homogeneous

Where “homogeneous” sits in English frequency

Definition

1. 1
   Of the same kind; alike, similar.
2. 2
   Having the same composition throughout; of uniform make-up.
3. 3
   In the same state of matter.
4. 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. 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. 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. 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. 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. 9
   In ordinary differential equations (by analogy with the case for polynomial and functional homogeneity):
10. 10
    In ordinary differential equations (by analogy with the case for polynomial and functional homogeneity):
11. 11
    In ordinary differential equations (by analogy with the case for polynomial and functional homogeneity):
12. 12
    In abstract algebra and geometry:
13. 13
    In abstract algebra and geometry:
14. 14
    In abstract algebra and geometry:
15. 15
    In abstract algebra and geometry:
16. 16
    In miscellaneous other senses:
17. 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).

This word in other languages

Common misspellings

Also misspelled as: hhomogeneous,hmoogeneous,homgoeneous,hommogeneous,homoegneous,homogeenous,homogeneosu,homogeneouss,homogeneuos,homogenneous,homogenoeus,homoggeneous,homogneeous,hoomgeneous,ohmogeneous

Misspelling Pattern Breakdown

How far each generated variant is from the correct spelling of homogeneous - measured in single-character edits (insert, delete, or substitute a letter). Larger bars are easier to catch; one-edit slips are the sneakiest.

Frequently Asked Questions