What does curvilinearity mean?
Curvilinearity is the quality of being formed by or following curved rather than straight lines. It appears most often in technical contexts. In art, architecture, and design, critics use it to describe compositions dominated by sweeping curves, such as the organic forms of Art Nouveau or Gaudí's Barcelona buildings. In statistics, curvilinearity has a precise meaning: it names the situation in which two variables are related by a curve instead of a straight line, so a linear model would misrepresent the pattern. Analysts test for it by examining residual plots, since unaddressed curvilinearity can weaken or distort conclusions drawn from regression. The word derives from curvilinear, itself built from Latin curvus (bent) and linea (line). Though uncommon in everyday speech, it is a useful term whenever precision matters about whether something bends — physically or statistically.
nounThe quality or state of being curvilinear; the degree to which a line, shape, path, or relationship is characterized by curved rather than straight forms. In statistics, it refers to a relationship between variables that is best described by a curve rather than a straight line.
- The quality of being bounded by or composed of curved lines (of shapes, designs, or paths).
- In statistics and data analysis: the property of a relationship between variables that follows a curve rather than a straight line.
- In geometry more broadly: deviation from rectilinear form; the extent to which a figure departs from straight lines and planes.
"The architect embraced the curvilinearity of the riverfront site, letting every walkway sweep in gentle arcs."
"Antoni Gaudí's buildings are celebrated for their flowing curvilinearity, with almost no straight edges anywhere in their façades."
"Before fitting a linear regression, analysts often plot residuals to check for curvilinearity, which would signal that a curved model fits better."
Rarely pluralized; the plural may appear when comparing multiple distinct instances or types of curvature across cases, but most writers keep the term singular even when discussing several examples.
"The study catalogued the curvilinearities of three different coastline profiles."
When researchers suspect a straight-line model is lying to them, they test for curvilinearity — the mathematical admission that real life rarely moves in perfect lines.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Etymology of curvilinearity
Curvilinearity derives from curvilinear, a term formed from Latin roots: curvus, meaning bent or crooked, and linea, meaning line, likely via post-classical Latin curvilineus. The adjective curvilinear became established in English by the late 17th century in geometric and architectural contexts, and the noun curvilinearity arose later as an abstract quality-noun from it. It shares its Latin lineage with words such as lineal, linear, and rectilinear.
Related word forms
How curvilinearity is actually used
A technical term used mainly in mathematics, statistics, architecture, and design criticism. It sounds formal and scholarly and is rare in casual conversation. In statistical writing it often appears when discussing violations of the linearity assumption in regression.
Easily confused with curvilinearity
Curvature is a measurable quantity describing how sharply a curve bends at a point, while curvilinearity is the general quality of consisting of or following curved lines.
Collinearity describes points lying on the same straight line (a problem in regression), whereas curvilinearity describes relationships that follow a curve rather than a line.