directrix

简明释义

英[dɪˈrektrɪks]美[dɪˈrektrɪks;daɪˈrektrɪks]

n. [数] 准线

复 数 d i r e c t r i x e s 或 d i r e c t r i c e s

英英释义

单词用法

同义词

反义词

例句

1.The directrix line of a conic.

二次曲线的准线。

2.The pity is that the first auxiliary directrix after modification is generally expressed in an algebraic form, because of the complexity of the vectorial expression.

遗憾的是，由于其矩阵表达式有些复杂，一般都将修改后的第一辅助准线表示为代数形式。

3.The pity is that the first auxiliary directrix after modification is generally expressed in an algebraic form, because of the complexity of the vectorial expression.

遗憾的是，由于其矩阵表达式有些复杂，一般都将修改后的第一辅助准线表示为代数形式。

4.When studying ellipses, the directrix helps in defining the eccentricity of the curve.

在研究椭圆时，导线有助于定义曲线的偏心率。

5.To construct a parabola, you can start by drawing the directrix and placing the focus above it.

要构建一个抛物线，您可以先画出导线并将焦点放在其上方。

6.The directrix plays a crucial role in determining the shape of the parabola.

导线在确定抛物线的形状中起着至关重要的作用。

7.In physics, the path of a projectile can be analyzed using the concept of directrix for better understanding.

在物理学中，可以使用导线的概念来分析抛射物体的路径，以便更好地理解。

8.In conic sections, the parabola is defined as the set of points equidistant from a point called the focus and a line known as the directrix.

在圆锥曲线中，抛物线被定义为与一个称为焦点的点和一条称为导线的线等距的点的集合。

作文

In the realm of mathematics, particularly in geometry, the term directrix refers to a fixed line used in the definition of a curve or surface. It plays a crucial role in conic sections, such as parabolas, ellipses, and hyperbolas. Understanding the concept of directrix can illuminate the relationship between algebra and geometry, showcasing how these two fields interconnect. For instance, when we consider a parabola, it is defined as the set of all points that are equidistant from a point known as the focus and a line called the directrix. This unique property of the parabola highlights the significance of the directrix in determining the shape and orientation of the curve. The distance from any point on the parabola to the focus is equal to the distance from that point to the directrix. This relationship not only provides a geometric understanding but also leads to various algebraic equations that describe parabolic behavior.Moreover, the concept of directrix extends beyond just parabolas. In the case of ellipses and hyperbolas, the directrix helps define their eccentricity, which is a measure of how much these curves deviate from being circular. For ellipses, there are two directrix lines, and the ratio of the distance from a point on the ellipse to one focus and the distance to the corresponding directrix remains constant. This constant ratio is what distinguishes ellipses from other conic sections.The directrix can also be observed in real-world applications, such as in satellite dishes and parabolic reflectors. These structures utilize the properties of parabolas, where signals or light rays parallel to the axis of symmetry converge at the focus after reflecting off the surface. The directrix serves as a reference line that helps engineers design these systems effectively, ensuring optimal performance by understanding the geometric principles at play.Furthermore, the study of directrix is not limited to pure mathematics; it has implications in physics, engineering, and computer graphics. In physics, for example, the trajectories of projectiles can be analyzed using parabolic equations, where the directrix aids in predicting the path of motion under the influence of gravity. Similarly, in computer graphics, algorithms often employ the principles of conic sections to render curves and surfaces accurately, making the understanding of directrix essential for graphic designers and animators.In conclusion, the term directrix encapsulates a fundamental concept in geometry that bridges the gap between abstract mathematical theories and practical applications. By grasping the significance of the directrix, one can appreciate the elegance of conic sections and their relevance in various fields. Whether in mathematical equations, engineering designs, or physical phenomena, the directrix remains a vital element that enhances our understanding of the world around us. As students and enthusiasts of mathematics delve deeper into this subject, recognizing the role of the directrix will undoubtedly enrich their comprehension and appreciation of both geometry and its applications in everyday life.

在数学领域，尤其是几何学中，术语directrix指的是用于定义曲线或表面的固定线。它在圆锥曲线中起着至关重要的作用，如抛物线、椭圆和双曲线。理解directrix的概念可以阐明代数与几何之间的关系，展示这两个领域如何相互交织。例如，当我们考虑抛物线时，它被定义为所有点的集合，这些点与称为焦点的点和称为directrix的线等距。抛物线这一独特性质突显了directrix在确定曲线形状和方向中的重要性。从抛物线上的任何一点到焦点的距离等于该点到directrix的距离。这种关系不仅提供了几何理解，还导致描述抛物线行为的各种代数方程。此外，directrix的概念不仅限于抛物线。在椭圆和双曲线的情况下，directrix帮助定义它们的离心率，这是一个衡量这些曲线偏离圆形程度的指标。对于椭圆，有两条directrix线，而椭圆上某一点到一个焦点的距离与对应的directrix的距离之比保持不变。这个常数比率使得椭圆与其他圆锥曲线区分开来。在现实世界的应用中也可以观察到directrix的存在，例如在卫星天线和抛物面反射器中。这些结构利用抛物线的性质，其中平行于对称轴的信号或光线在反射后汇聚到焦点。directrix作为参考线，帮助工程师有效地设计这些系统，通过理解所涉及的几何原理确保最佳性能。此外，directrix的研究不限于纯数学；它在物理学、工程学和计算机图形学中都有影响。例如，在物理学中，抛体的轨迹可以通过抛物线方程进行分析，其中directrix有助于预测在重力影响下的运动路径。同样，在计算机图形学中，算法通常利用圆锥曲线的原理准确渲染曲线和表面，因此理解directrix对图形设计师和动画师至关重要。总之，术语directrix概括了几何学中的一个基本概念，架起了抽象数学理论与实际应用之间的桥梁。通过掌握directrix的重要性，人们可以欣赏圆锥曲线的优雅及其在各个领域的相关性。无论是在数学方程、工程设计还是物理现象中，directrix始终是一个重要元素，增强了我们对周围世界的理解。随着学生和数学爱好者深入研究这一主题，认识到directrix的作用无疑会丰富他们的理解和对几何及其在日常生活中的应用的欣赏。