# homogeneous

> English word · Adjective · IPA /ˌhɒm.ə(ʊ)ˈd͡ʒiː.nɪəs/ · frequency rank #21,824

## Definitions
1. Of the same kind; alike, similar.
2. Having the same composition throughout; of uniform make-up.
3. In the same state of matter.
4. 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. 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. 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. 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. 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. In ordinary differential equations (by analogy with the case for polynomial and functional homogeneity):
10. In ordinary differential equations (by analogy with the case for polynomial and functional homogeneity):
11. In ordinary differential equations (by analogy with the case for polynomial and functional homogeneity):
12. In abstract algebra and geometry:
13. In abstract algebra and geometry:
14. In abstract algebra and geometry:
15. In abstract algebra and geometry:
16. In miscellaneous other senses:
17. In miscellaneous other senses:

## 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).

## Easily confused with
- **homogenous** (https://plainspell.com/en/vs/homogeneous-vs-homogenous)

## Common misspellings (15)
`hhomogeneous`, `hmoogeneous`, `homgoeneous`, `hommogeneous`, `homoegneous`, `homogeenous`, `homogeneosu`, `homogeneouss`, `homogeneuos`, `homogenneous`, `homogenoeus`, `homoggeneous`, `homogneeous`, `hoomgeneous`, `ohmogeneous`

## Source
Compiled from Wiktionary via kaikki.org (CC BY-SA). Data vintage: 2026-05-06.
Canonical page: https://plainspell.com/en/word/homogeneous