elliptic paraboloid

简明释义

椭圆抛物面

英英释义

例句

1.The graph of the function forms an elliptic paraboloid 椭圆抛物面, which can be visualized in three dimensions.

该函数的图形形成了一个elliptic paraboloid 椭圆抛物面，可以在三维空间中可视化。

2.The mathematical properties of an elliptic paraboloid 椭圆抛物面 make it useful in various optimization problems.

一个elliptic paraboloid 椭圆抛物面的数学性质使其在各种优化问题中非常有用。

3.In architecture, the roof of the building was designed as an elliptic paraboloid 椭圆抛物面 to enhance aesthetic appeal and structural integrity.

在建筑学中，这座建筑的屋顶设计成了一个elliptic paraboloid 椭圆抛物面，以增强美观性和结构完整性。

4.Engineers often use an elliptic paraboloid 椭圆抛物面 shape for designing reflective surfaces in optical devices.

工程师们常常使用elliptic paraboloid 椭圆抛物面形状来设计光学设备中的反射表面。

5.The shape of the satellite dish is an elliptic paraboloid 椭圆抛物面, which helps focus signals to a single point.

卫星天线的形状是一个elliptic paraboloid 椭圆抛物面，这有助于将信号集中到一个点上。

作文

In the realm of mathematics and geometry, various surfaces can be defined based on their unique properties. One such surface that has intrigued mathematicians and engineers alike is the elliptic paraboloid. The elliptic paraboloid is a three-dimensional surface that can be described by a quadratic equation in three variables. This surface is characterized by its distinctive shape, which resembles an upward or downward facing bowl. The general equation of an elliptic paraboloid can be expressed as z = (x^2/a^2) + (y^2/b^2), where 'a' and 'b' are constants that determine the curvature of the surface in the x and y directions.Understanding the properties of the elliptic paraboloid is essential in various fields such as architecture, physics, and computer graphics. For instance, in architecture, the design of certain structures, like roofs or domes, often utilizes the principles of the elliptic paraboloid to create aesthetically pleasing and structurally sound forms. The curvature of the elliptic paraboloid allows for even distribution of weight, making it an ideal choice for large-span constructions.In physics, the elliptic paraboloid plays a role in the study of potential energy surfaces and the behavior of particles under various forces. The shape of the elliptic paraboloid can represent potential energy wells, where the lowest point corresponds to the most stable state of a system. This concept is crucial when analyzing the stability of different physical systems and understanding how they respond to external influences.Furthermore, in computer graphics, the elliptic paraboloid is often used in modeling and rendering surfaces. Its mathematical properties allow for smooth transitions and realistic representations of objects. By utilizing the equations governing the elliptic paraboloid, graphic designers can create intricate designs and animations that mimic real-world phenomena. The ability to manipulate the parameters 'a' and 'b' provides artists with the flexibility to explore various forms and shapes, enhancing the visual appeal of their creations.In conclusion, the elliptic paraboloid is not just a mathematical abstraction; it has practical applications across multiple disciplines. From the construction of innovative architectural designs to the analysis of physical systems and the creation of stunning visual effects in digital media, the elliptic paraboloid serves as a fundamental concept that bridges theory and practice. By delving deeper into the properties and applications of the elliptic paraboloid, one can appreciate the beauty and complexity of this geometric shape and its significance in our understanding of the world around us.

在数学和几何的领域中，各种表面可以根据其独特的属性进行定义。其中一个引起数学家和工程师兴趣的表面是椭圆抛物面。椭圆抛物面是一种三维表面，可以用三个变量的二次方程来描述。该表面的特征是其独特的形状，类似于向上或向下的碗。椭圆抛物面的一般方程可以表示为z = (x²/a²) + (y²/b²)，其中'a'和'b'是决定表面在x和y方向上曲率的常数。理解椭圆抛物面的性质对于建筑、物理和计算机图形等多个领域至关重要。例如，在建筑学中，某些结构（如屋顶或穹顶）的设计通常利用椭圆抛物面的原理，以创造美观且结构稳固的形式。椭圆抛物面的曲率允许重量均匀分布，使其成为大跨度建筑的理想选择。在物理学中，椭圆抛物面在研究势能表面和粒子在各种力作用下的行为时发挥着作用。椭圆抛物面的形状可以表示势能井，其中最低点对应于系统的最稳定状态。这个概念在分析不同物理系统的稳定性以及理解它们如何响应外部影响时至关重要。此外，在计算机图形学中，椭圆抛物面经常用于建模和渲染表面。它的数学性质允许平滑过渡和现实的对象表现。通过利用控制椭圆抛物面的方程，图形设计师可以创建复杂的设计和动画，模拟现实世界现象。操控参数'a'和'b'的能力为艺术家提供了探索各种形式和形状的灵活性，增强了其创作的视觉吸引力。总之，椭圆抛物面不仅仅是一个数学抽象；它在多个学科中具有实际应用。从创新建筑设计的构建到物理系统的分析，再到数字媒体中令人惊叹的视觉效果的创建，椭圆抛物面作为一个基本概念，连接了理论与实践。通过深入研究椭圆抛物面的性质和应用，人们可以欣赏到这一几何形状的美丽与复杂，以及它在我们理解周围世界中的重要性。