模块八 5.4 Length of a plane curve(下) 微积分是高等数学中研究函数的微分、积分以及有关概念和应用的数学分支,它是数学的一个基础学科,是理工科院校一门重要的基础理论课。它推动了其他学科的发展,推动了人类文明与科学技术的发展,它的作用是举足轻重的。微积分(I
A method for measuring the length of a curve in a plane is proposed based on the mean of the projections of the curve in equi-spaced directions. A further simplification can be made by not measuring the projections but instead counting the number of intersections of the curve with a randomly...
Contracting convex immersed closed plane curves with slow speed of curvature The authors study the contraction of a convex immersed plane curve with speed , where is a constant, and show that, if the blow-up rate of the curvature is... YC Lin,CC Poon,DH Tsai - 《Transactions of the Amer...
Since the pedal curve of a smooth simple plane closed curve can be fairly complicated and have self-intersections and overlapping parts, we introduce and essentially use a notion of its interior based on the winding numbers and orientations of certain closed parts of the pedal curve forming its...
1. the longest extent of anything as measured from end to end: the length of a river. 2. the measure of the greatest dimension of a plane or solid figure. 3. extent from beginning to end of a series, enumeration, account, book, etc.: a report 300 pages in length. 4. extent in...
The concepts we used to find the arc length of a curve can be extended to find the surface area of a surface of revolution. Surface area is the total area of the outer layer of an object. For objects such as cubes or bricks, the surface area of the object is the sum of th...
A large part of this paper is devoted to translating the concept of length of a curve to generalized metric spaces. The Finsler manifold (S,F) and Riemannian manifolds are considered. In the appendix a remarkable example for the plane 2 is given. Reviewer's remarks: The Riemannian space (...
We prove that the length difference between a closed periodic curve and its parallel curve at a sufficiently small distance is proportional to the rotation index. As an application, the rotation index of a curve could be estimated by means of Cauchy-Crofton formula. 关键词: Mathematics - Differe...
Length of a curve: If {eq}y=f(x) {/eq} has a continuous derivative {eq}f^\prime {/eq} in {eq}[a,b] {/eq}, the arc length of {eq}f {/eq} between {eq}a {/eq} and {eq}b {/eq} is given by {eq}\displaystyle s=\int_a^b\sqrt{1+[f^\pr...
(a) {eq}x = \cos t + t \sin t, y = \sin t - t \cos t, 0 \leq t \leq \pi {/eq} (b) {eq}r = 1 - \cos \theta, 0 \leq \theta \leq \pi {/eq} Length of Polar and Parametric Curve {eq}{/eq...