# homogeneous

[ hoh-muh-jee-nee-uhs, -jeen-yuhs, hom-uh- ]
See synonyms for homogeneous on Thesaurus.com
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.

1. Mathematics.

• having a common property throughout: a homogeneous solid figure.

• having all terms of the same degree: a homogeneous equation.

• 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.

• relating to a differential equation in which a linear combination of derivatives is set equal to zero.

## Origin of homogeneous

1
1635–45; <Medieval Latin homogeneus, equivalent to homogene- (stem of Greek homogenḗs of the same kind; see homo-, gene) + -us-ous

## Other words from homogeneous

• non·ho·mo·ge·ne·ous·ness, noun
• un·ho·mo·ge·ne·ous·ness, noun

## Words that may be confused with homogeneous

Dictionary.com Unabridged Based on the Random House Unabridged Dictionary, © Random House, Inc. 2023

## British Dictionary definitions for homogeneous

homogeneous

/ (ˌhəʊməˈdʒiːnɪəs, ˌhɒm-) /

1. composed of similar or identical parts or elements

2. of uniform nature

1. similar in kind or nature

2. having a constant property, such as density, throughout

3. maths

• (of a polynomial) containing terms of the same degree with respect to all the variables, as in x ² + 2 xy + y 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

• (of an equation) containing a homogeneous function made equal to 0

4. chem of, composed of, or concerned with a single phase: Compare heterogeneous

• Also (for senses 1–4): homogenous

## Derived forms of homogeneous

• homogeneity (ˌhəʊməʊdʒɪˈniːɪtɪ, ˌhɒm-), noun