parabolic curve

简明释义

抛物曲线

英英释义

例句

1.The trajectory of a thrown ball follows a parabolic curve 抛物线 due to the effects of gravity.

投掷球的轨迹遵循一条抛物线 parabolic curve，这是因为重力的影响。

2.Graphing the equation reveals a parabolic curve 抛物线 that opens upwards.

绘制该方程的图形显示出一条向上开启的抛物线 parabolic curve。

3.The design of this bridge incorporates a parabolic curve 抛物线 for aesthetic and structural reasons.

这座桥的设计融入了一条抛物线 parabolic curve，以满足美观和结构的需求。

4.In physics, we often analyze the motion of objects along a parabolic curve 抛物线 when they are subject to projectile motion.

在物理学中，我们常常分析物体在受到抛体运动时沿着抛物线 parabolic curve的运动。

5.The satellite's orbit can be approximated by a parabolic curve 抛物线 during certain phases of its trajectory.

在其轨道的某些阶段，卫星的轨道可以用一条抛物线 parabolic curve来近似。

作文

In the realm of mathematics and physics, the concept of a parabolic curve plays a significant role in understanding various phenomena. A parabolic curve is defined as the graph of a quadratic function, which takes the form of a U-shaped curve. This curve can be seen in many real-world applications, from the trajectory of a thrown object to the design of satellite dishes. Understanding the properties and equations that define a parabolic curve can provide insights into both theoretical and practical aspects of science and engineering.One of the most fascinating aspects of a parabolic curve is its symmetry. The curve is symmetric about a vertical line known as the axis of symmetry. This line passes through the vertex of the parabola, which is the highest or lowest point of the curve, depending on its orientation. For instance, in the equation y = ax² + bx + c, the vertex can be found using the formula x = -b/(2a). This symmetry not only aids in graphing the function but also simplifies calculations in various applications.In physics, the parabolic curve represents the path of an object under the influence of gravity when it is projected into the air. This phenomenon is often referred to as projectile motion. For example, when a ball is thrown, it follows a parabolic curve due to the constant acceleration of gravity acting on it. The shape of this curve can be analyzed to determine the maximum height reached by the object, the distance it travels, and the time it spends in the air. By applying the principles of kinematics, one can derive the equations that govern this motion, further illustrating the importance of the parabolic curve in understanding physical laws.Additionally, the parabolic curve finds its application in engineering, particularly in the design of reflective surfaces such as satellite dishes and parabolic mirrors. These devices utilize the unique property of a parabolic curve where all incoming parallel rays of light or signals are reflected to a single focal point. This characteristic makes parabolic curves highly efficient for collecting and focusing energy, whether it be in the form of light or radio waves. Engineers and designers must consider the precise dimensions and orientation of these curves to optimize their functionality.Moreover, the parabolic curve has artistic implications as well. Artists and architects have long been inspired by the elegance of this shape, often incorporating it into their designs. The fluidity and balance that a parabolic curve provides can evoke feelings of harmony and grace, making it a popular choice in both modern and classical architecture. From bridges to buildings, the aesthetic appeal of a parabolic curve cannot be underestimated.In conclusion, the parabolic curve is a fundamental concept that transcends multiple disciplines, including mathematics, physics, engineering, and art. Its unique properties and applications make it a topic worthy of exploration and study. By understanding the characteristics of a parabolic curve, we can gain deeper insights into the world around us and harness its principles for innovation and creativity. Whether in the classroom or in practical applications, the parabolic curve serves as a bridge between theory and reality, illustrating the profound connections that exist within our universe.

在数学和物理的领域中，抛物线的概念在理解各种现象中扮演着重要角色。抛物线被定义为二次函数的图像，其形状呈U型曲线。这条曲线在许多现实世界的应用中都能看到，从抛物体的轨迹到卫星天线的设计。理解定义抛物线的性质和方程，可以为科学和工程的理论和实践方面提供见解。抛物线最迷人的一个方面是它的对称性。该曲线关于一条称为对称轴的垂直线是对称的。这条线穿过抛物线的顶点，即曲线的最高点或最低点，具体取决于其方向。例如，在方程y = ax² + bx + c中，可以使用公式x = -b/(2a)找到顶点。这种对称性不仅有助于绘制函数图像，还简化了各种应用中的计算。在物理学中，抛物线代表了在重力影响下物体的路径，当物体被抛入空中时，这种现象通常被称为抛射运动。例如，当一个球被投掷时，由于重力的持续加速度，它遵循一条抛物线。通过分析这条曲线，可以确定物体达到的最大高度、它的行进距离以及在空中停留的时间。通过应用运动学原理，可以推导出支配这种运动的方程，进一步说明了抛物线在理解物理法则中的重要性。此外，抛物线在工程中也找到了应用，特别是在反射表面的设计中，例如卫星天线和抛物面镜。这些设备利用抛物线的独特属性，即所有平行的光线或信号都反射到一个焦点。这一特性使得抛物线在收集和聚焦能量方面非常高效，无论是光还是无线电波。工程师和设计师必须考虑这些曲线的精确尺寸和方向，以优化它们的功能。此外，抛物线在艺术上也有重要意义。艺术家和建筑师长期以来受到这一形状优雅的启发，常常将其融入他们的设计中。抛物线所提供的流畅性和均衡感可以唤起和谐与优雅的感觉，使其成为现代和古典建筑中受欢迎的选择。从桥梁到建筑，抛物线的美学吸引力不容小觑。总之，抛物线是一个基本概念，跨越多个学科，包括数学、物理、工程和艺术。其独特的性质和应用使其成为值得探索和研究的主题。通过理解抛物线的特征，我们可以深入了解我们周围的世界，并利用其原理进行创新和创造。无论是在课堂上还是在实际应用中，抛物线都作为理论与现实之间的桥梁，展示了我们宇宙中存在的深刻联系。