# homogeneous

[ hoh-muh-jee-nee-uhs, -jeen-yuhs, hom-uh- ]
/ ˌhoʊ məˈdʒi ni əs, -ˈdʒin yəs, ˌhɒm ə- /

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: x2y3 is a homogeneous expression of degree 5.
4. relating to a differential equation in which a linear combination of derivatives is set equal to zero.

## Origin of homogeneous

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

heterogeneous heterogenous homogeneous homogenous homogeneous homogenous

## Example sentences from the Web for homogeneous

homogeneous
/ (ˌhəʊməˈdʒiːnɪəs, ˌhɒm-) /

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 phase Compare heterogeneous
Also (for senses 1–4): homogenous

## Derived forms of homogeneous

homogeneity (ˌhəʊməʊdʒɪˈniːɪtɪ, ˌhɒm-), noun homogeneously, adverb homogeneousness, noun

## Medical definitions for homogeneous

homogeneous
[ hō′mə-jēnē-əs, -jēnyəs ]