How to know when a curve has maximum curvature and why? The curvature is what makes the difference between a straight line and a curve, i e a measure of "non-straightness" And it is intuitive that a curve of constant curvature is a circle
differential geometry - Understanding the formula for curvature . . . For this reason, curvature requires differentiating T (t) with respect to arc length, S (t), instead of the parameter t" I feel this is not a sufficient explanation and more explanation is needed to clarify the formula
calculus - Why is the radius of curvature = 1 (curvature . . . @RockyRock considering curvature was defined like that (definition in my textbook), a problem arises because radius of curvature is the radius of an imaginary circle of which the arc of the curve is a part of, and it seems that radius of curvature is a more basic property
Purpose of sectional curvature - Mathematics Stack Exchange The Riemann curvature tensor doesn't contain any more information than all sectional curvatures The only intrinsic curvature we really define is Gaussian curvature of a surface at a point
Intrinsic and Extrinsic curvature - Mathematics Stack Exchange I want to understand the basic conceptual idea about intrinsic and extrinsic curvature If we consider a plane sheet of paper (whose intrinsic curvature is zero) rolled into a cylindrical shape, th
Calculating the curvature of a surface - Mathematics Stack Exchange The principal curvatures are the basis for all types of curvature on a two-dimensional surface: Gauss curvature is the product of principal curvatures and mean curvature is the average of principal curvatures