incommensurable number

简明释义

不可通约数

英英释义

例句

1.The diagonal of a square is an incommensurable number when compared to its side length.

正方形的对角线与其边长相比是一个不可通约数。

2.In mathematics, the concept of an incommensurable number refers to a quantity that cannot be expressed as a ratio of two integers.

在数学中，不可通约数的概念指的是无法表示为两个整数的比率的量。

3.When discussing irrational numbers, we often refer to incommensurable numbers like √2 or π.

在讨论无理数时，我们常常提到像√2或π这样的不可通约数。

4.The discovery of incommensurable numbers challenged the ancient Greek understanding of mathematics.

对不可通约数的发现挑战了古希腊对数学的理解。

5.Two lengths are incommensurable numbers if there is no common measure that can divide both lengths evenly.

如果没有共同的度量可以均匀地分割这两个长度，则这两个长度是不可通约数。

作文

In mathematics, the concept of an incommensurable number refers to a type of number that cannot be expressed as a ratio of two integers. This idea dates back to ancient Greece, where mathematicians discovered that certain lengths, such as the diagonal of a square, could not be measured using whole numbers. The realization that not all quantities could be compared in this way was revolutionary and led to significant developments in mathematical theory. For instance, the famous Pythagorean theorem illustrates how the diagonal of a unit square is equal to the square root of two, a number that is classified as incommensurable because it cannot be precisely represented as a fraction. The implications of incommensurable numbers extend beyond pure mathematics into various fields, including physics, engineering, and even philosophy. In physics, for example, the relationship between different physical quantities often leads to incommensurable values that challenge our understanding of measurement and comparison. When scientists attempt to measure quantities such as time and space, they often encounter situations where traditional methods of comparison fail, necessitating a deeper exploration of the nature of these measurements.Moreover, the philosophical ramifications of incommensurable numbers provoke intriguing discussions about the limits of human understanding. If certain quantities cannot be measured or compared in a conventional sense, what does that say about our perception of reality? This question has been a topic of debate among philosophers for centuries, prompting inquiries into the nature of existence and the frameworks we use to understand the world around us.In practical terms, the presence of incommensurable numbers in everyday life can be observed in various scenarios. For instance, when architects design buildings, they often work with dimensions that include incommensurable ratios, requiring them to use approximations and estimations to achieve their desired outcomes. Similarly, artists may find themselves grappling with incommensurable numbers when trying to create proportions that are aesthetically pleasing but cannot be easily quantified.Despite the challenges posed by incommensurable numbers, they also offer opportunities for creativity and innovation. By embracing the complexity and ambiguity that comes with these concepts, mathematicians, scientists, and artists alike can push the boundaries of their respective fields. This pursuit of understanding and expression ultimately enriches our knowledge and appreciation of the world.In conclusion, the notion of incommensurable numbers serves as a reminder of the limitations inherent in our attempts to quantify and comprehend reality. It encourages us to explore new ways of thinking and to appreciate the beauty found in the complexities of mathematics and the universe. As we continue to encounter incommensurable numbers in various aspects of life, we must remain open to the lessons they impart, fostering a deeper understanding of both the measurable and immeasurable aspects of existence.

在数学中，不可度量的数这一概念指的是一种无法用两个整数的比率来表示的数字。这个思想可以追溯到古希腊，当时的数学家们发现某些长度，例如正方形的对角线，无法用整数来测量。意识到并非所有数量都可以以这种方式进行比较是革命性的，并导致了数学理论的重大进展。例如，著名的毕达哥拉斯定理说明了单位正方形的对角线等于平方根2，而这个数字被归类为不可度量的数，因为它不能精确地表示为分数。不可度量的数的影响超越了纯数学，延伸到物理学、工程学甚至哲学等多个领域。在物理学中，例如，不同物理量之间的关系常常导致不可度量的值，这挑战了我们对测量和比较的理解。当科学家们试图测量时间和空间等数量时，他们常常遇到传统比较方法失效的情况，这需要更深入地探讨这些测量的本质。此外，不可度量的数的哲学意义引发了关于人类理解极限的有趣讨论。如果某些数量无法以传统的方式测量或比较，这对我们对现实的感知意味着什么？这个问题在几个世纪以来一直是哲学家们辩论的主题，促使他们探讨存在的本质以及我们用来理解周围世界的框架。在实际生活中，不可度量的数的存在可以在各种场景中观察到。例如，当建筑师设计建筑时，他们常常处理包含不可度量的比例的尺寸，要求他们使用近似值和估算值来实现所需的结果。同样，艺术家在创作美学上令人愉悦但无法轻易量化的比例时，可能会面临不可度量的数的困扰。尽管不可度量的数带来了挑战，但它们也为创造力和创新提供了机会。通过接受与这些概念相关的复杂性和模糊性，数学家、科学家和艺术家都可以推动各自领域的边界。这种对理解和表达的追求最终丰富了我们对世界的知识和欣赏。总之，不可度量的数的概念提醒我们，在量化和理解现实的尝试中固有的局限性。它鼓励我们探索新的思维方式，欣赏数学和宇宙复杂性中的美。随着我们在生活的各个方面继续遇到不可度量的数，我们必须保持开放，领悟它们传授的教训，深化对存在的可测量和不可测量方面的理解。