binormal: meaning, definition, pronunciation and examples
Very LowHighly Technical
Quick answer
What does “binormal” mean?
In mathematics (differential geometry), a line perpendicular to both the tangent and the principal normal to a space curve at a given point.
Audio
Pronunciation
Definition
Meaning and Definition
In mathematics (differential geometry), a line perpendicular to both the tangent and the principal normal to a space curve at a given point.
Specifically, in the moving trihedron (Frenet–Serret frame) of a three-dimensional space curve, the binormal vector is the unit vector orthogonal to both the tangent (direction of motion) and the principal normal (direction of curvature). It defines the torsion of the curve.
Dialectal Variation
British vs American Usage
Differences
No differences in definition or application between British and American mathematical literature.
Connotations
Purely technical, neutral connotation in both dialects.
Frequency
Extremely rare outside advanced mathematics textbooks and papers. Identical frequency in both dialects within its niche.
Grammar
How to Use “binormal” in a Sentence
The binormal (to the curve at point P)The binormal vector B(t)B = T × N (where T is tangent, N is normal)Vocabulary
Collocations
Examples
Examples of “binormal” in a Sentence
adjective
British English
- The binormal vector is crucial for calculating torsion.
- We need the binormal component for the simulation.
American English
- The binormal direction completes the Frenet frame.
- Calculate the binormal vector at the given point.
Usage
Meaning in Context
Business
Not used.
Academic
Exclusively used in advanced mathematics, physics, and engineering contexts involving three-dimensional curve analysis.
Everyday
Never used.
Technical
Core term in differential geometry, computer graphics (for modelling curves), and robotics (path planning).
Vocabulary
Synonyms of “binormal”
Neutral
Watch out
Common Mistakes When Using “binormal”
- Using it as a synonym for 'abnormal' or 'not normal'.
- Confusing it with 'bilateral' or 'binary'.
- Attempting to use it in non-mathematical contexts.
FAQ
Frequently Asked Questions
No. Despite the 'bi-' prefix, it has no semantic connection to the word 'normal' in the sense of 'ordinary'. It is a strictly technical geometric term.
In technical writing, it is commonly used as a noun phrase ('the binormal') shorthand for 'the binormal vector'.
Yes. For a plane flying along a curved path: its nose direction is the tangent, the lift force direction is the principal normal, and the wing direction (pointing from one wingtip to the other, perpendicular to both) is analogous to the binormal.
Not at all. It is a highly specialised term only relevant for learners in advanced STEM fields like mathematics, physics, or computer graphics.
In mathematics (differential geometry), a line perpendicular to both the tangent and the principal normal to a space curve at a given point.
Binormal is usually highly technical in register.
Binormal: in British English it is pronounced /ˌbaɪˈnɔː.məl/, and in American English it is pronounced /ˌbaɪˈnɔːr.məl/. Tap the audio buttons above to hear it.
Learning
Memory Aids
Mnemonic
Bi-normal: think 'twice normal'—it's the second normal vector you find after the principal normal, perpendicular to both the direction you're going (tangent) and the curve's bend (normal).
Conceptual Metaphor
If a car moves along a twisted road, the tangent is its direction, the normal points to the center of the curve, and the binormal points straight up out of the road surface, indicating the twist of the path.
Practice
Quiz
What field of study uses the term 'binormal' as a core concept?