HOMOGENEOUS

homogeneous, homogenous

(adjective) all of the same or similar kind or nature; “a close-knit homogeneous group”

Source: WordNet® 3.1

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Etymology

Adjective

homogeneous (not comparable)

Of the same kind; alike, similar.

Having the same composition throughout; of uniform make-up.

(chemistry) in the same state of matter.

(mathematics) Of which the properties of a smaller set apply to the whole; scalable.

The function $\backslash (f(x,y)=x^2+y^2\backslash )$ is homogeneous of degree 2 because $\backslash (f(\backslash alpha\; x,\backslash alpha\; y)=\backslash alpha^2\; f(x,y)\backslash )$.

Antonyms

• heterogeneous

Source: Wiktionary

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Ho`mo*ge"ne*ous, a. Etym: [Gr. homogène. See Same, and Kin.]

1. Of the same kind of nature; consisting of similar parts, or of elements of the like nature; -- opposed to heterogeneous; as, homogeneous particles, elements, or principles; homogeneous bodies.

2. (Alg.)

Definition: Possessing the same number of factors of a given kind; as, a homogeneous polynomial.

Source: Webster’s Unabridged Dictionary 1913 Edition

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