curls

Curls, in the context of hair, refer to hair strands that curve in a spiraled or serpentine pattern rather than lying straight. Curl patterns vary widely and are commonly described as loose waves, waves, curls, or coils. The shape is influenced by genetics, hair follicle structure, and hair elasticity. Hair care for curly textures focuses on moisture retention, minimizing frizz, and defining shape, often using sulfate-free cleansers, conditioning, leave-in products, and diffused or low-heat styling. Protective styling and gentle detangling help reduce breakage. Curl pattern can be altered temporarily by heat styling or chemically altering the hair, which may affect texture and health.

In mathematics, the curl is a vector operator that describes the rotation of a vector field. For a vector field F(x, y, z) = (Fx, Fy, Fz), the curl is ∇ × F, a vector whose components are (∂Fz/∂y − ∂Fy/∂z, ∂Fx/∂z − ∂Fz/∂x, ∂Fy/∂x − ∂Fx/∂y). The curl points in the direction of the axis of rotation and magnitude indicates the rotation strength; the right-hand rule gives the orientation. Physically, curl measures local circulation. It is fundamental in fluid dynamics, describing vorticity, and in electromagnetism, appearing in Maxwell's equations. In two dimensions, the curl reduces to a scalar representing rotation about the perpendicular axis.