Curvature is not a law technically, it is an old English law that was introduced in America and became a social practice rather than written law. Curvature was an old way of thinking, about women. Back in the 1780s well off into the 1900s women were thought to take on their husbands identity when they married. The law of Feme and Barron, he was the sole provider of the household. Women were not allowed to own or sell property, or enjoy their own money. All land or property belonging to the wife would transfer to the husband at the time of marriage. She would bare his children, and take care of the household for him. This was a time well before women suffragist movements, or such, so Curvature refers to women who were entirely submissive to their husbands. Women did not have the liberty to contract or apply for any jobs without her husband consent, assuming they will be hired in the first place. So when you speak of Curvature, this is what it means.
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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.
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
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.
The radius of curvature of a circle, or an arc of a circle is the same as the radius of the circle.For a curve (other than a circle) the radius of curvature at a given point is obtained by finding a circular arc that best fits the curve around that point. The radius of that arc is the radius of curvature for the curve at that point.The radius of curvature for a straight line is infinite.
The radius of curvature and the focal length mean the same so the radius of curvature is also 15 cm.