haversine

简明释义

英[ˈhævəˌsaɪn]美[ˈhævərˌsiːn]

n. [数] 半正矢

英英释义

单词用法

同义词

反义词

例句

1.The Haversine formula is used generally for computing great-circle distances between two pairs of coordinates on a sphere.

该矢公式用于计算之间的两对大圈的距离，一般在一个球体上的坐标。

2.The Haversine formula is used generally for computing great-circle distances between two pairs of coordinates on a sphere.

该矢公式用于计算之间的两对大圈的距离，一般在一个球体上的坐标。

3.The haversine formula is used to calculate the distance between two points on the Earth's surface.

使用haversine公式可以计算地球表面上两点之间的距离。

4.When developing a navigation app, we implemented the haversine algorithm to improve accuracy.

在开发导航应用时，我们实施了haversine算法以提高准确性。

5.The haversine function helps in determining the shortest path between cities.

haversine函数有助于确定城市之间的最短路径。

6.The haversine method is particularly useful for aviation and marine navigation.

对于航空和海洋导航，haversine方法特别有用。

7.To find out how far apart two locations are, you can use the haversine distance formula.

要找出两个地点之间的距离，可以使用haversine距离公式。

作文

The term haversine refers to a mathematical formula used to calculate the distance between two points on the surface of a sphere, given their longitudes and latitudes. This concept is particularly important in fields such as navigation, aviation, and geolocation. The haversine formula accounts for the curvature of the Earth, which is essential for accurate distance measurement over large distances. In this essay, we will explore the significance of the haversine formula, its applications, and how it enhances our understanding of geographical distances.To begin with, the haversine formula is derived from the haversine function, which is itself a mathematical transformation of the sine function. It is defined as: haversin(θ) = sin²(θ/2). This transformation helps to avoid numerical instability when dealing with very small angles, making the calculations more reliable. The complete haversine formula is expressed as: a = haversin(Δφ) + cos(φ1) * cos(φ2) * haversin(Δλ) c = 2 * atan2(√a, √(1−a)) d = R * cwhere φ is the latitude, λ is the longitude, Δφ is the difference in latitude, Δλ is the difference in longitude, and R is the radius of the Earth.Understanding the haversine formula is crucial for various practical applications. For instance, in aviation, pilots use this formula to determine the shortest flight path between two airports. By accurately calculating the distance using the haversine formula, pilots can optimize fuel consumption and reduce travel time. Similarly, in maritime navigation, sailors rely on the haversine formula to chart courses across vast oceans, ensuring they reach their destinations efficiently and safely.Moreover, the haversine formula is widely used in geographic information systems (GIS) and mapping software. When users input coordinates into these systems, the haversine formula allows the software to calculate distances between various locations, facilitating route planning and spatial analysis. This application is particularly useful in urban planning, where city planners need to analyze distances between different facilities, such as schools, hospitals, and transportation hubs.In addition to its practical uses, the haversine formula also contributes to our understanding of the Earth's geography. By providing a reliable method for calculating distances, it allows researchers to study patterns in human movement, migration, and trade across different regions. This understanding can lead to better infrastructure development and resource allocation, ultimately improving the quality of life for communities around the world.In conclusion, the haversine formula is an essential tool in various fields that require accurate distance measurements on the Earth's surface. Its mathematical foundation ensures reliability and stability in calculations, making it invaluable for navigation, GIS applications, and geographical research. As technology continues to advance, the importance of the haversine formula will only grow, further enhancing our ability to understand and navigate the world around us. Whether in the cockpit of an airplane or the comfort of a home, the haversine formula plays a crucial role in connecting people and places, demonstrating the power of mathematics in our daily lives.

术语haversine指的是一种数学公式，用于计算球面上两点之间的距离，给定它们的经度和纬度。这个概念在导航、航空和地理定位等领域尤为重要。haversine公式考虑了地球的曲率，这对大距离的准确测量至关重要。在这篇文章中，我们将探讨haversine公式的重要性、其应用以及它如何增强我们对地理距离的理解。首先，haversine公式源于haversine函数，这本身是正弦函数的一种数学变换。它被定义为：haversin(θ) = sin²(θ/2)。这种变换有助于避免在处理非常小的角度时出现数值不稳定，使得计算更加可靠。完整的haversine公式表达为： a = haversin(Δφ) + cos(φ1) * cos(φ2) * haversin(Δλ) c = 2 * atan2(√a, √(1−a)) d = R * c其中φ是纬度，λ是经度，Δφ是纬度差，Δλ是经度差，R是地球的半径。理解haversine公式对各种实际应用至关重要。例如，在航空领域，飞行员使用该公式来确定两个机场之间的最短飞行路径。通过使用haversine公式准确计算距离，飞行员可以优化燃料消耗并减少旅行时间。类似地，在海洋导航中，水手依赖haversine公式在广阔的海洋中绘制航线，确保他们高效安全地到达目的地。此外，haversine公式在地理信息系统（GIS）和制图软件中得到广泛应用。当用户将坐标输入这些系统时，haversine公式使软件能够计算不同位置之间的距离，便于路线规划和空间分析。这一应用在城市规划中尤其有用，城市规划者需要分析不同设施之间的距离，例如学校、医院和交通枢纽。除了实际用途，haversine公式还促进了我们对地球地理的理解。通过提供可靠的距离计算方法，它使研究人员能够研究人类运动、迁移和贸易在不同地区的模式。这种理解可以导致更好的基础设施发展和资源分配，最终改善全球社区的生活质量。总之，haversine公式是各种需要准确测量地球表面距离的领域中的一个基本工具。其数学基础确保了计算的可靠性和稳定性，使其在导航、GIS应用和地理研究中不可或缺。随着技术的不断进步，haversine公式的重要性只会增加，进一步增强我们理解和导航周围世界的能力。无论是在飞机的驾驶舱还是在家中的舒适环境中，haversine公式在连接人与地点方面发挥着至关重要的作用，展示了数学在我们日常生活中的力量。