euclidian

简明释义

英[juːˈklɪdiən]美[jʊˈklɪdɪən]

adj. 欧几里得的；欧几里得几何学的

英英释义

单词用法

同义词

反义词

例句

1.We recall the characteristics of the groups with hyperbolic symmetry and improve the IFS iterated function systems which are used to construct the classical fractal sets in the Euclidian plane.

方法分析双曲对称群的特点，改造欧式平面上构造经典分形的IFS迭代函数系，利用这种迭代函数系与双曲平面对称变换构造出组合IFS，通过随机挑选组合IFS中的仿射变换，构造双曲排列的分形集。

2.We recall the characteristics of the groups with hyperbolic symmetry and improve the IFS iterated function systems which are used to construct the classical fractal sets in the Euclidian plane.

方法分析双曲对称群的特点，改造欧式平面上构造经典分形的IFS迭代函数系，利用这种迭代函数系与双曲平面对称变换构造出组合IFS，通过随机挑选组合IFS中的仿射变换，构造双曲排列的分形集。

3.Based on the dual variables, the Hamiltonian system theory is introduced into plane orthotropy elasticity, the transformation from Euclidian space to symplectic space is realized.

通过引入对偶变量，将平面正交各向异性问题导入哈密顿体系，实现从欧几里德几何空间向辛几何空间的转换。

4.In our geometry class, we learned about euclidian 欧几里得的 principles that govern flat surfaces.

在我们的几何课上，我们学习了关于欧几里得的 欧几里得的 原则，这些原则支配着平面。

5.The euclidian 欧几里得的 distance is often used in machine learning algorithms to calculate similarity.

在机器学习算法中，欧几里得的 欧几里得的 距离常用于计算相似性。

6.Architects often rely on euclidian 欧几里得的 geometry for designing buildings and structures.

建筑师常常依赖于欧几里得的 欧几里得的 几何来设计建筑和结构。

7.The concept of euclidian 欧几里得的 space helps in understanding basic geometric shapes.

欧几里得的 欧几里得的 空间的概念有助于理解基本的几何形状。

8.In physics, euclidian 欧几里得的 geometry is used to model the motion of objects in a straight line.

在物理学中，欧几里得的 欧几里得的 几何用于模拟物体沿直线的运动。

作文

In the realm of mathematics, the term euclidian (欧几里得的) geometry holds a significant place. It refers to the system of geometry based on the postulates and propositions formulated by the ancient Greek mathematician Euclid in his seminal work, 'Elements'. This branch of mathematics deals primarily with flat, two-dimensional surfaces and three-dimensional spaces, where the familiar concepts of points, lines, angles, and shapes are defined. The principles of euclidian (欧几里得的) geometry have been foundational for many areas of mathematics and science, influencing how we understand space and form. The essence of euclidian (欧几里得的) geometry can be captured through its five basic postulates. The first postulate states that a straight line can be drawn between any two points. This simple idea is the cornerstone of all geometric constructions. The second postulate asserts that a finite straight line can be extended indefinitely in both directions, which allows for the concept of infinite space. The third postulate introduces the idea of circles, stating that a circle can be drawn with any center and radius. The fourth and fifth postulates deal with right angles and parallel lines, respectively, establishing the framework for understanding angles and their relationships. One of the most intriguing aspects of euclidian (欧几里得的) geometry is its application in real-world scenarios. Architects and engineers rely on these principles when designing buildings and structures, ensuring that everything fits together harmoniously. For example, the Pythagorean theorem, which is derived from euclidian (欧几里得的) principles, is used extensively in construction to calculate distances and angles. Without the groundwork laid by Euclid, modern engineering would not be as precise or reliable. However, it is essential to note that euclidian (欧几里得的) geometry is not the only type of geometry. In the 19th century, mathematicians began exploring non-Euclidean geometries, which challenge some of the assumptions made by Euclid. These include hyperbolic and elliptic geometries, which have profound implications in fields such as cosmology and theoretical physics. Non-Euclidean geometries have shown that the universe may not adhere strictly to euclidian (欧几里得的) principles, particularly when considering the curvature of space-time. Despite the emergence of these new geometrical frameworks, the influence of euclidian (欧几里得的) geometry remains strong. It serves as a critical foundation for understanding more complex mathematical concepts. Students worldwide are introduced to euclidian (欧几里得的) geometry in their early education, learning to apply its principles in various contexts. From calculating areas and volumes to solving real-life problems, the applications of euclidian (欧几里得的) geometry are vast and varied. In conclusion, the term euclidian (欧几里得的) embodies a rich history and an essential framework within mathematics. Its principles not only provide a basis for much of classical geometry but also continue to inform various disciplines today. Understanding euclidian (欧几里得的) geometry is crucial for anyone interested in mathematics, science, or engineering, as it lays the groundwork for further exploration into the nature of space and form. As we delve deeper into the complexities of our universe, the relevance of euclidian (欧几里得的) geometry will undoubtedly endure, reminding us of the timeless wisdom of Euclid and the enduring power of mathematical thought.

在数学领域，术语euclidian（欧几里得的）几何占据着重要地位。它指的是基于古希腊数学家欧几里得在其开创性作品《几何原本》中提出的公设和命题的几何体系。这一数学分支主要处理平面二维表面和三维空间，其中点、线、角和形状等熟悉的概念被定义。euclidian（欧几里得的）几何的原则为许多数学和科学领域奠定了基础，影响了我们对空间和形状的理解。 euclidian（欧几里得的）几何的本质可以通过其五个基本公设来概括。第一个公设指出，可以在任意两点之间画一条直线。这个简单的想法是所有几何构造的基石。第二个公设断言，有限的直线可以在两个方向上无限延伸，这使得无限空间的概念成为可能。第三个公设引入了圆的概念，声明可以以任何中心和半径画出一个圆。第四和第五个公设分别涉及直角和平行线，建立了理解角度及其关系的框架。 euclidian（欧几里得的）几何的一个最引人入胜的方面是其在现实世界场景中的应用。建筑师和工程师在设计建筑和结构时依赖这些原则，以确保一切和谐地结合在一起。例如，源自euclidian（欧几里得的）原则的勾股定理，被广泛用于建筑中计算距离和角度。如果没有欧几里得奠定的基础，现代工程将不会如此精确或可靠。 然而，值得注意的是，euclidian（欧几里得的）几何并不是唯一的几何类型。在19世纪，数学家们开始探索非欧几里得几何，这些几何挑战了欧几里得的一些假设。这包括双曲几何和椭圆几何，它们在宇宙学和理论物理等领域具有深远的影响。非欧几里得几何表明，宇宙可能并不严格遵循euclidian（欧几里得的）原则，特别是在考虑时空的曲率时。 尽管出现了这些新的几何框架，euclidian（欧几里得的）几何的影响仍然强大。它作为理解更复杂数学概念的重要基础。世界各地的学生在早期教育中接触euclidian（欧几里得的）几何，学习在各种上下文中应用其原则。从计算面积和体积到解决现实问题，euclidian（欧几里得的）几何的应用范围广泛而多样。 总之，术语euclidian（欧几里得的）体现了丰富的历史和数学中的基本框架。它的原则不仅为经典几何的大部分内容提供了基础，而且今天仍继续影响各种学科。理解euclidian（欧几里得的）几何对于任何对数学、科学或工程感兴趣的人来说至关重要，因为它为进一步探索空间和形状的本质奠定了基础。当我们深入探讨宇宙的复杂性时，euclidian（欧几里得的）几何的相关性无疑会持续存在，提醒我们欧几里得的永恒智慧和数学思维的持久力量。