hyperbolic position line

简明释义

双曲线船位线

英英释义

例句

1.The hyperbolic position line is essential in geolocation technologies for determining precise locations.

双曲线位置线在地理定位技术中对于确定精确位置至关重要。

2.The engineer plotted the hyperbolic position line to determine the optimal trajectory for the satellite.

工程师绘制了双曲线位置线以确定卫星的最佳轨迹。

3.To improve GPS accuracy, the team analyzed the hyperbolic position line data from multiple satellites.

为了提高GPS精度，团队分析了来自多个卫星的双曲线位置线数据。

4.In navigation, the hyperbolic position line helps in pinpointing the location of a vessel using triangulation.

在导航中，双曲线位置线通过三角测量帮助确定船只的位置。

5.The surveyor used a hyperbolic position line to accurately map the land boundaries.

测量员使用双曲线位置线准确绘制土地边界。

作文

In the field of geometry and navigation, the concept of a hyperbolic position line plays a crucial role in determining locations and distances. A hyperbolic position line is defined as a line generated by the intersection of hyperbolas, which are curves formed by the set of points where the difference of the distances to two fixed points (foci) is constant. This mathematical concept is not only fundamental in theoretical studies but also has practical applications in various technologies, including GPS and other navigational systems.To understand the significance of a hyperbolic position line, we can consider how it is utilized in navigation. When a vessel or an aircraft is equipped with multiple signals from different sources, it can determine its position by analyzing the time it takes for those signals to reach it. Each signal source creates a hyperbolic position line based on the time delay between the signals received. By plotting these lines on a map, the exact location of the vessel or aircraft can be pinpointed at the intersection of these lines.The beauty of the hyperbolic position line lies in its mathematical properties. Hyperbolas have unique characteristics that allow for accurate distance measurements. Unlike circles, which represent equal distances from a single point, hyperbolas provide information about the difference in distances from two points. This is particularly useful in scenarios where multiple reference points are available, allowing for precise triangulation of positions.Moreover, the use of hyperbolic position lines extends beyond navigation. In telecommunications, for example, the principles behind hyperbolic positioning are applied to enhance signal accuracy and reliability. By employing multiple antennas and measuring the time it takes for signals to travel, engineers can create a network of hyperbolic position lines that ensures better coverage and connectivity.In conclusion, the hyperbolic position line is more than just a mathematical concept; it is a vital tool that aids in navigation and technology. Its ability to provide accurate positioning through the intersection of hyperbolas has transformed how we interact with our environment. As technology continues to evolve, the importance of understanding and utilizing hyperbolic position lines will only increase, making it essential for future advancements in various fields. Whether in aviation, maritime navigation, or telecommunications, the implications of this concept are profound and far-reaching.

在几何和导航领域，双曲线位置线的概念在确定位置和距离方面发挥着至关重要的作用。双曲线位置线被定义为通过双曲线的交点生成的线，这些双曲线是由一组点形成的，其中到两个固定点（焦点）的距离之差是恒定的。这个数学概念不仅在理论研究中是基础，在各种技术中也有实用应用，包括全球定位系统（GPS）和其他导航系统。为了理解双曲线位置线的重要性，我们可以考虑它在导航中的应用。当船只或飞机配备有来自不同来源的多个信号时，它可以通过分析这些信号到达所需的时间来确定其位置。每个信号源根据接收到的信号之间的时间延迟创建一条双曲线位置线。通过在地图上绘制这些线，可以在这些线的交点精确定位船只或飞机。双曲线位置线的美在于其数学特性。双曲线具有独特的特性，可以实现准确的距离测量。与表示从单一点等距离的圆不同，双曲线提供了关于两点之间距离差的信息。这在可用多个参考点的情况下尤其有用，使得能够精确三角测量位置。此外，双曲线位置线的使用超越了导航。在电信行业，例如，双曲线定位背后的原理被应用于增强信号的准确性和可靠性。通过采用多个天线并测量信号传播所需的时间，工程师可以创建一个双曲线位置线网络，确保更好的覆盖和连接。总之，双曲线位置线不仅仅是一个数学概念；它是一个关键工具，有助于导航和技术。通过双曲线的交点提供准确定位的能力改变了我们与环境的互动方式。随着技术的不断发展，理解和利用双曲线位置线的重要性只会增加，这使得它在各个领域的未来进步中至关重要。无论是在航空、海洋导航还是电信领域，这一概念的影响都是深远而广泛的。