orthocenter

简明释义

英[ˈɔːθəˌsentə(r)]美[ˈɔrθəˌsentər]

n. 垂心

英英释义

单词用法

同义词

反义词

例句

1.This paper explores into the distance formula between median point, orthocenter, circumcenter and inner point of triangle by means of two related formulas of vector methods.

应用两个向量法相关公式探讨了三角形重心、垂心、外心以及内心之间的距离公式。

2.This paper explores into the distance formula between median point, orthocenter, circumcenter and inner point of triangle by means of two related formulas of vector methods.

应用两个向量法相关公式探讨了三角形重心、垂心、外心以及内心之间的距离公式。

3.The method is greatly improved on an old one by calculating traverse error orthocenter, coordinate transformation and separation.

该方法通过求导线误差重心，坐标变换和分离的手段对原方法作了重大的改进，从而使计算变得简单。

4.In a triangle, the point where the three altitudes intersect is called the orthocenter.

在一个三角形中，三条高的交点被称为高心。

5.To find the orthocenter, you need to construct the altitudes of the triangle.

要找到高心，你需要构造三角形的高。

6.The orthocenter can be inside, outside, or on the vertex of the triangle depending on its type.

根据三角形的类型，高心可以位于三角形内部、外部或在顶点上。

7.In an acute triangle, the orthocenter lies inside the triangle.

在一个锐角三角形中，高心位于三角形内部。

8.For an obtuse triangle, the orthocenter is located outside the triangle.

对于一个钝角三角形，高心位于三角形外部。

作文

In the realm of geometry, the concept of the orthocenter plays a crucial role in understanding the properties of triangles. The orthocenter is defined as the point where the three altitudes of a triangle intersect. This seemingly simple definition opens up a world of exploration into the relationship between various elements of a triangle and its intrinsic characteristics. To grasp the significance of the orthocenter, one must first understand what an altitude is. An altitude of a triangle is a perpendicular line segment drawn from a vertex to the line containing the opposite side. Each triangle has three vertices, and consequently, it has three altitudes. The intersection point of these three lines is what we refer to as the orthocenter. The position of the orthocenter varies depending on the type of triangle. In an acute triangle, where all angles are less than 90 degrees, the orthocenter lies inside the triangle. Conversely, in a right triangle, the orthocenter coincides with the vertex of the right angle, making it a unique case. Finally, in an obtuse triangle, where one angle exceeds 90 degrees, the orthocenter is located outside the triangle. This variation illustrates how the properties of triangles can lead to different geometric configurations. Understanding the orthocenter also has practical applications in various fields such as architecture, engineering, and computer graphics. For instance, when designing structures, architects must consider the stability and balance of triangular shapes, which often serve as the foundation for more complex designs. By analyzing the orthocenter and the altitudes, architects can ensure that their designs are not only aesthetically pleasing but also structurally sound. Moreover, the orthocenter is one of several important points associated with a triangle, including the centroid and circumcenter. The centroid, which is the point where the three medians of a triangle intersect, serves as the center of mass. The circumcenter, on the other hand, is the point where the perpendicular bisectors of the sides intersect, and it is equidistant from all three vertices. Each of these points provides valuable insights into the triangle’s properties, and together they form a comprehensive understanding of triangular geometry. In conclusion, the orthocenter is not just a mere point in a triangle; it represents a deeper connection between the triangle's geometry and its various properties. By studying the orthocenter, one can appreciate the elegance and complexity of triangles, which are fundamental shapes in mathematics. Whether in theoretical studies or practical applications, the orthocenter remains a vital concept that enriches our understanding of geometry and its real-world implications.

在几何学的领域中，正交中心的概念在理解三角形的性质方面起着至关重要的作用。正交中心被定义为三条高线交汇的点。这个看似简单的定义开启了探索三角形各个元素之间关系及其内在特征的世界。 要理解正交中心的重要性，首先必须了解什么是高线。三角形的高线是从一个顶点垂直于包含对边的直线段。每个三角形都有三个顶点，因此它有三条高线。这三条线的交点就是我们所称的正交中心。 正交中心的位置因三角形的类型而异。在锐角三角形中，所有角都小于90度，正交中心位于三角形内部。相反，在直角三角形中，正交中心与直角的顶点重合，形成一种独特情况。最后，在钝角三角形中，某个角超过90度，正交中心则位于三角形外部。这种变化说明了三角形的性质如何导致不同的几何配置。 理解正交中心在建筑、工程和计算机图形学等多个领域也具有实际应用。例如，在设计结构时，建筑师必须考虑三角形形状的稳定性和平衡性，这通常作为更复杂设计的基础。通过分析正交中心和高线，建筑师可以确保他们的设计不仅美观，而且结构稳固。 此外，正交中心是与三角形相关的几个重要点之一，包括重心和外心。重心是三条中线交汇的点，作为质心。而外心是三条边的垂直平分线交汇的点，与所有三个顶点等距。这些点中的每一个都提供了三角形性质的宝贵见解，它们共同构成了对三角几何的全面理解。 总之，正交中心不仅仅是三角形中的一个点；它代表了三角形几何与其各种属性之间更深层次的联系。通过研究正交中心，人们可以欣赏到三角形的优雅与复杂性，而三角形在数学中是基本形状。无论是在理论研究还是实际应用中，正交中心始终是丰富我们对几何及其现实世界影响理解的重要概念。