在局部微分几何中，圆柱螺线是很重要的一种曲线。
In local differential geometry, the cylindrical spiral is a very important curve.
经典微分几何研究三维欧氏空间中曲线曲面理论，其最具有特色的研究是主曲率函数满足某些关系的魏因加吞曲面。
In the classical differential geometry which deals with the theory of curves and surfaces of three dimensional Euclidean space, the most distinctive study is the Weingarten surface.
接着，仿微分几何的曲线论，建立了基本公式和唯一存在定理。
Then the basic formulae and the theorem on its unique existence have been established as doing in the curve theory in Differential Geometry.
由于弹性杆的中心线或弹性细丝可以抽象成空间曲线，然后根据空间曲线论和微分几何的知识进行处理。
The centerline of elastic rod or elastic filament can be abstracted as space curves to deal with them by the knowledge of the theory of space curve and differential geometry.
针对一般控制系统，利用微分几何中的曲线理论提出了形状变量、被控形状轨迹曲线和形状合同控制等概念。
Based on the curve theory in differential geometry, we introduce for general control systems the concepts of shape variable, the controlled shape-trace curve and the shape congruence control.
结合微分几何的曲线论和分布荷载作用下索的受力模型，研究了索膜结构中边索、脊索和谷索的受力分析和形状分析。
Combined the curve theory of differential geometry and the cable model applied distributed load, form analysis and tension analysis of boundary cable, ridge cable and valley cable were performed.
关于两段正则曲线在公共节点处的几何连续性的问题可以从微分几何和代数的角度考虑。
The geometric continuity of two regular curves at the connection point can be discussed from differential geometry and Algebra.
几何，三角，微分，积分，圆锥曲线，微分方程，和他们的多维和多元——这些都有重要的应用。
Geometry, trigonometry, differentiation, integration, conic sections, differential equations, and their multidimensional and multivariate versions - these all have important applications.
文章采用微分几何的方法建立了销齿轮齿形的曲线方程，设计了销齿轮传动的动态设计软件。
In this paper, the curvilinear equations of pin gear tooth outline are deduced by the differential geometry method, and the software for the dynamic design of pin gear transmission is designed.
由微分几何基本公式导得圆弧曲线梁中预应力等代荷载的精确公式，预应力钢索在曲梁中竖弯与平弯均较平缓，此时公式可得以简化。
A precise formula for equivalent load of prestressing force in curved girder of arc form is derived from the fundamental formulae of differential geometry.
该算法对离散的曲线进行光顺、拟合和采样，使用空间曲线微分几何性质计算各采样点的曲率和弗朗·内特标架。
After smoothing, fitting and sampling the discrete space curves, the algorithm calculated Frenet frame and curvature for each sampling point.
应用微分几何理论，导出了等距曲线的方程，证明了它是具有任意两条平行切线之间距离都相等的卵形线。
Equation about isometric polygon curve is set up with differential geometry theory. The curve is proved to be convex curve which the distance between any parallel tangent lines is equal.
微分的定义步骤有一个几何解释，最简单的观念就是一条曲线的切线。
The procedure used to define the derivative has a geometric interpretation which leads in a natural way to the idea of a tangent line to a curve.
微分的定义步骤有一个几何解释，最简单的观念就是一条曲线的切线。
The procedure used to define the derivative has a geometric interpretation which leads in a natural way to the idea of a tangent line to a curve.
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