# homogeneous

[ hoh-muh-jee-nee-uhs, -jeen-yuhs, hom-uh- ]
/ ˌhoʊ məˈdʒi ni əs, -ˈdʒin yəs, ˌhɒm ə- /
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adjective
composed of parts or elements that are all of the same kind; not heterogeneous: a homogeneous population.
of the same kind or nature; essentially alike.
Mathematics.
1. having a common property throughout: a homogeneous solid figure.
2. having all terms of the same degree: a homogeneous equation.
3. relating to a function of several variables that becomes multiplied by some power of a constant when each variable is multiplied by that constant: x2y3is a homogeneous expression of degree 5.
4. relating to a differential equation in which a linear combination of derivatives is set equal to zero.

## OTHER WORDS FOR homogeneous

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## Origin ofhomogeneous

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

## WORDS THAT MAY BE CONFUSED WITH homogeneous

1. heterogeneous, heterogenous, homogeneous , homogenous2. homogeneous , homogenous
Dictionary.com Unabridged Based on the Random House Unabridged Dictionary, © Random House, Inc. 2023

## British Dictionary definitions for homogeneous

homogeneous
/ (ˌhəʊməˈdʒiːnɪəs, ˌhɒm-) /

adjective
composed of similar or identical parts or elements
of uniform nature
similar in kind or nature
having a constant property, such as density, throughout
maths
1. (of a polynomial) containing terms of the same degree with respect to all the variables, as in x ² + 2 xy + y ²
2. (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
3. (of an equation) containing a homogeneous function made equal to 0
chem of, composed of, or concerned with a single phaseCompare heterogeneous
Also (for senses 1–4): homogenous

## Derived forms of homogeneous

homogeneity (ˌhəʊməʊdʒɪˈniːɪtɪ, ˌhɒm-), nounhomogeneously, adverbhomogeneousness, noun
Collins English Dictionary - Complete & Unabridged 2012 Digital Edition © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012
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