conic section

简明释义

锥形截线

英英释义

例句

1.The intersection of a plane and a cone results in a conic section (圆锥曲线) such as an ellipse, parabola, or hyperbola.

平面与锥体的交集形成了conic section（圆锥曲线），例如椭圆、抛物线或双曲线。

2.Astronomers use the properties of conic sections (圆锥曲线) to describe the orbits of planets and comets.

天文学家利用conic sections（圆锥曲线）的性质来描述行星和彗星的轨道。

3.In calculus, we often analyze the curvature of conic sections (圆锥曲线) to understand their geometric properties.

在微积分中，我们常常分析conic sections（圆锥曲线）的曲率，以理解它们的几何特性。

4.The equation of a parabola is one of the simplest forms of a conic section (圆锥曲线), often represented as y = ax² + bx + c.

抛物线的方程是最简单的conic section（圆锥曲线）形式之一，通常表示为y = ax² + bx + c。

5.In geometry, a circle is a special type of conic section (圆锥曲线) that can be defined as the set of all points equidistant from a center point.

在几何学中，圆是一个特殊类型的conic section（圆锥曲线），可以定义为与中心点等距的所有点的集合。

作文

The study of geometry has fascinated mathematicians and scientists for centuries, leading to the discovery of various shapes and forms that govern our understanding of space. Among these shapes, the term conic section refers to the curves obtained by intersecting a right circular cone with a plane. These curves include circles, ellipses, parabolas, and hyperbolas, each possessing unique properties and applications in both theoretical and practical contexts. Understanding conic sections is essential not only in mathematics but also in physics, engineering, and even art.To begin with, let's explore the different types of conic sections. A circle is formed when the intersecting plane is perpendicular to the axis of the cone. The result is a perfectly symmetrical shape where every point is equidistant from the center. Circles are often seen in nature and are fundamental in various applications, such as wheels, gears, and lenses.Next, we have ellipses, which occur when the plane intersects the cone at an angle that is less steep than that of the cone's side. An ellipse can be thought of as a stretched circle, having two focal points. This shape is significant in astronomy; for instance, the orbits of planets around the sun are elliptical, a discovery made by Johannes Kepler.Parabolas arise when the intersecting plane is parallel to the slant height of the cone. This shape has remarkable properties, particularly in physics. For example, the trajectory of projectiles under the influence of gravity follows a parabolic path. Additionally, parabolas are used in satellite dishes and reflectors because they can focus parallel rays of light or sound to a single point.Lastly, hyperbolas are formed when the plane cuts through both halves of the cone. This yields two separate curves that mirror each other. Hyperbolas appear in various real-world scenarios, such as in navigation systems and in the design of certain types of cooling towers.The importance of conic sections extends beyond their mathematical definitions. In physics, they help describe the paths of celestial bodies and the behavior of objects in motion. Engineers utilize these curves in designing various structures, ensuring stability and efficiency. Moreover, artists incorporate conic sections into their works, using their aesthetic properties to create visually appealing compositions.In conclusion, the concept of conic sections is a vital aspect of geometry that bridges the gap between pure mathematics and its applications in the real world. Whether it is the circular motion of a planet, the trajectory of a thrown ball, or the design of a beautiful piece of art, conic sections play an integral role. By understanding these curves, we gain a deeper appreciation for the mathematical principles that underlie the universe around us, showcasing the interconnectedness of mathematics, science, and art. Therefore, the study of conic sections is not merely an academic exercise; it is a gateway to understanding the fundamental laws that govern our world.

几何学的研究吸引了数学家和科学家几个世纪，导致了各种形状和形式的发现，这些形状和形式支配着我们对空间的理解。在这些形状中，术语圆锥曲线指的是通过与一个直圆锥体的平面相交而获得的曲线。这些曲线包括圆、椭圆、抛物线和双曲线，每种曲线都具有独特的性质和在理论与实践中的应用。理解圆锥曲线不仅在数学中是必不可少的，在物理学、工程学甚至艺术中也同样重要。首先，让我们探索不同类型的圆锥曲线。当相交的平面垂直于圆锥的轴时，就形成了一个圆。结果是一个完美对称的形状，其中每个点都与中心等距。圆在自然界中经常出现，并且在各种应用中是基础，例如车轮、齿轮和透镜。接下来，我们有椭圆，当平面以比圆锥侧面更平缓的角度与圆锥相交时，就会形成椭圆。可以将椭圆视为一个拉伸的圆，具有两个焦点。这种形状在天文学中具有重要意义；例如，行星围绕太阳的轨道是椭圆的，这是约翰内斯·开普勒发现的。抛物线是在与圆锥的斜高平行的平面相交时产生的。这种形状具有显著的特性，特别是在物理学中。例如，受重力影响的抛射物的轨迹遵循抛物线。此外，抛物线还用于卫星天线和反射器，因为它们可以将平行的光或声音射线聚焦到一个点上。最后，双曲线是当平面切过圆锥的两个半部时形成的。这将产生两个相互镜像的独立曲线。双曲线出现在各种现实场景中，例如导航系统和某些类型冷却塔的设计。圆锥曲线的重要性超出了它们的数学定义。在物理学中，它们帮助描述天体的路径和物体运动的行为。工程师利用这些曲线来设计各种结构，确保稳定性和效率。此外，艺术家将圆锥曲线融入他们的作品中，利用其美学特性创造出视觉上令人愉悦的构图。总之，圆锥曲线的概念是几何学的一个重要方面，它弥合了纯数学与现实世界应用之间的鸿沟。无论是行星的圆形运动、投掷物体的轨迹，还是一件美丽艺术品的设计，圆锥曲线都发挥着不可或缺的作用。通过理解这些曲线，我们对支配我们周围宇宙的数学原理有了更深的欣赏，展示了数学、科学和艺术之间的相互联系。因此，学习圆锥曲线不仅仅是学术上的练习；它是理解支配我们世界的基本法则的一个入口。