign + as a + b, or 3 + 2.

1755 J. Landen Math. Lucubrations ix. 132 By the Binomial Theorem ^p/ _{1 + x} is = 1 + px + ^{p.p − 1}/ ₂x² + ^{p.p − 1. p − 2}/ _2.3x³ &c.

1796 C. Hutton Math. & Philos. Dict. (new ed.) I. 208/2 He [sc. Newton] happily discovered that, by considering powers and roots in a continued series,..the same binomial series would serve for them all, whether the index should be fractional or integral.

1814 P. Barlow New Math. & Philos. Dict. Binomial equation, is any equation of two terms, but more commonly applied to the higher order of equations of the form xⁿ = 1.

1848 A. De Morgan in Cambr. & Dublin Math. Jrnl. III. 239 Use the binomial expansion up to the term in (x − b)⁻⁽ⁿ⁻¹⁾.

1870 F. C. Bowen Logic xii. 410 The Binomial Theorem..is a true Law of Nature according to our definition.

1889 Cent. Dict. Binomial coefficient.

1911 G. U. Yule Introd. Theory Statistics xv. 305 The binomial distribution,..only becomes approximately normal when n is large, and this limitation must be remembered in applying the table..to cases in which the distribution is strictly binomial.

1914 Biometrika 10 36 Binomial frequencies belong to the teetotum class of chances.

1925 R. A. Fisher Statist. Methods iii. 65 The binomial distribution is well known as the first example of a theoretical distribution to be established.

1948 J. V. Uspensky Theory Equations i. 26 The particular binomial equation xⁿ = 1, defining the so-called roots of unity of degree n, is of special interest.

1949 W. L. Ferrar Higher Algebra Schools v. 73 The binomial expansion can be used to find the value of expressions such as (1·002)¹³, (1·01)⁷ to any desired number of significant figures.

1959 G. James & R. C. James Math. Dict. (ed. 2) 31/1 The (r + 1)th binomial coefficient of order n (n a positive integer) is n!/[r!(n − r)!], the number of combinations of n things r at a time.

1961 P. G. Guest Numerical Methods Curve Fitting iv. 72 The binomial distribution for rare events..approximates to the Poisson form.

1966 McGraw-Hill Encycl. Sci. & Technol. (rev. ed.) XII. 191/2 One of the most important power series is the binomial series.

2. Having or characterized by two names; = binominal adj.

ΘΚΠ

the mind > language > naming > [adjective] > having two names

binominous1612

binomial1656

dionymal1656

binominated1857

binominal1880

1656 T. Blount Glossographia Binomial, that hath two names.

1850 Gardeners' Chron. 405/2 The binomial system, adopted..in every department of science since the days of Linnæus.

1880 T. H. Huxley Crayfish 16 The terms of this binomial nomenclature.

B. n.

1. An algebraic expression consisting of two terms joined by the sign + or −: formerly only when connected by +. (Cf. binomy n.) Also elliptical for binomial distribution at sense A. 1, etc.

ΘΚΠ

the world > relative properties > number > algebra > [noun] > expression > consisting of specific number of terms

binomial1557

binomy1571

trinomy1571

quadrinomial1673

multinomiala1690

polynomiala1690

trinomiala1690

monomial1706

nomial1717

monome1736

infinitinomial1763

polynome1828

mononomial1844

quantic1854

form1859

Jacobi polynomial1882

Jacobi's function1882

ternariant1882

triquaternion1902

term1957

arity1968

1557 R. Record Whetstone of Witte sig. Ppiv The nombers that be compounde with + be called Bimedialles... If their partes be of 2 denominations, then are thei named Binomialles properly. Howbeit many vse to call Binomialles all compounde nombers that haue +.

1720 J. Raphson & S. Cunn tr. I. Newton Universal Arithmetick 223 The Binomial a − ^q/ _3a, or a + b.

1806 C. Hutton Course Math. (ed. 5) I. 214 To extract any Root of a Binomial.

1835 Penny Cycl. IV. 412/2 The general theorems of which the binomial is a particular case.

1914 Biometrika 10 64 The binomial is built up on the assumption of the repetition n times of a number of independent events, of which the chance of occurrence is identical and equal to q.

