loxodromic curve

简明释义

恒向线

英英释义

例句

1.In mathematics, the equation of a loxodromic curve can be derived using spherical coordinates.

在数学中，航线曲线的方程可以通过球坐标系推导出来。

2.Sailors often prefer a loxodromic curve for navigation because it simplifies the steering process.

水手们通常更喜欢使用航线曲线进行导航，因为这简化了驾驶过程。

3.The path taken by a ship sailing from one point to another on the globe often follows a loxodromic curve, which allows for a constant compass direction.

一艘船从一个点航行到另一个点时，通常遵循一条航线曲线，这使得船可以保持恒定的航向。

4.When plotting a course on a map, navigators use the loxodromic curve to ensure they stay on the correct heading.

在地图上绘制航线时，导航员使用航线曲线以确保他们保持正确的航向。

5.The concept of a loxodromic curve is crucial in aviation, as pilots need to maintain a consistent bearing during long flights.

在航空领域，航线曲线的概念至关重要，因为飞行员需要在长途飞行中保持一致的航向。

作文

The world we live in is filled with complex geometries and fascinating mathematical concepts. One such concept that has intrigued mathematicians and navigators alike is the loxodromic curve. This term refers to a specific type of curve on the surface of a sphere, which crosses all meridians at the same angle. In simpler terms, it is a path that a ship or an airplane would follow when navigating across the globe while maintaining a constant compass bearing. Understanding the loxodromic curve is essential for comprehending how navigation works on a spherical surface, such as the Earth.Historically, the loxodromic curve played a crucial role in maritime navigation. Before the advent of modern GPS technology, sailors relied on charts and compasses to guide their journeys across the vast oceans. The loxodromic curve allowed them to plot a course that would keep them on a steady heading, making it easier to reach distant ports without constantly adjusting their direction. This method of navigation is particularly useful because it simplifies the process of plotting a route on a map, which is typically represented in two dimensions.In mathematics, the loxodromic curve can be described using equations that take into account the curvature of the Earth. It is a type of spiral that winds around the sphere, getting progressively closer to the poles but never actually reaching them. This property makes the loxodromic curve distinct from other types of curves, such as great circles, which represent the shortest distance between two points on the surface of a sphere. While great circles are often preferred for long-distance travel due to their efficiency, the loxodromic curve provides a practical alternative for maintaining a consistent heading.Another interesting aspect of the loxodromic curve is its relationship to the field of cartography. Maps are inherently two-dimensional representations of a three-dimensional world, and projecting the loxodromic curve onto a flat surface can lead to distortions. Various map projections attempt to preserve certain properties, such as angles or areas, but the loxodromic curve does not maintain its true shape when transferred to a flat map. This distortion poses challenges for navigators who wish to use traditional maps for planning their routes.In conclusion, the loxodromic curve is a remarkable mathematical concept with significant practical applications in navigation and cartography. Its ability to cross all meridians at a constant angle makes it invaluable for sailors and pilots who must maintain a steady course over long distances. Although modern technology has transformed navigation, understanding the loxodromic curve remains important for appreciating the history and development of navigation techniques. As we continue to explore our world, the principles behind the loxodromic curve will undoubtedly remain relevant, guiding us through the complexities of our navigational endeavors.

我们生活的世界充满了复杂的几何形状和迷人的数学概念。其中一个引起数学家和导航员关注的概念是航向曲线。这个术语指的是球面上的一种特定类型的曲线，它以相同的角度穿过所有经线。简单来说，它是船只或飞机在全球导航时遵循的路径，保持恒定的罗盘方位。理解航向曲线对于理解如何在球面上进行导航是至关重要的，例如地球。历史上，航向曲线在海洋导航中发挥了至关重要的作用。在现代GPS技术出现之前，水手依靠图表和罗盘来指导他们穿越广阔海洋的旅程。航向曲线使他们能够绘制一条保持稳定航向的航线，使他们更容易到达遥远的港口，而无需不断调整方向。这种导航方法特别有用，因为它简化了在地图上绘制路线的过程，地图通常以二维形式表示。在数学中，航向曲线可以使用考虑地球曲率的方程进行描述。它是一种螺旋形曲线，围绕球体旋转，逐渐接近极点，但永远不会真正到达它们。这一特性使得航向曲线与其他类型的曲线，如大圆（代表球面上两点之间的最短距离），有所不同。虽然大圆因其高效性而常被用于长途旅行，但航向曲线为保持一致的航向提供了实用的替代方案。航向曲线的另一个有趣方面是它与制图学领域的关系。地图本质上是三维世界的二维表示，将航向曲线投影到平面表面上可能会导致失真。各种地图投影试图保留某些属性，例如角度或面积，但航向曲线在转移到平面地图上时并不保持其真实形状。这种失真给希望使用传统地图规划航线的导航员带来了挑战。总之，航向曲线是一个显著的数学概念，在导航和制图中具有重要的实际应用。它以恒定角度穿过所有经线的能力使其对必须在长距离上保持稳定航向的水手和飞行员而言是无价的。尽管现代技术已经改变了导航，但理解航向曲线仍然对欣赏导航技术的历史和发展至关重要。当我们继续探索我们的世界时，航向曲线背后的原理无疑将保持相关性，引导我们穿越导航工作中的复杂性。