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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.
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6 days ago · In general, there are two important types of curvature: extrinsic curvature and intrinsic curvature. The extrinsic curvature of curves in two- and three-space was the first type of curvature to be studied historically, culminating in the Frenet formulas, which describe a space curve entirely in terms of its "curvature," torsion , and the ...
Feb 27, 2022 · Definition 1.3.1. The circle which best approximates a given curve near a given point is called the circle of curvature or the osculating circle 2 at the point. The radius of the circle of curvature is called the radius of curvature at the point and is normally denoted. The curvature at the point is.
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Learn how to measure how much a curve curves at each point using the radius of curvature and the curvature. Follow the steps to compute the curvature of a parametric curve using the unit tangent vector and the arc length derivative.
- no it's not a stupid question:), you can prove the formula of the curvature by assuming a circle which touch the curve at some point (x,y) and then...
- Actually for a surface, curvature would depend on the direction of the cross-section you take at the point, and in general, if I recall correctly,...
- No. We do not differentiate the velocity vector. We differentiate the position vector, in order to get the velocity vector, and normalize that. Tha...
- there is a math way to demonstrate that: if you take the derivative of the dot product T·T=1; d/dt(T·T)=d/dt(1); d/dt(T)·T+T·d/dt(T)=0; 2 d/dt(T)·T...
- It's a sarcastic tag to poke fun at wikipedia wanting to site EVERYTHING, including the fact that 2 isn't 1. xkcd likes to poke fun at this.
Nov 16, 2022 · The curvature measures how fast a curve is changing direction at a given point. There are several formulas for determining the curvature for a curve. The formal definition of curvature is, κ = ∥∥ ∥d →T ds ∥∥ ∥ κ = ‖ d T → d s ‖. where →T T → is the unit tangent and s s is the arc length.
Jun 5, 2020 · Curvature. A collective term for a series of quantitative characteristics (in terms of numbers, vectors, tensors) describing the degree to which some object (a curve, a surface, a Riemannian space, etc.) deviates in its properties from certain other objects (a straight line, a plane, a Euclidean space, etc.) which are considered to be flat.