1966 J. S. Meyer & S. Hanlon Fun with New Math viii. 105 Perhaps you have forgotten how to multiply a binomial (an algebraic expression of two terms) by a binomial.

1968 P. A. P. Moran Introd. Probability Theory ii. 77 If we require a distribution with a variance smaller than that of a binomial we can use a hypergeometric distribution.

2. Biology. The two-part Latin name of a plant or an animal.

ΘΚΠ

the mind > language > naming > name or appellation > [noun] > scientific or technical name > with two (or more) terms

polyonym1889

binomial1945

1945 Rhodora XLVII. 372 Binomials had appeared sporadically in the publications of Bauhin, Cornut, and others.

1957 W. T. Stearn Linnaeus's Species Plantarum i. 2 In Linnaeus's work the binomial became more than a two-word label; it functioned as a point of reference within a vast logically devised and integrated system.

3. Philology. An expression consisting of two words of the same form-class.

ΚΠ

1959 Lingua VIII. 113 In the typical newspaper headline Cold and snow grip the nation it is proper to set off the segment cold and snow as a binomial.

1964 Linguistics May 69 In A-Tokharian texts we find numerous combinations of two synonymous words or words expressing nearly related—or, in some cases, opposite—conceptions. The meaning of such a binomial obviously approaches that of a dvandva.

Draft additions 1997

biˈnomially adv. (a) Biology (rare), in accordance with the binomial system of nomenclature; = binominally adv. at binominal adj. Additions; (b) Statistics in accordance with the binomial distribution.

ΘΚΠ

the world > life > biology > taxonomy > [adverb] > of systems of nomenclature

binomially1889

binominally1971

the world > relative properties > number > probability or statistics > [adverb] > in accordance with a particular distribution

normally1885

binomially1889

modally1936

log-normally1945

1889 Cent. Dict. Binomially, in a binomial manner; after the binomial method of nomenclature in zoölogy and botany.

1976 Biometrika 63 441 A binomially distributed random variable.

This entry has not yet been fully updated (first published 1887; most recently modified version published online March 2019).

