[计] 二项式定理

[ noun ]
a theorem giving the expansion of a binomial raised to a given power
<noun.cognition>

Theorem \The"o*rem\, n. [L. theorema, Gr. ? a sight,
speculation, theory, theorem, fr. ? to look at, ? a
spectator: cf. F. th['e]or[`e]me. See {Theory}.]
1. That which is considered and established as a principle;
hence, sometimes, a rule.

Not theories, but theorems (?), the intelligible
products of contemplation, intellectual objects in
the mind, and of and for the mind exclusively.
--Coleridge.

By the theorems,
Which your polite and terser gallants practice,
I re-refine the court, and civilize
Their barbarous natures. --Massinger.

2. (Math.) A statement of a principle to be demonstrated.

Note: A theorem is something to be proved, and is thus
distinguished from a problem, which is something to be
solved. In analysis, the term is sometimes applied to a
rule, especially a rule or statement of relations
expressed in a formula or by symbols; as, the binomial
theorem; Taylor's theorem. See the Note under
{Proposition}, n., 5.

{Binomial theorem}. (Math.) See under {Binomial}.

{Negative theorem}, a theorem which expresses the
impossibility of any assertion.

{Particular theorem} (Math.), a theorem which extends only to
a particular quantity.

{Theorem of Pappus}. (Math.) See {Centrobaric method}, under
{Centrobaric}.

{Universal theorem} (Math.), a theorem which extends to any
quantity without restriction.


Binomial \Bi*no"mi*al\, a.
1. Consisting of two terms; pertaining to binomials; as, a
binomial root.

2. (Nat. Hist.) Having two names; -- used of the system by
which every animal and plant receives two names, the one
indicating the genus, the other the species, to which it
belongs.

{Binomial theorem} (Alg.), the theorem which expresses the
law of formation of any power of a binomial.