approximations

简明释义

英[əˌprɒk.sɪˈmeɪ.ʃənz]美[əˌprɑːk.sɪˈmeɪ.ʃənz]

[数] 近似值

英英释义

单词用法

同义词

反义词

例句

1.Such linear calculations, of course, can only be very rough approximations.

这一系列的计算可能仅仅是粗略的估计。

2.I was using what trainers call "approximations," rewarding the small steps toward learning a whole new behavior.

我用的是驯兽师称为“渐进法”的技巧——奖励学习全新行为过程中的每一个小进步。

3.So approximations must be made, especially when larger molecules such as proteins are involved.

因此，近似法必须被采用，特别是对于有类似蛋白质这样的大分子参与的化学过程。

4.OK, so what about approximations?

什么是近似？

5.Well we can go look up here, looking at the differential, there are no approximations here.

好的我们可以看这儿,看这个微分方程，这里没有做近似。

6.Such estimates should be considered only as crude approximations.

上述估算结果只能是粗略的近似值。

7.In mathematics, we often use approximations to simplify complex equations.

在数学中，我们常常使用近似值来简化复杂的方程。

8.The scientist provided approximations of the results based on preliminary data.

科学家根据初步数据提供了结果的近似值。

9.When budgeting for a project, we rely on approximations to estimate costs.

在为项目预算时，我们依赖于近似值来估算成本。

10.In physics, many formulas involve approximations to account for real-world conditions.

在物理学中，许多公式涉及近似值以考虑现实条件。

11.The engineer used approximations to predict the stress on the materials.

工程师使用近似值来预测材料的应力。

作文

In the realm of mathematics and science, the concept of approximations plays a crucial role in how we understand and interpret complex phenomena. An approximation is essentially an estimated value or representation that is close to, but not exactly equal to, a certain quantity. This idea is particularly important when dealing with real-world situations where exact measurements are often impossible to obtain due to various constraints such as time, resources, or technology. For example, when calculating the area of irregular shapes, mathematicians often rely on approximations to provide a workable solution. One common instance where approximations are used is in the field of physics. When scientists study the motion of planets, they frequently use approximations to simplify complex equations. The gravitational force between two objects can be described with precision; however, in practice, many variables complicate this relationship. By employing approximations, physicists can create models that accurately predict planetary movements without needing to account for every minor detail. This not only saves time but also allows for easier communication of ideas and findings among researchers.In daily life, we also encounter approximations regularly, even if we do not consciously recognize them. For instance, when cooking, recipes often call for specific measurements, yet most cooks will adjust these amounts based on their taste preferences or available ingredients. This intuitive use of approximations demonstrates the flexibility required in practical scenarios. A pinch of salt, for example, is not a precise measurement, but it serves as an effective approximation for enhancing flavor.Moreover, in the field of economics, approximations are vital for modeling market behaviors and predicting economic trends. Economists often utilize simplified models that make approximations about consumer behavior, market demand, and supply dynamics. While these models may not capture every nuance of the economy, they provide valuable insights that help policymakers and businesses make informed decisions. Without the ability to use approximations, understanding the complexities of economic systems would be exceedingly challenging.Additionally, in the digital age, technology has advanced our ability to make approximations more accurately. Algorithms and machine learning techniques rely on vast amounts of data to produce refined approximations that can lead to improved predictions and outcomes. For instance, recommendation systems on streaming platforms analyze user behavior and preferences to offer personalized content suggestions. These systems depend heavily on approximations derived from user data, demonstrating how integral this concept has become in our modern lives.In conclusion, approximations are an indispensable part of mathematics, science, daily life, and economics. They allow us to navigate complexity and uncertainty with greater ease and efficiency. Whether we are solving mathematical problems, conducting scientific research, or simply trying to follow a recipe, the ability to make approximations enables us to function effectively in a world filled with variables and unknowns. Understanding the nature of approximations not only enhances our analytical skills but also enriches our problem-solving capabilities, making it a fundamental concept worth mastering.

在数学和科学领域，近似值的概念在我们理解和解释复杂现象中发挥着至关重要的作用。近似值本质上是一个估计值或表示，接近但不完全等于某个数量。当处理现实世界中的情况时，这一思想尤其重要，因为由于时间、资源或技术等各种限制，通常无法获得精确的测量。例如，在计算不规则形状的面积时，数学家们经常依赖于近似值来提供可行的解决方案。近似值被使用的一个常见实例是在物理学领域。当科学家研究行星的运动时，他们经常使用近似值来简化复杂的方程。两个物体之间的引力可以精确描述；然而，在实践中，许多变量使这种关系变得复杂。通过采用近似值，物理学家可以创建准确预测行星运动的模型，而无需考虑每一个细微的细节。这不仅节省了时间，还使研究人员之间的思想和发现交流变得更加容易。在日常生活中，我们也经常遇到近似值，即使我们并不自觉地意识到它们。例如，在烹饪时，食谱通常要求特定的测量，但大多数厨师会根据他们的口味偏好或可用的食材调整这些数量。这种直观使用近似值的方法展示了在实际场景中所需的灵活性。例如，一撮盐并不是一个精确的测量，但它作为增强风味的有效近似值。此外，在经济学领域，近似值对于建模市场行为和预测经济趋势至关重要。经济学家们经常利用简化模型来对消费者行为、市场需求和供给动态进行近似值。虽然这些模型可能无法捕捉经济的每一个细微差别，但它们提供了有价值的见解，帮助政策制定者和企业做出明智的决策。如果没有使用近似值的能力，理解经济系统的复杂性将是极具挑战性的。此外，在数字时代，技术提升了我们更准确地进行近似值的能力。算法和机器学习技术依赖于大量数据来产生精细的近似值，从而改善预测和结果。例如，流媒体平台上的推荐系统分析用户行为和偏好，以提供个性化的内容建议。这些系统在很大程度上依赖于用户数据得出的近似值，展示了这一概念在我们现代生活中变得多么重要。总之，近似值是数学、科学、日常生活和经济学中不可或缺的一部分。它们使我们能够更轻松有效地应对复杂性和不确定性。无论我们是在解决数学问题、进行科学研究，还是仅仅试图按照食谱进行操作，进行近似值的能力使我们能够在充满变量和未知数的世界中有效运作。理解近似值的本质不仅增强了我们的分析能力，还丰富了我们的解决问题的能力，使其成为值得掌握的基本概念。