# homogeneous

## homogeneous

[hoh-muh-jee-nee-uhs, -jeen-yuhs, hom-uh-]
adjective
1.
composed of parts or elements that are all of the same kind; not heterogeneous: a homogeneous population.
2.
of the same kind or nature; essentially alike.
3.
Mathematics.
a.
having a common property throughout: a homogeneous solid figure.
b.
having all terms of the same degree: a homogeneous equation.
c.
relating to a function of several variables that becomes multiplied by some power of a constant when each variable is multiplied by that constant: x 2 y 3 is a homogeneous expression of degree 5.
d.
relating to a differential equation in which a linear combination of derivatives is set equal to zero.

Origin:
1635–45; < Medieval Latin homogeneus, equivalent to homogene- (stem of Greek homogenḗs of the same kind; see homo-, gene) + -us -ous

homogeneously, adverb
nonhomogeneous, adjective
nonhomogeneously, adverb
nonhomogeneousness, noun
unhomogeneous, adjective
unhomogeneously, adverb
unhomogeneousness, noun

1. heterogeneous, heterogenous, homogeneous, homogenous ; 2. homogeneous, homogenous.

1. unvarying, unmixed, alike, similar, identical.
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Based on the Random House Dictionary, © Random House, Inc. 2014.
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World English Dictionary
 homogeneous (ˌhəʊməˈdʒiːnɪəs, ˌhɒm-) —adj 1. composed of similar or identical parts or elements 2. of uniform nature 3. similar in kind or nature 4. having a constant property, such as density, throughout 5. maths a.  (of a polynomial) containing terms of the same degree with respect to all the variables, as in x² + 2xy + y² b.  (of a function) containing a set of variables such that when each is multiplied by a constant, this constant can be eliminated without altering the value of the function, as in cos x/y + x/y c.  (of an equation) containing a homogeneous function made equal to 0 6. chem Compare heterogeneous of, composed of, or concerned with a single phase homogeneity —n homo'geneously —adv homo'geneousness —n

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Dictionary.com's 21st Century Lexicon
 Main Entry: homogeneous Part of Speech: adj Definition: in chemistry, involving substances in the same phase (solid, liquid, or gas) Example: A homogeneous substance is salt, NaCl.
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Etymonline
Word Origin & History

homogeneous
1640s, from M.L. homogeneus, from Gk. homogenes "of the same kind," from homos "same" (see same) + genos "kind, gender, race, stock" (see genus). Earlier in this sense was homogeneal (c.1600). Homogenize "make similar" formed in Eng. 1886; its sense
of "render milk uniform in consistency" is from 1904.
Online Etymology Dictionary, © 2010 Douglas Harper
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American Heritage
Medical Dictionary

homogeneous ho·mo·ge·ne·ous (hō'mə-jē'nē-əs, -jēn'yəs)
adj.

1. Of the same or similar nature or kind.

2. Uniform in structure or composition throughout, as of a chemical mixture.

The American Heritage® Stedman's Medical Dictionary
Copyright © 2002, 2001, 1995 by Houghton Mifflin Company. Published by Houghton Mifflin Company.
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FOLDOC
Computing Dictionary

### homogeneous definition

(Or "homogenous") Of uniform nature, similar in kind.
1. In the context of distributed systems, middleware makes heterogeneous systems appear as a homogeneous entity. For example see: interoperable network.
Constrast heterogeneous.
2. (Of a polynomial) containing terms of the same degree with respect to all the variables, as in x^2 + 2xy + y^2.
3. (Of a function) containing a set of variables such that when each is multiplied by a constant, this constant can be eliminated without altering the value of the function, as in cos x/y + x/y.
4. (of an equation) containing a homogeneous function made equal to 0.
(1999-05-06)
The Free On-line Dictionary of Computing, © Denis Howe 2010 http://foldoc.org
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Example sentences
Seattle was too homogeneous, too provincial and too rainy for his taste, he
said.
Suburban developments were settled by mostly white families, giving suburbs a
homogeneous reputation.
King's nostalgic prescriptions imply a static, homogeneous student body that
simply does not exist in most schools today.
The overseas market is not a homogeneous market.
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