polar planimeter

简明释义

定极求积仪

英英释义

例句

1.Using a polar planimeter, the architect calculated the area needed for the new building design.

建筑师使用极坐标测量仪计算新建筑设计所需的面积。

2.The research team employed a polar planimeter to determine the surface area of various biological specimens.

研究团队使用极坐标测量仪确定各种生物样本的表面积。

3.The polar planimeter proved to be an invaluable tool during the land surveying project.

在土地测量项目中，极坐标测量仪被证明是一个不可或缺的工具。

4.The engineer used a polar planimeter to accurately measure the area of the irregular plot of land.

工程师使用极坐标测量仪准确测量不规则土地的面积。

5.In our geometry class, we learned how to operate a polar planimeter for calculating areas of complex shapes.

在我们的几何课上，我们学习了如何操作极坐标测量仪来计算复杂形状的面积。

作文

In the world of mathematics and engineering, the need for precise measurements is paramount. One of the fascinating tools that have been developed to aid in this endeavor is the polar planimeter. A polar planimeter is an instrument used to measure the area of a two-dimensional shape by tracing its perimeter. Unlike traditional methods that often rely on complex calculations, the polar planimeter offers a more intuitive and direct approach to measuring areas, making it a valuable tool for engineers, architects, and mathematicians alike.The basic principle behind the polar planimeter is relatively simple yet ingenious. It consists of a tracer arm that follows the outline of the shape being measured and a fixed arm that remains stationary at a pivot point. As the tracer arm moves around the perimeter of the shape, the device records the distance traveled, which can then be converted into an area measurement. This method is especially useful for irregularly shaped objects where standard geometric formulas may not apply.One of the key advantages of using a polar planimeter is its ability to provide quick and accurate measurements without requiring extensive mathematical knowledge. Users can simply trace the outline of the shape, and the device does the rest. This feature makes it particularly appealing for professionals who need to make rapid assessments in the field, such as land surveyors or construction managers. Additionally, the polar planimeter can be used for various applications, from calculating land areas to determining the surface areas of mechanical components.Moreover, the polar planimeter has historical significance in the development of measurement techniques. Invented in the 19th century, it represents a shift towards more practical and user-friendly tools in mathematics and engineering. Before its invention, measuring areas often required tedious calculations and was prone to errors. The polar planimeter streamlined this process, allowing for greater accuracy and efficiency.In educational settings, the polar planimeter serves as an excellent teaching tool. It provides students with hands-on experience in measuring areas and helps them understand the concepts of integration and geometry in a tangible way. By using the polar planimeter, students can visualize how area calculations work and see the immediate results of their efforts, which can enhance their learning experience.Despite the rise of digital technology and computer-aided design (CAD) software, the polar planimeter remains relevant today. Many professionals still prefer its simplicity and reliability, especially in situations where electronic devices may not be practical. Furthermore, the polar planimeter is often more affordable than high-tech alternatives, making it accessible to a broader audience.In conclusion, the polar planimeter is a remarkable tool that has stood the test of time in the fields of mathematics and engineering. Its ability to measure areas accurately and efficiently makes it indispensable for various applications. Whether in a professional setting or an educational environment, the polar planimeter continues to play a crucial role in helping individuals understand and quantify the world around them. As we move forward, it is essential to appreciate the innovations that have shaped our understanding of measurement and to recognize the value of tools like the polar planimeter that contribute to our ongoing quest for precision and knowledge.

在数学和工程的世界中，精确测量的需求至关重要。为了帮助实现这一目标，开发了一种迷人的工具——极坐标面域仪。极坐标面域仪是一种用于通过沿着形状的周边进行描迹来测量二维形状面积的仪器。与传统方法常常依赖复杂计算不同，极坐标面域仪提供了一种更直观、直接的面积测量方法，使其成为工程师、建筑师和数学家等专业人士的宝贵工具。极坐标面域仪的基本原理相对简单而又巧妙。它由一个追踪臂组成，该臂沿着被测形状的轮廓移动，而一个固定臂则保持在一个支点上不动。当追踪臂围绕形状的周边移动时，设备记录所经过的距离，这可以转换为面积测量。这种方法在不规则形状物体的测量中尤其有用，因为标准几何公式可能不适用。使用极坐标面域仪的一个主要优点是能够快速、准确地提供测量，而无需广泛的数学知识。用户只需沿着形状的轮廓进行描迹，设备便会完成其余工作。这一特点使得它在需要快速评估的领域（如土地测量或建筑管理）特别受欢迎。此外，极坐标面域仪可以用于各种应用，从计算土地面积到确定机械部件的表面积。此外，极坐标面域仪在测量技术的发展中具有历史意义。它于19世纪发明，代表了数学和工程工具向更实用、更用户友好的转变。在其发明之前，测量面积往往需要繁琐的计算，并且容易出错。极坐标面域仪简化了这一过程，提高了准确性和效率。在教育环境中，极坐标面域仪是一个出色的教学工具。它为学生提供了实际测量面积的经验，帮助他们以具体的方式理解积分和几何概念。通过使用极坐标面域仪，学生可以直观地了解面积计算的工作原理，并看到他们努力的即时结果，这可以增强他们的学习体验。尽管数字技术和计算机辅助设计（CAD）软件的兴起，极坐标面域仪今天仍然保持着相关性。许多专业人士仍然更喜欢其简便性和可靠性，尤其是在电子设备可能不实用的情况下。此外，极坐标面域仪通常比高科技替代品更实惠，使其能够被更广泛的受众所接受。总之，极坐标面域仪是一种卓越的工具，在数学和工程领域经受住了时间的考验。它能够准确、高效地测量面积，使其在各种应用中不可或缺。无论是在专业环境还是教育环境中，极坐标面域仪继续在帮助个人理解和量化周围世界方面发挥着关键作用。随着我们向前发展，欣赏塑造我们测量理解的创新，并认识到像极坐标面域仪这样的工具在我们不断追求精确和知识中的价值，是至关重要的。