Binomi

Binomi is a term used in several languages as the equivalent of the English binomial. In mathematics, a binomi is an expression with exactly two terms, such as a + b. The two terms can be numbers, variables, or more general expressions.

The study of binomials is central to the binomial theorem, which provides a formula for expanding any power of a binomial: (a + b)^n = sum_{k=0}^n binom(n,k) a^{n-k} b^k. The factor binom(n,k), called the binomial coefficient, counts the number of ways to choose k items from n and appears in Pascal's triangle. Binomials also include differences, such as a − b.

Beyond algebra, the concept extends to probability. The binomial distribution describes the number of successes in n independent Bernoulli trials with a fixed probability of success p, and its probabilities again rely on binomial coefficients.

In biology, binomial nomenclature uses two names to identify species: genus and species, a system introduced by Carl Linnaeus. Though not a direct mathematical binomial, the term shares the two-term naming idea in its name.

Etymology: binomi derives from Latin bi- "two" and nomen "name", reflecting the two-term structure in the concept.

See also: binomial, binomial theorem, binomial distribution, binomial nomenclature.