conics

简明释义

英[ˈkɒnɪks]美[ˈkɑːnɪks]

n. 锥线论；圆锥曲线论

英英释义

单词用法

同义词

反义词

例句

1.The parallel-connection and variable-speed operation characters of the centrifugal pump groups are studied by conics fitting of the character curves in the high efficiency area.

通过对离心式水泵高效工作区的性能曲线进行二次拟合，分析了离心式水泵机组并联调速运行特性。

2.In this paper, instead of corresponding image points which are widely used in the literature, corresponding image conics are used to calibrate a rotating camera.

研究探讨了一种基于平面二次曲线的纯旋转摄像机自标定方法。

3.The parallel-connection and variable-speed operation characters of the centrifugal pump groups are studied by conics fitting of the character curves in the high efficiency area.

通过对离心式水泵高效工作区的性能曲线进行二次拟合，分析了离心式水泵机组并联调速运行特性。

4.High School: Algebra, Geometry, Advanced Algebra, Trigonometry, Pre-Calculus (conics and limits)?

高中：代数，几何，高等代数，三角学，？(圆锥和极限)？

5.Apply the theory of pencil of conics to reveal the geometric significance of simultaneous equations of second degree with two unknows.

应用二次曲线束理论揭示解二元二次方程组的几何意义。

6.This paper deals with the graphics of the intersections and common tangents of two conics according to projective geometry .

在射影几何的范畴内，全面地论述了两二次曲线的公有点和公切线的图解问题。

7.And five standard equations of conics are also directly deduced.

并直接推出了二级曲线的五种标准方程。

8.Conics is a difficult section in the Analytic Geometry for senior high school students.

圆锥曲线是高中生解析几何学习中的一个难点。

9.Engineers often use conics to design parabolic reflectors.圆锥曲线

工程师常常使用圆锥曲线来设计抛物面反射器。

10.The trajectory of a projectile can be analyzed using conics.圆锥曲线

可以使用圆锥曲线分析抛射物的轨迹。

11.The equation of a circle is one of the simplest forms of conics.圆锥曲线

圆的方程是最简单的圆锥曲线形式之一。

12.In high school, we learned about the properties of different shapes in conics.圆锥曲线

在高中，我们学习了不同形状在圆锥曲线中的性质。

13.In college, I took a course focused on conics and their applications.圆锥曲线

在大学，我选修了一门专注于圆锥曲线及其应用的课程。

作文

Conics, or 圆锥曲线, are one of the fundamental topics in mathematics that have fascinated scholars for centuries. They arise from the intersection of a plane with a double-napped cone, leading to the formation of different curves based on the angle of intersection. The four primary types of 圆锥曲线 include ellipses, parabolas, hyperbolas, and circles. Each of these shapes has unique properties and applications that make them essential in various fields such as physics, engineering, and computer graphics.The study of 圆锥曲线 begins with understanding their geometric definitions. An ellipse is formed when the intersecting plane cuts through one nappe of the cone at an angle. It resembles an elongated circle and can be defined as the set of points where the sum of the distances from two fixed points (foci) is constant. This property makes ellipses particularly interesting in astronomy, as the orbits of planets around the sun are elliptical in shape.On the other hand, a parabola is created when the plane is parallel to the edge of the cone. It has the distinctive property that any point on the curve is equidistant from a fixed point called the focus and a line known as the directrix. This characteristic is what makes parabolas ideal for applications such as satellite dishes and car headlights, where the reflection of light or signals is critical.Hyperbolas occur when the plane intersects both nappes of the cone. They consist of two separate curves known as branches. The defining feature of a hyperbola is that the difference in distances from any point on the curve to the two foci is constant. Hyperbolas are frequently used in navigation systems and in describing certain types of motion in physics.Circles, the simplest form of 圆锥曲线, are formed when the intersecting plane is perpendicular to the axis of the cone. A circle can be defined as the set of all points that are equidistant from a central point. Circles have numerous applications in everyday life, from wheels and gears to the design of circular tracks in sports.The mathematical equations representing these 圆锥曲线 are also significant. For example, the standard equation of a circle is (x - h)² + (y - k)² = r², where (h, k) is the center, and r is the radius. The general form of an ellipse is (x - h)²/a² + (y - k)²/b² = 1, where (h, k) is the center, and a and b are the semi-major and semi-minor axes, respectively. Understanding these equations allows mathematicians and scientists to model real-world phenomena accurately.In conclusion, 圆锥曲线 play a crucial role in mathematics and its applications across various disciplines. Their unique properties and the ability to describe complex shapes and motions make them indispensable tools for engineers, architects, and scientists. As we continue to explore the world of mathematics, the study of 圆锥曲线 remains a vital area of research that connects theoretical concepts with practical applications.

圆锥曲线是数学中一个基本的主题，几个世纪以来吸引着学者们的关注。它们源于平面与双锥体的交集，根据交角的不同形成不同的曲线。主要的四种圆锥曲线包括椭圆、抛物线、双曲线和圆。这些形状各自具有独特的性质和应用，使它们在物理学、工程学和计算机图形学等多个领域中至关重要。对圆锥曲线的研究始于理解它们的几何定义。当交叉平面以一定角度切割锥体的一个部分时，形成了椭圆。它类似于一个拉长的圆，可以定义为从两个固定点（焦点）到某一点的距离之和是恒定的。这一特性使得椭圆在天文学中尤为有趣，因为行星围绕太阳的轨道是椭圆形的。另一方面，当平面与锥体的边缘平行时，会形成抛物线。抛物线的独特特性是曲线上的任何一点到固定点（焦点）和一条称为准线的直线的距离相等。这一特性使得抛物线在卫星天线和汽车前灯等应用中非常理想，反射光线或信号至关重要。双曲线发生在平面同时与锥体的两个部分相交时。它由两个独立的曲线组成，称为分支。双曲线的定义特征是，从曲线上的任何一点到两个焦点的距离之差是恒定的。双曲线通常用于导航系统以及描述物理学中某些类型的运动。圆，作为最简单的圆锥曲线，是当交叉平面垂直于锥体的轴时形成的。圆可以定义为与中心点等距的所有点的集合。圆在日常生活中有着众多应用，从车轮和齿轮到体育场的圆形跑道。表示这些圆锥曲线的数学方程同样重要。例如，圆的标准方程是(x - h)² + (y - k)² = r²，其中(h, k)是圆心，r是半径。椭圆的一般形式是(x - h)²/a² + (y - k)²/b² = 1，其中(h, k)是圆心，a和b分别是半长轴和半短轴。理解这些方程使数学家和科学家能够准确地模拟现实世界现象。总之，圆锥曲线在数学及其在多个学科中的应用中扮演着至关重要的角色。它们独特的性质和描述复杂形状与运动的能力使它们成为工程师、建筑师和科学家的不可或缺的工具。随着我们继续探索数学的世界，圆锥曲线的研究仍然是一个重要的研究领域，将理论概念与实际应用联系起来。