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What is mean by centre of curvature?
This means the vented of a circle. It is the radius of the circle that is perpendicular to a line tangent to any point on the concave side of a smooth curve.
What is the difference between the measure of an arc and arc length?
They are normally the same. However, the measure of the arc could refer to the angle subtended at the centre of the radius of curvature.
What does curvature ratio mean in tubing?
Radius of curvature divided by tube diameter. To get the radius of curvature, imaging the bend in the tube is a segment of a circle, the radius of curvature is the radius of that circle.
What is curvature in differential geometry?
There are two most 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 initial starting point and direction. There is also a curvature of surfaces in three-space. The main curvatures that emerged from this scrutiny are the mean curvature, Gaussian curvature, and the shape operator. I advice to read the following article: http://mathworld.wolfram.com/Curvature.html Moreover, I advise add-on for Mathematica CAS, which do calculations in differential geometry. http://digi-area.com/Mathematica/atlas There is a tutorial about the invariants including curvature which calculates for curves and surfaces. http://digi-area.com/Mathematica/atlas/ref/Invariants.php
How can find the radius of curvature?
There is a specific formula for finding the radius of a curvature, used often when one is measuring a mirror. The formula is: Radius of curvature = R =2*focal length.
