File:Osculating.svg · Wikimedia Commons · See Wikimedia Commons
curvature
Sign in to savethumb|A migrating wild-type Dictyostelium discoideum cell whose boundary is colored by curvature. Scale bar: 5 μm.
In the Vinony graph
Vinony's link graph records 610 inbound references to curvature, and connects out to tangent, normal and differential geometry of curves.
It sits within the topics Curvature (mathematics) and Multivariable calculus.
Vinony links it to 44 Wikipedia language editions.
Wikidata facts
- Subclass of
- reciprocal length
Show 4 more facts
- Commons category
- Illustrations for curvature and torsion of curves
- topic's main category
- Category:Curvature (mathematics)
- maintained by WikiProject
- WikiProject Mathematics
- topic has template
- Template:Curvature
Sources (2)
via Wikidata · CC0
~41 min read
Encyclopedic overview
34 sectionsContents
- History
- Curves
- Arc-length parametrization
- General parametrization
- Curvature vector
- Osculating circle
- Curvature from arc and chord length
- Exceptional cases
- Examples
- Circle
- Parabola
- Plane curves
- Signed curvature
- Graph of a function
- Implicit curve
- Polar coordinates
- Curvature comb
- Frenet–Serret formulas for plane curves
- Curves in three dimensions
- Surfaces
- Curves on surfaces
- Principal curvature
- Normal sections
- Developable surfaces
- Gaussian curvature
- Mean curvature
- Second fundamental form
- Shape operator
- Curvature of space{{anchor|Space}}
- Generalizations
- See also
- Notes
- References
- External links
thumb|A migrating wild-type Dictyostelium discoideum cell whose boundary is colored by curvature. Scale bar: 5 μm.
In mathematics, curvature is any of several strongly related concepts in geometry that intuitively measure the amount by which a curve deviates from being a straight line or by which a surface deviates from being a plane. If a curve or surface is contained in a larger space, curvature can be defined extrinsically relative to the ambient space. Curvature of Riemannian manifolds of dimension at least two can be defined intrinsically without reference to a larger space.
Excerpted from Wikipedia’s “curvature” article, available under the CC BY-SA 4.0 licence.