hyperbolic line of position

简明释义

双曲位置线

英英释义

例句

1.By plotting two hyperbolic lines of position, the pilot was able to pinpoint the aircraft's coordinates.

通过绘制两条双曲线位置线，飞行员能够精确定位飞机的坐标。

2.To improve accuracy, the surveyor relied on multiple hyperbolic lines of position during the mapping process.

为了提高准确性，测量员在绘图过程中依赖多条双曲线位置线。

3.In maritime navigation, a hyperbolic line of position helps sailors find their way using time differences.

在海洋导航中，双曲线位置线帮助水手利用时间差找到航向。

4.The concept of hyperbolic lines of position is essential for understanding how GPS works.

双曲线位置线的概念对于理解GPS的工作原理至关重要。

5.The navigator used a hyperbolic line of position to determine the ship's location accurately.

导航员使用双曲线位置线准确确定船只的位置。

作文

In the realm of navigation and cartography, understanding various concepts is crucial for accurate positioning and mapping. One such concept is the hyperbolic line of position, which plays a significant role in determining one's location on the Earth's surface. This term refers to a geometric representation that helps navigators ascertain their position based on the difference in distances from two known points. By utilizing this method, sailors and aviators can effectively triangulate their location, enhancing their ability to navigate through vast and often treacherous waters or skies.To comprehend the hyperbolic line of position, it is essential to delve into the principles of hyperbolic navigation. This technique emerged prominently in the 19th century when mariners faced the challenge of precise navigation across open seas. The advent of chronometers allowed navigators to measure time accurately, which was vital for calculating longitude. By comparing the time of departure from a known point with the time of arrival at another, navigators could establish a hyperbola—a curve formed by the intersection of a plane with a double cone.The hyperbolic line of position is defined by two points: the known locations of two reference stations, which could be lighthouses or radio towers. When a navigator measures the time it takes for a signal to travel from these stations to their vessel, they can determine the distance to each station. The difference in these distances creates a hyperbola, which represents all the potential locations of the vessel relative to the two stations. Thus, the navigator can plot their position on a chart, significantly improving their navigational accuracy.This method of navigation is not only limited to maritime applications but also extends to aviation and even modern GPS technology. The principles behind the hyperbolic line of position are foundational in understanding how signals are transmitted and received, allowing for precise location tracking. As technology has evolved, the basic concepts of hyperbolic navigation have been integrated into more sophisticated systems, yet the underlying mathematics remains relevant.Moreover, the hyperbolic line of position highlights the importance of mathematical concepts in practical applications. It emphasizes how geometry and algebra can be utilized to solve real-world problems, making it an excellent example of interdisciplinary study. Students of mathematics and engineering can appreciate the elegance of hyperbolic functions while recognizing their utility in navigation.In conclusion, the hyperbolic line of position is a vital concept in navigation that illustrates the intersection of mathematics and practical application. Understanding this concept allows navigators to determine their location with greater precision, ultimately leading to safer travels. As we continue to advance technologically, the principles of hyperbolic navigation will remain integral to our understanding of positioning and mapping, proving that even centuries-old methods can inform modern practices. The study of the hyperbolic line of position not only enriches our knowledge of navigation but also enhances our appreciation for the mathematical principles that govern our world.

在导航和制图领域，理解各种概念对于准确定位和绘图至关重要。其中一个概念是双曲线位置线，它在确定人们在地球表面的位置方面发挥着重要作用。这个术语指的是一种几何表示，帮助导航员根据与两个已知点的距离差来确定他们的位置。通过利用这种方法，水手和飞行员可以有效地三角测量他们的位置，提高他们在广阔且往往危险的海域或空域中导航的能力。要理解双曲线位置线，必须深入探讨双曲线导航的原理。这种技术在19世纪显著出现，当时的航海者面临着在公海上精确导航的挑战。计时器的出现使导航员能够准确测量时间，这对于计算经度至关重要。通过比较从已知点出发的时间与到达另一个点的时间，导航员可以建立一条双曲线——这是一个由平面与双锥相交形成的曲线。双曲线位置线由两个点定义：两个参考站的已知位置，这些参考站可以是灯塔或无线电塔。当导航员测量信号从这些站点传输到他们的船只所需的时间时，他们可以确定到每个站的距离。这些距离之间的差异创建了一条双曲线，代表了船只相对于两个站点的所有潜在位置。因此，导航员可以在图表上绘制他们的位置，从而显著提高他们的导航准确性。这种导航方法不仅限于海洋应用，还扩展到航空甚至现代GPS技术。双曲线位置线背后的原理是理解信号如何被传输和接收的基础，使得精确的定位跟踪成为可能。随着技术的发展，双曲线导航的基本概念已经融入到更复杂的系统中，但其基础数学仍然相关。此外，双曲线位置线突显了数学概念在实际应用中的重要性。它强调了几何和代数如何被利用来解决现实世界的问题，使其成为跨学科研究的优秀范例。数学和工程的学生可以欣赏双曲函数的优雅，同时认识到它们在导航中的实用性。总之，双曲线位置线是导航中的一个重要概念，展示了数学与实际应用的交汇。理解这一概念使导航员能够更精确地确定他们的位置，最终导致更安全的旅行。随着我们继续推进技术，双曲线导航的原理将仍然是我们理解定位和绘图的重要组成部分，证明即使是几个世纪前的方法也能为现代实践提供信息。对双曲线位置线的研究不仅丰富了我们对导航的知识，也增强了我们对支配我们世界的数学原理的欣赏。