curvature
thumb|A migrating wild-type Dictyostelium discoideum cell whose boundary is colored by curvature. Scale bar: 5 μm.
Article
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.