homogeneus

Homogeneus is commonly considered a misspelling of homogeneous. In standard English, the correct form is homogeneous, with the noun form homogeneity. The root comes from Greek homo- meaning “same” and -genous meaning “kind, race,” and the term describes things that have a uniform composition or character throughout.

In general use, a homogeneous substance or mixture has the same properties at every point. For example, a solution such as salt dissolved in water is homogeneous because the composition is the same throughout. By contrast, a heterogeneous substance contains distinguishable parts or phases, such as a salad or a rock with mineral inclusions.

In mathematics and related fields, homogeneous describes objects with uniform behavior under scaling. A function is homogeneous of degree n if multiplying its input by a factor t scales the function output by t^n. A homogeneous polynomial contains terms all of the same total degree. In geometry and physics, a homogeneous space or medium is one that appears identical at every point or location, such as a perfectly uniform material with constant properties.

In cosmology and statistics, the term appears in specific concepts: the cosmological principle describes the large-scale universe as homogeneous (and isotropic), while statistics uses homogeneity to denote stable properties across samples, such as equal variances (homoscedasticity).

Notable related terms include homogeneity, the quality of being homogeneous, and heterogeneity, the opposite property.