homogeneous

Meaning

1. (not-comparable) Of the same kind; alike, similar.
2. (not-comparable) Having the same composition throughout; of uniform make-up.
3. (not-comparable) In the same state of matter.
4. (not-comparable) In any of several technical senses uniform; scalable; having its behavior or form determined by, or the same as, its behavior on or form at a smaller component (of its domain of definition, of itself, etc.).
5. (not-comparable) In any of several technical senses uniform; scalable; having its behavior or form determined by, or the same as, its behavior on or form at a smaller component (of its domain of definition, of itself, etc.).
6. (not-comparable) In any of several technical senses uniform; scalable; having its behavior or form determined by, or the same as, its behavior on or form at a smaller component (of its domain of definition, of itself, etc.).
7. (not-comparable) In any of several technical senses uniform; scalable; having its behavior or form determined by, or the same as, its behavior on or form at a smaller component (of its domain of definition, of itself, etc.).
8. (not-comparable) The function f(x,y)#61;x²#43;x²ʸ#43;y² is not homogeneous on all of #92;mathbb#123;R#125;² because f(2,2)#61;16#92;neq 2ᵏ#42;3#61;2ᵏf(1,1) for any k, but f is homogeneous on the subspace of #92;mathbb#123;R#125;² spanned by (1,0) because f(#92;alphax,#92;alphay)#61;#92;alphax²#61;#92;alpha²f(x,y) for all (x,y)#92;in#92;operatorname#123;Span#125;#92;#123;(1,0)#92;#125;.
9. (not-comparable) In ordinary differential equations (by analogy with the case for polynomial and functional homogeneity):
10. (not-comparable) In ordinary differential equations (by analogy with the case for polynomial and functional homogeneity):
11. (not-comparable) In ordinary differential equations (by analogy with the case for polynomial and functional homogeneity):
12. (not-comparable) In abstract algebra and geometry:
13. (not-comparable) In abstract algebra and geometry:
14. (not-comparable) In abstract algebra and geometry:
15. (not-comparable) In abstract algebra and geometry:
16. (not-comparable) In miscellaneous other senses:
17. (not-comparable) In miscellaneous other senses:

Synonyms

uniform

similar

alike

homogeneity

analogous

even

consistent

homogenous

equal

unvarying

like

comparable

isotropic

scalable

solid

unchanged

uniformity

unity

unvaried

congeneric

isotrope

same quality

same nature

homogen

homogenic

of the same descent

similar race

akin

Homog

authentic

connected

genuine

identical

iso

kindred

likeness

monotonous

neat

organic

parallel

resemble

Translations

homogène

homogen

omogeneo

homogéneo

homogêneo

homogeen

ομοιογενής

homogéneo

ομογενής

homogeni

gleichartig

homogênea

Pronounced as (IPA)

/ˌhɒ.mə(ʊ)ˈdʒiː.nɪəs/

Etymology

From Medieval Latin homogeneus, from Ancient Greek ὁμογενής (homogenḗs, “of the same race, family or kind”), from ὁμός (homós, “same”) + γένος (génos, “kind”). Compare homo- (“same”) and -ous (adjectival suffix).

Sentences

We can reflect this movement by dividing the homogeneous coordinate by a constant .