What does noncollinear mean?
Noncollinear describes points, lines, vectors, or other geometric objects that do not lie on the same straight line. The word is most often encountered in geometry, where the relationship among points or vectors determines which constructions and calculations are possible. For example, three noncollinear points determine a unique plane, while two distinct points alone determine only a line. The term is also relevant to vectors, transformations, and analytic geometry, where conditions such as independent or noncollinear directions are used to express essential structure. Although “non-linear” may sometimes appear as an informal approximation, “noncollinear” is the precise standard term when collinearity is what is meant. Its negative prefix makes the concept explicit and allows writers to distinguish a genuinely different geometric arrangement from the everyday idea of something simply not being arranged in a straight line.
adjectiveNot lying on the same straight line. In geometry, noncollinear points or objects do not belong to one common line.
- Not lying on the same straight line.
"Three noncollinear points determine a unique plane in Euclidean geometry."
"The vertices of the triangle are noncollinear, so they define a plane."
"The vectors must be noncollinear for the transformation to preserve area."
Three noncollinear points are enough to determine a unique plane, making this little prefix a key to a fundamental idea in geometry.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Where does noncollinear come from?
“Noncollinear” was formed in English by adding the negative prefix non- to “collinear.” “Collinear” comes from Latin collinearis, meaning “on the same line,” and is based on the Latin prefix com- and linea, “line.” The related English words “collineal” and “collineate” reflect the same Latin root, while “noncollinear” specifically came into use as a mathematical term.
How noncollinear is actually used
This is a technical term used mainly in mathematics, geometry, and related sciences. It is more precise than saying that objects are simply “not in a line,” because it refers specifically to the absence of collinearity.
Easily confused with noncollinear
Collinear points lie on the same straight line, whereas noncollinear points do not.