单词	binomial
释义	binomialadj.n. /bʌɪˈnəʊmɪəl/ Etymology: < late Latin binōmius (see binomy n.) + -al suffix¹; compare French binôme. A. adj. 1. Mathematics. Consisting of two terms; see B. Also, relating to or derived from the binomial theorem or the binomial distribution; binomial coefficient: a coefficient of a term in a binomial expansion; binomial distribution: a frequency distribution of the possible number of successful outcomes in a given number of trials in each of which there is the same probability of success; binomial equation: an equation reducible to the form xⁿ − A = 0; binomial expansion: an expansion of a power of a binomial; binomial series: an infinite series obtained by expanding (x + y)ⁿ, where n is not a positive integer or zero; also, a binomial expansion; binomial theorem: the general algebraic formula, discovered by Newton, by which any power of a binomial quantity may be found without performing the progressive multiplications. ΘΚΠ the world > relative properties > number > algebra > [adjective] > relating to expressions > involving specific number of terms binomial1570 multinomial1608 quadrinomial1673 solinomial1690 polynomial1704 trinomial1704 infinitinomial1706 monomial1801 tetranomial1817 unipartite1819 monome1829 mononomial1861 polynomic1868 tripartite1869 multinominal1940 the world > relative properties > number > algebra > [noun] > expression > formula binomial theorem1755 formula1794 Rankine's formula1868 proportionality1882 Hero's formula1886 Rutherford's law1913 Mellin transform1927 Langevin equation1943 the world > relative properties > number > algebra > [noun] > expression > equation equation1570 cardanic equation1684 binomial equation1814 simultaneous equation1816 characteristic equation1828 characteristic equation1841 characteristic equation1849 intrinsic equation of a curve1849 complete primitive1859 primitive1862 Poisson's equation1873 Jacobi equation1882 formulaic equation1884 adjoint1889 recursion formula1895 characteristic equation1899 characteristic equation1900 Pell equation1910 Lotka–Volterra equations1937 Langevin equation1943 the world > relative properties > number > algebra > [noun] > expression > consisting of specific number of terms > method relating to Horner's method1842 binomial expansion1848 the world > relative properties > number > algebra > [noun] > expression > consisting of specific number of terms > method relating to > coefficient of binomial coefficient1889 the world > relative properties > number > probability or statistics > [noun] > distribution distribution1854 random distribution1882 frequency distribution1895 probability distribution1895 Poisson distribution1898 binomial distribution1911 Student's t-distribution1925 sampling distribution1928 probability density1931 Poisson1940 beta distribution1941 Cauchy distribution1948 geometric distribution1950 the world > relative properties > number > mathematical number or quantity > numerical arrangement > [noun] > set > sequence > series > infinite secundan1685 infinite series1706 Taylor('s) series1816 Maclaurin's series1881 power series1884 Fibonacci('s) series1891 Laurent's expansion1893 Fibonacci('s) numbers1914 majorant1925 tetrahedral numbers1939 Fibonacci('s) sequence1964 binomial series1966 1570 H. Billingsley tr. Euclid Elements Geom. x. f. 258 If two rationall lines commensurable in power onely be added together: the whole line is irrationall, and is called a binomium, or a binomiall line. 1673 J. Kersey Elem. Algebra I. ii. i. 137 (heading) Production of Powers, from Roots Binomial, Trinomial, &c. 1706 Phillips's New World of Words (new ed.) (at cited word) A binomial Quantity or Root, i.e. a Quantity or Root that consists of two Names or Parts joyn'd together by the Sign + as a + b, or 3 + 2. 1755 J. Landen Math. Lucubrations ix. 132 By the Binomial Theorem ^p/ _{1 + x} is = 1 + px + ^{p.p − 1}/ ₂x² + ^{p.p − 1. p − 2}/ _2.3x³ &c. 1796 C. Hutton Math. & Philos. Dict. (new ed.) I. 208/2 He [sc. Newton] happily discovered that, by considering powers and roots in a continued series,..the same binomial series would serve for them all, whether the index should be fractional or integral. 1814 P. Barlow New Math. & Philos. Dict. Binomial equation, is any equation of two terms, but more commonly applied to the higher order of equations of the form xⁿ = 1. 1848 A. De Morgan in Cambr. & Dublin Math. Jrnl. III. 239 Use the binomial expansion up to the term in (x − b)⁻⁽ⁿ⁻¹⁾. 1870 F. C. Bowen Logic xii. 410 The Binomial Theorem..is a true Law of Nature according to our definition. 1889 Cent. Dict. Binomial coefficient. 1911 G. U. Yule Introd. Theory Statistics xv. 305 The binomial distribution,..only becomes approximately normal when n is large, and this limitation must be remembered in applying the table..to cases in which the distribution is strictly binomial. 1914 Biometrika 10 36 Binomial frequencies belong to the teetotum class of chances. 