symmetrical spherical triangles

简明释义

球面对称三角形

英英释义

例句

1.The navigation system relies on calculations involving symmetrical spherical triangles (对称球面三角形) to determine the shortest path between two points on the globe.

导航系统依赖于涉及对称球面三角形 (symmetrical spherical triangles) 的计算，以确定地球上两点之间的最短路径。

2.In computer graphics, symmetrical spherical triangles (对称球面三角形) can be used to model surfaces of spheres more efficiently.

在计算机图形学中，对称球面三角形 (symmetrical spherical triangles) 可用于更有效地建模球体的表面。

3.In advanced geometry, we often study symmetrical spherical triangles (对称球面三角形) to understand their unique properties.

在高级几何学中，我们常常研究对称球面三角形 (symmetrical spherical triangles) 来理解它们的独特性质。

4.Architects may use symmetrical spherical triangles (对称球面三角形) in the design of geodesic domes for aesthetic and structural efficiency.

建筑师可能会在设计球面穹顶时使用对称球面三角形 (symmetrical spherical triangles) 以达到美观和结构效率。

5.Mathematicians explore symmetrical spherical triangles (对称球面三角形) to derive formulas for calculating area and angles.

数学家探索对称球面三角形 (symmetrical spherical triangles) 以推导计算面积和角度的公式。

作文

In the study of geometry, particularly in the realm of spherical geometry, one encounters various fascinating shapes and figures. Among these, symmetrical spherical triangles stand out due to their unique properties and applications. A symmetrical spherical triangle is defined as a triangle on the surface of a sphere where at least two of its sides or angles are equal, exhibiting a form of symmetry. This concept not only holds theoretical significance but also finds practical applications in fields such as astronomy, navigation, and even art.To understand symmetrical spherical triangles, we must first grasp the basics of spherical geometry. Unlike planar geometry, where shapes exist on a flat surface, spherical geometry deals with figures that reside on the surface of a sphere. The most notable difference is that the sum of the angles in a spherical triangle exceeds 180 degrees, which is a fundamental characteristic of spherical triangles. This property arises from the curvature of the sphere, leading to intriguing geometric relationships.The symmetry in symmetrical spherical triangles introduces an element of balance and harmony. For instance, consider a spherical triangle formed by three points on the surface of a sphere. If two of these points are equidistant from a third point, the resulting triangle will be symmetrical. This symmetry can be visually appreciated when the triangle is represented on a globe, where the equal angles and sides create an aesthetically pleasing shape.One of the key applications of symmetrical spherical triangles is in navigation. Navigators often use spherical triangles to chart courses across the globe. By utilizing the principles of spherical trigonometry, they can calculate distances and angles between different points on Earth. This method is particularly useful for air and sea travel, where the curvature of the Earth must be taken into account. The ability to understand and apply the properties of symmetrical spherical triangles enables navigators to plot efficient routes and ensure safe passage.In addition to navigation, symmetrical spherical triangles also play a role in astronomy. Astronomers utilize these triangles to calculate positions of celestial bodies. The sky can be viewed as a vast sphere surrounding the Earth, and understanding the relationships between stars and planets often involves creating spherical triangles. For instance, if an astronomer wants to determine the angle between two stars as seen from Earth, they can form a symmetrical spherical triangle using the Earth and the two stars as vertices. This geometric approach aids in the precise mapping of the night sky.Moreover, the concept of symmetrical spherical triangles extends beyond scientific applications; it also influences art and design. Artists often draw inspiration from geometric shapes, including triangles, to create balanced and harmonious compositions. The symmetry found in symmetrical spherical triangles can evoke feelings of stability and beauty, making it a popular choice in various artistic endeavors.In conclusion, symmetrical spherical triangles represent a captivating intersection of mathematics, science, and art. Their unique properties and applications in navigation, astronomy, and design highlight the importance of understanding geometric principles in our everyday lives. As we continue to explore the vastness of both the universe and the world around us, the study of symmetrical spherical triangles will undoubtedly remain a vital area of inquiry, bridging the gap between abstract theory and practical application.

在几何学的研究中，特别是在球面几何领域，人们会遇到各种迷人的形状和图形。其中，对称球面三角形因其独特的性质和应用而脱颖而出。对称球面三角形被定义为在球面上形成的三角形，其中至少两条边或角相等，展现出一种对称性。这一概念不仅具有理论意义，而且在天文学、导航甚至艺术等领域找到了实际应用。要理解对称球面三角形，我们必须首先掌握球面几何的基础。与平面几何不同，平面几何中的形状存在于平坦的表面上，而球面几何则处理存在于球面上的图形。最显著的区别是，球面三角形的角度总和超过180度，这是球面三角形的一个基本特征。这一特性源于球体的曲率，导致了引人入胜的几何关系。对称球面三角形中的对称性引入了一种平衡与和谐的元素。例如，考虑在球面上形成的一个球面三角形。如果这三个点中的两个与第三个点等距，则形成的三角形将是对称的。当三角形在地球仪上表示时，这种对称性可以在视觉上得到欣赏，其中相等的角和边创造出一种美感。对称球面三角形的一个关键应用是在导航中。导航员通常使用球面三角形来绘制穿越地球的航线。通过利用球面三角法则的原理，他们可以计算地球上不同点之间的距离和角度。这种方法对于空中和海上旅行尤其有用，因为必须考虑地球的曲率。理解和应用对称球面三角形的性质使导航员能够规划高效的航线，确保安全通行。除了导航，对称球面三角形在天文学中也发挥着作用。天文学家利用这些三角形来计算天体的位置。天空可以视为包围地球的巨大球体，理解恒星和行星之间的关系往往涉及创建球面三角形。例如，如果天文学家想要确定从地球看到的两颗星星之间的角度，他们可以使用地球和这两颗星星作为顶点来形成一个对称球面三角形。这种几何方法有助于精确绘制夜空。此外，对称球面三角形的概念超越了科学应用，也影响了艺术和设计。艺术家们经常从几何形状中汲取灵感，包括三角形，以创造平衡和谐的构图。在对称球面三角形中发现的对称性可以唤起稳定和美感，使其成为各种艺术创作中的热门选择。总之，对称球面三角形代表了数学、科学和艺术之间迷人的交汇点。它们在导航、天文学和设计中的独特性质和应用凸显了理解几何原理在我们日常生活中的重要性。随着我们继续探索宇宙和周围世界的广阔，对称球面三角形的研究无疑将继续成为一个重要的研究领域，架起抽象理论与实际应用之间的桥梁。