excess of a triangle

简明释义

三角形角盈

英英释义

例句

1.During the construction process, we had to account for the excess of a triangle 三角形的多余部分 in our calculations.

在施工过程中，我们必须在计算中考虑excess of a triangle 三角形的多余部分。

2.The engineer used the excess of a triangle 三角形的多余部分 to optimize the structural integrity of the bridge.

工程师利用excess of a triangle 三角形的多余部分来优化桥梁的结构完整性。

3.In geometry class, we learned how to find the excess of a triangle 三角形的多余部分 using various formulas.

在几何课上，我们学习了如何使用各种公式找到excess of a triangle 三角形的多余部分。

4.The architect calculated the excess of a triangle 三角形的多余部分 to ensure the roof design was stable.

建筑师计算了excess of a triangle 三角形的多余部分以确保屋顶设计的稳定性。

5.The artist incorporated the excess of a triangle 三角形的多余部分 into her painting to create a sense of depth.

艺术家将excess of a triangle 三角形的多余部分融入她的画作中，以创造深度感。

作文

The concept of the excess of a triangle is a fascinating and essential topic in the field of geometry. To understand this term, we first need to grasp what is meant by the angles of a triangle. A triangle is defined as a polygon with three edges and three vertices. The sum of the interior angles of any triangle is always 180 degrees. However, when we talk about the excess of a triangle (三角形的超额), we are referring to a specific scenario that occurs in spherical geometry, where the rules differ from those in Euclidean geometry.In spherical geometry, triangles are formed on the surface of a sphere rather than on a flat plane. This leads to some intriguing properties. For instance, the sum of the interior angles of a spherical triangle exceeds 180 degrees. The amount by which the sum of the angles exceeds 180 degrees is referred to as the excess of a triangle. This excess is directly related to the area of the triangle on the sphere. The larger the excess, the larger the area of the triangle.To illustrate this concept further, consider a triangle formed by three points on the surface of a sphere, such as the North Pole and two points along the equator. The angles at each vertex will be greater than those in a flat triangle, leading to a significant excess of a triangle. In fact, in spherical triangles, the formula for calculating the area involves the excess. Specifically, the area can be calculated using the formula: Area = Excess, where the excess is measured in steradians.This relationship between the excess of a triangle and its area is not only mathematically interesting but also has practical applications in fields such as astronomy and navigation. For example, navigators use spherical triangles to determine distances and directions on the Earth’s surface, which is approximately spherical in shape.Moreover, understanding the excess of a triangle can enhance our comprehension of more complex geometric concepts. It serves as a bridge between basic geometry and advanced topics like topology and differential geometry. By studying how triangles behave on different surfaces, we can gain insights into the nature of space itself.In conclusion, the excess of a triangle is a key concept in understanding the differences between flat and spherical geometries. It highlights the unique properties of triangles formed on curved surfaces and underscores the importance of geometry in various scientific fields. As we explore the depths of mathematics and its applications, the concept of the excess of a triangle reminds us of the beauty and complexity of the shapes that surround us in our universe.

三角形的超额这一概念是几何学中一个引人入胜且重要的话题。要理解这个术语，我们首先需要掌握三角形的角度的含义。三角形被定义为一种具有三条边和三个顶点的多边形。任何三角形的内角之和总是180度。然而，当我们谈论三角形的超额（excess of a triangle）时，我们指的是在球面几何中发生的特定情况，在这种情况下，规则与欧几里得几何不同。在球面几何中，三角形是在球体表面上形成的，而不是在平面上。这导致了一些有趣的性质。例如，球面三角形的内角之和超过180度。内角之和超过180度的量被称为三角形的超额。这个超额与球面上三角形的面积直接相关。超额越大，三角形的面积越大。为了进一步说明这一概念，考虑一个由球面上的三个点形成的三角形，比如北极和赤道上的两个点。每个顶点的角度将大于平面三角形中的角度，从而导致显著的三角形超额。实际上，在球面三角形中，计算面积的公式涉及到超额。具体而言，面积可以通过公式计算：面积 = 超额，其中超额以弧度为单位测量。三角形的超额与其面积之间的这种关系不仅在数学上有趣，而且在天文学和导航等领域也有实际应用。例如，导航员使用球面三角形来确定地球表面的距离和方向，而地球的形状大致为球形。此外，理解三角形的超额可以增强我们对更复杂几何概念的理解。它作为基本几何与拓扑学和微分几何等高级主题之间的桥梁。通过研究三角形在不同表面上的行为，我们可以获得对空间本质的洞察。总之，三角形的超额是理解平面几何与球面几何之间差异的关键概念。它突显了在曲面上形成的三角形的独特性质，并强调了几何学在各个科学领域中的重要性。当我们探索数学及其应用的深度时，三角形的超额这一概念提醒我们宇宙中围绕我们的形状的美丽和复杂性。