hyperbolic paraboloid

简明释义

双曲抛物面

英英释义

例句

1.The roof of the building is designed in the shape of a hyperbolic paraboloid (双曲抛物面) to allow for better drainage.

这座建筑的屋顶设计成hyperbolic paraboloid（双曲抛物面）的形状，以便更好地排水。

2.The seating area was designed using a hyperbolic paraboloid (双曲抛物面) to maximize space efficiency.

座位区采用hyperbolic paraboloid（双曲抛物面）设计，以最大限度地提高空间效率。

3.Engineers often use the hyperbolic paraboloid (双曲抛物面) shape in modern architecture for its strength and aesthetic appeal.

工程师们经常在现代建筑中使用hyperbolic paraboloid（双曲抛物面）形状，因为它的强度和美学吸引力。

4.In mathematics, a hyperbolic paraboloid (双曲抛物面) is a doubly ruled surface that can be generated by moving a line through space.

在数学中，hyperbolic paraboloid（双曲抛物面）是一个双重规则曲面，可以通过在空间中移动一条直线生成。

5.The designer chose a hyperbolic paraboloid (双曲抛物面) structure for the pavilion to create an eye-catching silhouette.

设计师选择了一个hyperbolic paraboloid（双曲抛物面）结构来创建一个引人注目的轮廓。

作文

The concept of a hyperbolic paraboloid is fascinating and plays a significant role in both mathematics and architecture. A hyperbolic paraboloid is a doubly curved surface that can be described mathematically by a specific equation. It is formed by the intersection of two parabolas, one oriented along the x-axis and the other along the y-axis. This unique shape can be visualized as a saddle, which curves upwards in one direction and downwards in the perpendicular direction. The mathematical representation of a hyperbolic paraboloid is given by the equation z = (x^2/a^2) - (y^2/b^2), where 'a' and 'b' are constants that determine the curvature of the surface.In architecture, the hyperbolic paraboloid has been employed to create stunning structures that are not only aesthetically pleasing but also structurally efficient. One of the most famous examples is the roof of the Sydney Opera House, which features a series of shell-like forms that resemble the shape of a hyperbolic paraboloid. This design allows for large spans without the need for extensive support, making it an ideal choice for modern buildings.The properties of a hyperbolic paraboloid make it an interesting subject of study in various fields. For instance, in engineering, the strength and stability of this shape allow it to withstand significant loads, which is why it is often used in the design of bridges and roofs. The ability to distribute weight evenly across its surface means that materials can be used more efficiently, reducing costs while maintaining safety.Moreover, the hyperbolic paraboloid has applications in the field of optics. Its unique curvature allows for the manipulation of light, making it useful in the design of certain types of lenses and reflectors. By understanding how light interacts with this shape, scientists and engineers can create devices that enhance vision or focus light in specific ways.In addition to its practical applications, the hyperbolic paraboloid is also a subject of artistic inspiration. Many artists and designers have drawn upon its unique form to create sculptures and installations that challenge our perceptions of space and structure. The interplay of light and shadow on a hyperbolic paraboloid surface can evoke a sense of movement and fluidity, inviting viewers to engage with the artwork on a deeper level.In conclusion, the hyperbolic paraboloid is more than just a mathematical concept; it is a shape that bridges the gap between science, art, and architecture. Its unique properties allow it to be utilized in various fields, from structural engineering to artistic expression. Understanding the hyperbolic paraboloid opens up a world of possibilities, encouraging innovative designs and solutions that push the boundaries of what is possible in both theory and practice.

“双曲抛物面”这一概念令人着迷，并在数学和建筑领域发挥着重要作用。“双曲抛物面”是一个双曲曲面，可以用特定的方程来描述。它是由两个抛物线的交集形成的，一个沿x轴方向，另一个沿y轴方向。这种独特的形状可以想象成一个鞍形，在一个方向上向上弯曲，在垂直方向上向下弯曲。“双曲抛物面”的数学表示为z = (x^2/a^2) - (y^2/b^2)，其中'a'和'b'是决定曲面曲率的常数。在建筑学中，“双曲抛物面”被用于创造令人惊叹的结构，这些结构不仅美观，而且在结构上高效。其中一个最著名的例子是悉尼歌剧院的屋顶，其特点是类似于“双曲抛物面”的一系列贝壳状构造。这种设计使得建筑能够在没有大量支撑的情况下实现大跨度，是现代建筑的理想选择。“双曲抛物面”的特性使其成为各个领域研究的有趣课题。例如，在工程学中，这种形状的强度和稳定性使其能够承受重大负荷，这就是为什么它常常用于桥梁和屋顶设计中的原因。能够均匀分配重量的能力意味着可以更有效地使用材料，从而降低成本，同时保持安全性。此外，“双曲抛物面”还在光学领域中有应用。其独特的曲率允许对光进行操控，使其在某些类型的透镜和反射器的设计中变得有用。通过理解光如何与这种形状相互作用，科学家和工程师可以创建增强视觉或以特定方式聚焦光的设备。除了实际应用之外，“双曲抛物面”也是艺术灵感的主题。许多艺术家和设计师汲取其独特的形状，创作出挑战我们对空间和结构感知的雕塑和装置。在“双曲抛物面”表面上光与影的交错可以唤起一种运动和流动感，邀请观众更深入地参与艺术作品。总之，“双曲抛物面”不仅仅是一个数学概念；它是一个连接科学、艺术和建筑之间的形状。其独特的属性使其在各个领域得以应用，从结构工程到艺术表现。理解“双曲抛物面”开启了一个可能性的世界，鼓励创新设计和解决方案，推动理论和实践的边界。