euclidean

简明释义

英[juːˈklɪdiən]美[juːˈklɪdiən;ˈjuːklɪdiən]

adj. 欧几里德的；欧几里德几何学的

英英释义

单词用法

同义词

反义词

例句

1.I have used Euclidean Distance but you could use any.

我用欧氏距离，但你可以使用任何。

2.Finally, weighted Euclidean distance classifier was utilized in recognition.

最后利用加权欧氏距离分类器进行识别。

3.Observer B concludes that there must be some connection between this 'force' and the non-Euclidean geometry she finds.

观察者B会做出这样的结论：在这种“力”和她发现的非欧几里德几何问题之间肯定存在有某种关系。

4.For example, Euclidean space is invariant under rotations and translations.

例如欧氏空间在旋转和平移下都不会改变。

5.In the third chapter, we discuss the annealing process on the Euclidean space.

第三章，我们考虑了欧氏空间上的退火过程。

6.I defined weights for each pair of cities as a function of the Euclidean distance between them and the number of friends between them.

我是这样进行定义的：将城市之间的欧式距离和城市之间的好友数量都作为一个函数进行权重分析，然后根据权重值在两市之间绘制标线。

7.Conventional flow mathematical models of coalbed methane are all based on Euclidean geometry.

传统的煤层气渗流数学模型均是建立在欧几里德几何基础上的。

8.In a euclidean geometry course, students learn about points, lines, and planes in a flat space.

在一个欧几里得几何课程中，学生学习平面空间中的点、线和面。

9.The principles of euclidean distance are often used in machine learning algorithms for clustering.

在机器学习算法中，欧几里得距离的原理常用于聚类。

10.Architects rely on euclidean concepts to create structures that are both functional and aesthetically pleasing.

建筑师依赖于欧几里得概念来创造既实用又美观的结构。

11.In euclidean space, the shortest distance between two points is a straight line.

在欧几里得空间中，两点之间的最短距离是一条直线。

12.The euclidean algorithm is a method for computing the greatest common divisor of two integers.

欧几里得算法是一种计算两个整数最大公约数的方法。

作文

In the realm of mathematics, the term euclidean refers to the geometric principles established by the ancient Greek mathematician Euclid. His work, primarily encapsulated in 'The Elements', laid the foundational framework for what we now consider classical geometry. The euclidean system is characterized by its use of flat space and the relationships between points, lines, and angles. This framework allows us to understand and analyze two-dimensional and three-dimensional shapes using a set of axioms and postulates that Euclid proposed over two thousand years ago. One of the most significant aspects of euclidean geometry is the concept of parallel lines. According to Euclid's fifth postulate, also known as the parallel postulate, if a line segment intersects two straight lines and forms interior angles on the same side that are less than two right angles, then the two lines must intersect on that side if extended far enough. This principle has profound implications in both theoretical and practical applications. In everyday life, euclidean geometry is used in various fields such as architecture, engineering, and computer graphics. For instance, architects rely on euclidean principles to design buildings and structures that are not only aesthetically pleasing but also structurally sound. The precise calculations involved in determining the dimensions and angles of a building's components ensure that they fit together harmoniously and can withstand environmental stresses. Moreover, the influence of euclidean geometry extends into the digital realm. In computer graphics, euclidean concepts are essential for rendering images and creating realistic simulations. The algorithms that drive these technologies often depend on euclidean principles to calculate distances, angles, and surface interactions, allowing for the creation of immersive experiences in video games and virtual reality. However, it is important to note that while euclidean geometry provides a robust framework for understanding many aspects of the world around us, it is not the only geometric system in existence. Non-euclidean geometries, such as hyperbolic and elliptic geometry, challenge the notions established by Euclid. These systems explore spaces that are curved rather than flat, leading to different interpretations of distance and angle. For example, in hyperbolic geometry, the sum of the angles of a triangle is less than 180 degrees, which contrasts sharply with the euclidean case where it is always equal to 180 degrees. The exploration of euclidean and non-euclidean geometries has profound implications not only in mathematics but also in physics. The theory of relativity, proposed by Albert Einstein, demonstrates that the fabric of space-time is not euclidean but rather curved by the presence of mass and energy. This revolutionary idea changed our understanding of gravity and the universe itself, showing that the principles of euclidean geometry are not universally applicable. In conclusion, the term euclidean encompasses a rich history of mathematical thought and application. From the ancient teachings of Euclid to modern-day applications in various fields, euclidean geometry remains a vital part of our understanding of the world. As we continue to explore and expand our knowledge of geometry, we must appreciate the foundational role that euclidean principles play while remaining open to the complexities introduced by non-euclidean frameworks. This balance between tradition and innovation is essential as we navigate the ever-evolving landscape of mathematics and science.

在数学领域，术语euclidean指的是古希腊数学家欧几里得建立的几何原则。他的著作主要体现在《元素》中，为我们现在所认为的经典几何奠定了基础框架。euclidean系统的特点是使用平面空间以及点、线和角之间的关系。这个框架使我们能够使用欧几里得提出的一组公理和公设来理解和分析二维和三维形状，这些公理和公设距今已有两千多年的历史。 euclidean几何最重要的方面之一是平行线的概念。根据欧几里得的第五公设，也称为平行公设，如果一条线段与两条直线相交，并在同一侧形成小于两个直角的内角，则如果继续延伸，这两条线必将在该侧相交。这个原理在理论和实际应用中都有深远的影响。 在日常生活中，euclidean几何被广泛应用于建筑、工程和计算机图形等多个领域。例如，建筑师依赖euclidean原则来设计既美观又结构稳固的建筑和结构。确定建筑组件的尺寸和角度的精确计算确保它们能够和谐地结合在一起，并能承受环境压力。 此外，euclidean几何的影响还扩展到数字领域。在计算机图形学中，euclidean概念对于渲染图像和创建真实模拟至关重要。这些技术背后的算法通常依赖于euclidean原则来计算距离、角度和表面交互，从而在视频游戏和虚拟现实中创造出沉浸式体验。 然而，重要的是要注意，虽然euclidean几何为我们理解周围世界的许多方面提供了一个坚实的框架，但它并不是唯一存在的几何系统。非euclidean几何，如双曲几何和椭圆几何，挑战了欧几里得建立的概念。这些系统探索的是弯曲而非平坦的空间，导致对距离和角度的不同解释。例如，在双曲几何中，三角形的内角之和小于180度，这与euclidean情况下总是等于180度形成鲜明对比。 对euclidean和非euclidean几何的探索不仅在数学上具有深远的意义，也在物理学中具有重要影响。阿尔伯特·爱因斯坦提出的相对论理论表明，时空的结构并不是euclidean的，而是由质量和能量的存在弯曲的。这个革命性的观点改变了我们对引力和宇宙本身的理解，表明euclidean几何的原理并不普遍适用。 总之，术语euclidean包含了丰富的数学思想和应用历史。从欧几里得的古代教学到现代各领域的应用，euclidean几何仍然是我们理解世界的重要组成部分。当我们继续探索和扩展我们的几何知识时，我们必须欣赏euclidean原则所发挥的基础性作用，同时保持开放的心态，接受非euclidean框架所带来的复杂性。在传统与创新之间找到这种平衡，对于我们在不断发展的数学和科学领域中导航至关重要。