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Radius of curvature and center of curvature. In differential geometry, the radius of curvature, R, is the reciprocal of the curvature. For a curve, it equals the radius of the circular arc which best approximates the curve at that point. For surfaces, the radius of curvature is the radius of a circle that best fits a normal section or ...
Radius of curvature, the reciprocal of the curvature in differential geometry Minimum railway curve radius , the shortest allowable design radius for the centerline of railway tracks Topics referred to by the same term
The curvature is the reciprocal of radius of curvature. That is, the curvature is =, where R is the radius of curvature [5] (the whole circle has this curvature, it can be read as turn 2π over the length 2π R). This definition is difficult to manipulate and to express in formulas.
The reciprocal of the curvature is called the radius of curvature. A circle with radius r has a constant curvature of κ ( t ) = 1 r {\displaystyle \kappa (t)={\frac {1}{r}}} whereas a line has a curvature of 0.
The Cesàro equation is obtained as a relation between arc length and curvature. The equation of a circle (including a line) for example is given by the equation κ ( s ) = 1 r {\displaystyle \kappa (s)={\tfrac {1}{r}}} where s {\displaystyle s} is the arc length, κ {\displaystyle \kappa } the curvature and r {\displaystyle r} the radius of ...
Görtler vortices in a boundary layer. In fluid dynamics, Görtler vortices are secondary flows that appear in a boundary layer flow along a concave wall. If the boundary layer is thin compared to the radius of curvature of the wall, the pressure remains constant across the boundary layer.
The center and radius of the osculating circle at a given point are called center of curvature and radius of curvature of the curve at that point. A geometric construction was described by Isaac Newton in his Principia:
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