| 释义 |
binomial, a. and n.|baɪˈnəʊmɪəl|
[f. late L. binōmi-us (see binomy) + -al1; cf. F. binôme.]
A. adj.
1. Math. 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..
1570Billingsley Euclid x. xxxvi. 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. 1706Phillips s.v., 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. 1725J. Kersey Algebra 137 Production of Powers from Roots Binomial, Trinomial, etc. 1755J. Landen Math. Lucubrations ix. 132 By the Binomial Theorem p / 1 + x is = 1 + px + p.p - 1 / 2 x2 + p.p - 1. p - 2 / 2.3 x3 &c. 1796C. Hutton Math. & Philos. Dict. 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. 1814P. 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. 1848A. De Morgan in Camb. & Dublin Math. Jrnl. III. 239 Use the binomial expansion up to the term in (x - b)-(n-1). 1870Bowen Logic xii. 410 The Binomial Theorem..is a true Law of Nature according to our definition. 1889Cent. Dict., Binomial coefficient. 1911G. 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. 1914Biometrika X. 36 Binomial frequencies belong to the teetotum class of chances. 1925R. A. Fisher Statistical Methods iii. 65 The binomial distribution is well known as the first example of a theoretical distribution to be established. 1948J. 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. 1949W. 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. 1959G. & R. C. James Math. Dict. 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. 1961P. G. Guest Numer. Meth. Curve Fitting iv. 72 The binomial distribution for rare events..approximates to the Poisson form. 1966McGraw-Hill Encycl. Sci. & Technol. XII. 191/2 One of the most important power series is the binomial series.
2. Having or characterized by two names; = binominal.
1656in Blount Glossogr. 1850Gard. Chron. 404 The binomial system adopted in every department of science since the days of Linnæus. 1880Huxley 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. binomium, binomy.) Also ellipt. for binomial distribution, theorem, etc.
1557Recorde Whetst. Pp iv a, 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 +. 1720Raphson Arith. 223 The Binomial a - q / 3a , or a + b. 1806Hutton Course Math. I. 214 To extract any Root of a Binomial. 1835Penny Cycl. IV. 412/2 The general theorems of which the binomial is a particular case. 1914Biometrika X. 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. 1966Meyer & 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. 1968P. 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. Biol. The two-part Latin name of a plant or an animal.
1945Rhodora XLVII. 372 Binomials had appeared sporadically in the publications of Bauhin, Cornut and others. 1957W. T. Stearn Linnæus'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. Philol. An expression consisting of two words of the same form-class.
1959Lingua 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. 1964Linguistics 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.
Add: Hence biˈnomially adv., (a) Biol. (rare), in accordance with the binomial system of nomenclature; = *binominally adv.; (b) Statistics, in accordance with the binomial distribution.
1889Cent. Dict., Binomially, in a binomial manner; after the binomial method of nomenclature in zoölogy and botany. 1976Biometrika LXIII. 441 A binomially distributed random variable. |