homogeneous
- 1The same all the way through, with no different parts.
Mix the batter until it is homogeneous and has no lumps.
The rock looks homogeneous, the same color all the way through.
Similaruniform, consistent
Oppositeheterogeneous
- 2All of the same kind, or very much alike.
The group was homogeneous, because everyone was the same age and came from the same town.
Small towns often have a homogeneous population.
Similaruniform
Oppositediverse, heterogeneous, mixed, varied
Note
- 3In chemistry, forming one single phase with no boundaries inside, such as a gas mixture or a liquid solution.
When both chemicals are gases, the reaction between them is homogeneous.
The catalyst is homogeneous because it is dissolved in the same liquid as the other chemicals.
Oppositeheterogeneous
Note
- 4In geometry, looking the same from every point, since a symmetry can move any point to any other.
A sphere is homogeneous, since you can turn it to move any point to any other.
Flat space is homogeneous, so every point in it is just like every other.
Note
- 5In maths, describes a polynomial whose terms all have the same total degree, like x² + xy + y².
The polynomial x² + 3xy is homogeneous because both terms have degree 2.
Is x² + y + 1 homogeneous? No, its terms have different degrees.
Note
Less common meanings
- 6In maths, describes a function where scaling all inputs by a number scales the output by a fixed power of it.
The function f(x) = 3x is homogeneous: double x and the answer doubles too.
If a function is homogeneous of degree 2, tripling the inputs makes the answer nine times bigger.
Note
- 7Said of a differential equation in which scaling the unknown and its derivatives by a number scales every term alike.
The equation y·y″ = (y′)² is homogeneous in y and its derivatives.
If y solves this homogeneous equation, then 5y solves it too.
Note
- 8Of a first-order differential equation that can be rewritten so that x and y appear only as the ratio y/x.
The equation dy/dx = y/x is homogeneous, so we can solve it by putting y = vx.
To solve a homogeneous equation, the teacher showed us the trick of setting y = vx.
Note
- 9In geometry, having to do with homogeneous coordinates, a special way of giving the position of a point.
- 10In maths, describes linear equations with no constant terms, so all unknowns equal to zero is always a solution.
- 11In math, said of a relation that links things in a set only to things in the same set.
- 12Of a linear map between graded spaces that shifts every piece by the same fixed step.
Practice
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Origin
From Greek homogenḗs, meaning “of the same kind”, from homos (“same”) + genos (“kind”).
Checked 31 Oct 2026 · 3 facts
- Homogeneous ultimately derives from Greek homogenḗs. en.wiktionary.org
- Greek homogenḗs means of the same kind. en.wiktionary.org
- The Greek word derives from homos meaning same and genos meaning kind. en.wikipedia.org