1925 R. A. Fisher Statist. Methods iii. 65 The binomial distribution is well known as the first example of a theoretical distribution to be established. 1948 J. V. Uspensky Theory Equations i. 26 The particular binomial equation xⁿ = 1, defining the so-called roots of unity of degree n, is of special interest. 1949 W. L. Ferrar Higher Algebra Schools v. 73 The binomial expansion can be used to find the value of expressions such as (1·002)¹³, (1·01)⁷ to any desired number of significant figures. 1959 G. James & R. C. James Math. Dict. (ed. 2) 31/1 The (r + 1)th binomial coefficient of order n (n a positive integer) is n!/[r!(n − r)!], the number of combinations of n things r at a time. 1961 P. G. Guest Numerical Methods Curve Fitting iv. 72 The binomial distribution for rare events..approximates to the Poisson form. 1966 McGraw-Hill Encycl. Sci. & Technol. (rev. ed.) XII. 191/2 One of the most important power series is the binomial series. 2. Having or characterized by two names; = binominal adj. ΘΚΠ the mind > language > naming > [adjective] > having two names binominous1612 binomial1656 dionymal1656 binominated1857 binominal1880 1656 T. Blount Glossographia Binomial, that hath two names. 1850 Gardeners' Chron. 405/2 The binomial system, adopted..in every department of science since the days of Linnæus. 1880 T. H. Huxley Crayfish 16 The terms of this binomial nomenclature. B. n. 1. An algebraic expression consisting of two terms joined by the sign + or −: formerly only when connected by +. (Cf. binomy n.) Also elliptical for binomial distribution at sense A. 1, etc. ΘΚΠ the world > relative properties > number > algebra > [noun] > expression > consisting of specific number of terms binomial1557 binomy1571 trinomy1571 quadrinomial1673 multinomiala1690 polynomiala1690 trinomiala1690 monomial1706 nomial1717 monome1736 infinitinomial1763 polynome1828 mononomial1844 quantic1854 form1859 Jacobi polynomial1882 Jacobi's function1882 ternariant1882 triquaternion1902 term1957 arity1968 1557 R. Record Whetstone of Witte sig. Ppiv The nombers that be compounde with + be called Bimedialles... If their partes be of 2 denominations, then are thei named Binomialles properly. Howbeit many vse to call Binomialles all compounde nombers that haue +. 1720 J. Raphson & S. Cunn tr. I. Newton Universal Arithmetick 223 The Binomial a − ^q/ _3a, or a + b. 1806 C. Hutton Course Math. (ed. 5) I. 214 To extract any Root of a Binomial. 1835 Penny Cycl. IV. 412/2 The general theorems of which the binomial is a particular case. 1914 Biometrika 10 64 The binomial is built up on the assumption of the repetition n times of a number of independent events, of which the chance of occurrence is identical and equal to q. 1966 J. S. Meyer & S. Hanlon Fun with New Math viii. 105 Perhaps you have forgotten how to multiply a binomial (an algebraic expression of two terms) by a binomial. 1968 P. A. P. Moran Introd. Probability Theory ii. 77 If we require a distribution with a variance smaller than that of a binomial we can use a hypergeometric distribution. 2. Biology. The two-part Latin name of a plant or an animal. ΘΚΠ the mind > language > naming > name or appellation > [noun] > scientific or technical name > with two (or more) terms polyonym1889 binomial1945 1945 Rhodora XLVII. 372 Binomials had appeared sporadically in the publications of Bauhin, Cornut, and others. 1957 W. T. Stearn Linnaeus's Species Plantarum i. 2 In Linnaeus's work the binomial became more than a two-word label; it functioned as a point of reference within a vast logically devised and integrated system. 3. Philology. An expression consisting of two words of the same form-class. ΚΠ 1959 Lingua VIII. 113 In the typical newspaper headline Cold and snow grip the nation it is proper to set off the segment cold and snow as a binomial. 1964 Linguistics May 69 In A-Tokharian texts we find numerous combinations of two synonymous words or words expressing nearly related—or, in some cases, opposite—conceptions. The meaning of such a binomial obviously approaches that of a dvandva. Draft additions 1997 biˈnomially adv. (a) Biology (rare), in accordance with the binomial system of nomenclature; = binominally adv. at binominal adj. Additions; (b) Statistics in accordance with the binomial distribution. ΘΚΠ the world > life > biology > taxonomy > [adverb] > of systems of nomenclature binomially1889 binominally1971 the world > relative properties > number > probability or statistics > [adverb] > in accordance with a particular distribution normally1885 binomially1889 modally1936 log-normally1945 1889 Cent. Dict. Binomially, in a binomial manner; after the binomial method of nomenclature in zoölogy and botany. 1976 Biometrika 63 441 A binomially distributed random variable. This entry has not yet been fully updated (first published 1887; most recently modified version published online March 2019). < adj.n.1557
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