parabolic cylinder

简明释义

抛物柱面

英英释义

例句

1.A parabolic cylinder is often used in satellite dishes to focus signals efficiently.

在卫星天线中，抛物面圆柱常用于有效聚焦信号。

2.The design of the new stadium features a roof shaped like a parabolic cylinder, which allows for optimal acoustics.

新体育场的设计采用了一个形状像抛物面圆柱的屋顶，可以实现最佳音响效果。

3.The water fountain was designed as a parabolic cylinder to enhance water flow and aesthetics.

这个喷泉的设计是一个抛物面圆柱，以增强水流和美观性。

4.In physics class, we learned how the trajectory of a projectile can be modeled using a parabolic cylinder in three dimensions.

在物理课上，我们学习了如何用三维中的抛物面圆柱来模拟投射物的轨迹。

5.The architect proposed using a parabolic cylinder for the entrance arch to create a visually striking effect.

建筑师建议使用抛物面圆柱作为入口拱门，以创造视觉冲击效果。

作文

The concept of a parabolic cylinder is fascinating and plays a significant role in various fields such as mathematics, physics, and engineering. A parabolic cylinder can be defined as a three-dimensional surface created by translating a parabola along a straight line. This geometric shape has unique properties that make it useful in many applications, especially in the design of optical devices and architectural structures.To understand the importance of a parabolic cylinder, we first need to explore what a parabola is. A parabola is a curve formed by the intersection of a right circular cone with a plane parallel to its side. It has a distinct U-shape and is characterized by its vertex, focus, and directrix. When we take this two-dimensional shape and extend it along a third dimension, we create a parabolic cylinder. This extension gives rise to a surface that retains the parabolic cross-section at every point along its length.One of the key features of a parabolic cylinder is its ability to focus light. This property is particularly valuable in the design of parabolic reflectors, which are commonly used in satellite dishes and solar concentrators. The reflective surface of a parabolic cylinder directs incoming parallel rays of light toward a single focal point, maximizing efficiency in capturing energy or signals. For instance, in solar energy applications, a parabolic cylinder can concentrate sunlight onto a receiver, increasing the temperature and efficiency of the energy collection process.In architecture, the parabolic cylinder can be found in various structures where aesthetics and functionality converge. The smooth, continuous curves of a parabolic cylinder not only provide structural integrity but also create visually appealing designs. Architects often use this shape in roofs, bridges, and other elements to enhance both the beauty and performance of their designs. The strength of the parabolic cylinder allows it to withstand significant loads while maintaining a lightweight form, making it an ideal choice for modern constructions.Moreover, the mathematical representation of a parabolic cylinder can be described using equations. In a Cartesian coordinate system, a parabolic cylinder can be represented by the equation z = ax², where 'a' is a constant that determines the width and direction of the parabola. This equation highlights the relationship between the x-axis and the height (z-axis) of the cylinder, demonstrating how changes in 'x' influence the overall shape of the structure.In conclusion, the parabolic cylinder is more than just a mathematical concept; it is a practical shape with numerous applications across various disciplines. Its unique properties, such as light focusing and structural strength, make it a valuable element in both theoretical studies and real-world applications. Whether in the realm of physics, engineering, or architecture, understanding the parabolic cylinder opens up new avenues for innovation and design. As we continue to explore and harness these geometric shapes, we can expect to see even more creative uses that push the boundaries of our understanding and capabilities.

抛物面柱体的概念令人着迷，并在数学、物理和工程等多个领域发挥着重要作用。抛物面柱体可以定义为通过沿直线平移抛物线而形成的三维曲面。这种几何形状具有独特的性质，使其在许多应用中非常有用，尤其是在光学设备和建筑结构的设计中。要理解抛物面柱体的重要性，我们首先需要探讨什么是抛物线。抛物线是通过将一个直圆锥与一条平行于其侧面的平面相交而形成的曲线。它具有独特的U形，并以其顶点、焦点和准线为特征。当我们将这种二维形状沿第三维度延伸时，就产生了抛物面柱体。这种延伸产生的表面在其长度的每个点上都保持抛物线的横截面。抛物面柱体的一个关键特征是其聚光能力。这一特性在抛物面反射器的设计中尤为宝贵，这些反射器通常用于卫星天线和太阳能集中器。抛物面柱体的反射表面将入射的平行光线引导到一个焦点，从而最大限度地提高捕获能量或信号的效率。例如，在太阳能应用中，抛物面柱体可以将阳光集中到接收器上，提高能量收集过程的温度和效率。在建筑学中，抛物面柱体可以在各种结构中找到，其中美学和功能性相结合。抛物面柱体的光滑连续曲线不仅提供了结构完整性，还创造了视觉上吸引人的设计。建筑师经常在屋顶、桥梁和其他元素中使用这一形状，以增强其设计的美感和性能。抛物面柱体的强度使其能够承受显著的载荷，同时保持轻巧的形式，使其成为现代建筑的理想选择。此外，抛物面柱体的数学表示可以通过方程式进行描述。在笛卡尔坐标系中，抛物面柱体可以用方程z = ax²表示，其中'a'是一个常数，决定了抛物线的宽度和方向。这个方程突出了x轴与高度（z轴）之间的关系，展示了'x'的变化如何影响整体形状。总之，抛物面柱体不仅仅是一个数学概念；它是一种具有众多应用的实用形状，跨越多个学科。其独特的性质，如聚光和结构强度，使其成为理论研究和实际应用中的宝贵元素。无论是在物理、工程还是建筑领域，理解抛物面柱体都为创新和设计开辟了新的途径。随着我们继续探索和利用这些几何形状，我们可以期待看到更多推动我们理解和能力边界的创造性应用。