曲线

For the application of Mathematica in the differential geometry,this paper introduces how to processe the curve curvature and the torsion questions,the graphic expression of the curvature and the torsions,and draw curves by the curvature and the torsions. Curvature ; torsion ; solution curve ; osculating plane ; natural parameter ; natural equation

利用Mathematica，只要输入有关系统命令就可以得到期望的结果。1曲率和挠率及其图形意义假设R3上的曲线一般参数表示为r=r它的曲率和挠率计算公式是：κ=‖r′×r&‖‖r′‖3τ=‖r′×r‖我们知道，空间曲线r=r在一点(s=s0)邻近的近似方程为ξ=sη=120κs2ζ=160κ0τs3通过近似方程可以确定曲线在其基本三棱形的三个平面(即密切平面，法平面，从切平面)上的投

Curve and the x, y-axis intersection (a, 0),(0, b) where a curve is called the intercept in the x-axis; b is called the curve y axis intercept .

曲线与x、y轴的交点（a，0），（0，b）其中a叫曲线在x轴上的截距；b叫曲线在y轴上的截距。

Curve and the x, y-axis intersection (a, 0),(0, b) where a call in the x-axis intercept curve; b is called the curve y axis intercept .

曲线与x、y轴的交点（a，0），（0，b）其中a叫曲线在x轴上的截距；b叫曲线在y轴上的截距。

A, b, and c are curve-fitting constants in the curve equation y="1"–a×(1–x)c and the complementary-curve equation y="a"×(1–x)c, where a is a coefficient, b is the lower limit for x and is less than one, and c is a power constant.

对绘曲线装置，y为规一化输出位变量，x为非零平均值（小于1）到1的规一化输入模拟电压。a、b和c为用曲线方程y=1–a×(1–x)c拟合的常数，补充曲线方程y=a×(1–x)c，在此，a为系数，b为x的较低限制，且小于1，c为功率常数。

A point at which a curve crosses itself and at which the two tangents to the curve coincide.

尖点，会切点曲线上的一个点，曲线在该点与其本身相交，曲线的两条切线在该点重合

Duplicate it then rescale it to about 0.87 and move it to around 2.254 of z axis and then duplicate again, rescale it to about 0.754 and move it to around 2.178 of z axis.

复制那条曲线，并将新复制出来的曲线在 xyz 轴上缩小到 0.87，在 z 轴方向上移动到 2.254 ；再次复制一条新的曲线，并将其在 xyz 轴上缩小到 0.754，在 z 轴方向上移动到 2.178 。

Recorded piston displacement versus incylinder pressure traces and other parameters by the developed system proved its accuracy and rebiability.

根据试验获得的活塞位移曲线、气缸压力曲线及压力位移曲线，证明本系统采集到的数据具有良好的可靠性。

This software requires less input parameters, use-friendly, easy to operate, and can output the curve of rock mechanics parameters, stress curve, collapsing pressure and rupture pressure curve, and can guided the Air-drilling Well body structure design and the field practicals.

软件要求输入的参数少，界面友好，操作方便，能输出岩石力学参数曲线、地应力曲线、坍塌压力与破裂压力曲线，对空气钻井井身结构设计以及施工具有很强的现实指导意义。

We can draw three parabolas of the economy growth rate, GDP and the government revenue.

由此，笔者以税率为自变量，模拟出经济增长率曲线、GDP曲线、税收收入曲线。

These means have following defects: I. parameter controls is too simple that will Fit the curve too roughly and can't give the configuration and characteristic of surge curve very good;II. The performance curve will change a lot when working condition changes,especially when woring temperature changes;III. Choking area will bring huge waste and is an area that the system oughts to avoid,but we haven't corresponding methods to watch and control it in the domestic till now.

这些措施具有以下缺点：1、控制参数过于简单，对曲线的拟合过于粗糙，不能很好的反映喘振曲线的形态和特点；2、当工作条件变化时，特别是工作温度有所变化时，性能曲线会发生很大变化；3、阻塞区会造成巨大的浪费，也是系统该避免的区域，可是目前国内还没有相应措施来监控它。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。