Keyword Analysis & Research: curvature


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What does curvature mean?

The radius of curvature at a point on a curve is, loosely speaking, the radius of a circle which fits the curve most snugly at that point. The curvature, denoted , is one divided by the radius of curvature. In formulas, curvature is defined as the magnitude of the derivative of a unit tangent vector function with respect to arc length:

What is normal curvature?

Normal curvature Given a regular surface and a curve within that surface, the normal curvature at a point is the amount of the curve's curvature in the direction of the surface normal. The curve on the surface passes through a point , with tangent , curvature and normal .Given the surface normal , the normal curvature is the length of the projection of onto , namely .

What is the formula for curvature?

the curve. Thus the curvature k at a point (x,y) on the curve is defined as the derivative k = dφ ds = dφ dt dt ds, where we have used the chain rule in the last equality. To compute the curvature from (x(t),y(t)) we note that tanφ(t) = y˙(t) x˙(t). Differentiating both sides of this equation implicitly with respect to t we find sec2 φ dφ dt = d dt y˙ x˙ =

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