hypocycloid

简明释义

英[ˌhaɪpəˈsaɪklɔɪd]美[ˌhaɪpəˈsaɪˌklɔɪd]

n. [数] 圆内旋轮线

英英释义

单词用法

同义词

反义词

例句

1.The method is very simple and the result is accurate enough. It suits different batch production of hypocycloid gears.

该方法计算简单，结果精确，适用于摆线轮各种批量的生产。

2.The method is very simple and the result is accurate enough. It suits different batch production of hypocycloid gears.

该方法计算简单，结果精确，适用于摆线轮各种批量的生产。

3.Based on the principle of the formation of hypocycloid, a kind of stepless gear speeder has been designed.

根据内摆线的形成原理，设计出一种齿轮无级变速器。

4.The envelope of moving line on the hypocycloid plane may be an epicycloid or cardioid and the…

摆线逆运动中与动切线成定角的直线，其包络也是圆周渐开线。

5.The path traced by a point on the circumference of a smaller circle rolling inside a larger circle is called a hypocycloid.

一个较小的圆在较大圆内滚动时，沿着其周长的某一点所描绘的路径称为抛物线。

6.In mathematics, a hypocycloid can be visualized using parametric equations.

在数学中，抛物线可以通过参数方程进行可视化。

7.Engineers often use the concept of hypocycloid gears for efficient mechanical designs.

工程师们常常使用抛物线齿轮的概念来设计高效的机械装置。

8.The shape of a hypocycloid can vary depending on the ratio of the radii of the circles involved.

一个抛物线的形状可以根据参与的圆的半径比而变化。

9.Artists have used the pattern of a hypocycloid to create intricate designs in their artwork.

艺术家们利用抛物线的图案在他们的艺术作品中创造了复杂的设计。

作文

The study of geometry has always fascinated mathematicians and scientists alike. Among the many intriguing shapes and curves that can be explored, the hypocycloid stands out as a particularly interesting example. A hypocycloid is a type of curve traced by a point on a smaller circle that rolls inside a larger fixed circle. This fascinating geometric figure not only has aesthetic appeal but also plays a crucial role in various applications in physics and engineering. To understand the hypocycloid better, let’s delve into its mathematical definition and properties. The basic equation for a hypocycloid can be derived from parametric equations, which describe the coordinates of points on the curve. For a hypocycloid generated by a circle of radius r rolling inside a larger circle of radius R, the parametric equations are given by: x(t) = (R - r) * cos(t) + r * cos((R - r)/r * t) y(t) = (R - r) * sin(t) - r * sin((R - r)/r * t) Here, t represents the parameter that varies over time as the smaller circle rolls around the inside edge of the larger circle. The resulting curve can take on various forms depending on the ratio of R to r. For instance, when the ratio is 2:1, the hypocycloid forms a shape with four cusps, known as a 'deltoid'. This property of having cusps makes the hypocycloid visually striking and mathematically significant. The hypocycloid is not just a theoretical construct; it has practical implications in real-world applications. One notable use of the hypocycloid is in the design of certain types of gears, known as hypocycloidal gears. These gears can transmit motion efficiently and are often used in mechanical systems where smooth motion is essential. The unique properties of the hypocycloid allow for a high degree of precision in these applications, making it an invaluable tool in engineering. In addition to its applications in mechanics, the hypocycloid also appears in physics, particularly in the study of waveforms and oscillations. The behavior of certain systems can be modeled using the hypocycloid, providing insights into the underlying principles governing their motion. This connection between geometry and physics highlights the interdisciplinary nature of mathematics and its relevance to our understanding of the natural world. Moreover, the hypocycloid has captured the imagination of artists and designers as well. Its unique shape and symmetry make it a popular subject in art and design, often inspiring patterns and motifs that can be found in various forms of creative expression. From architecture to graphic design, the hypocycloid continues to influence and inspire, showcasing the beauty of mathematics in the visual arts. In conclusion, the hypocycloid is much more than just a mathematical curve; it embodies a rich intersection of geometry, physics, and art. By exploring its properties and applications, we can appreciate the depth of its significance in both theoretical and practical contexts. Whether in the realm of engineering or the world of art, the hypocycloid serves as a reminder of the elegance and utility of mathematics in our everyday lives.

几何学的研究一直以来都吸引着数学家和科学家们。在许多可以探索的迷人形状和曲线中，hypocycloid（内摆线）作为一个特别有趣的例子脱颖而出。hypocycloid是由一个较小的圆在一个较大的固定圆内滚动时，圆上的一个点所描绘的曲线。这种迷人的几何图形不仅具有美学吸引力，而且在物理学和工程学的各种应用中也发挥着至关重要的作用。 为了更好地理解hypocycloid，让我们深入探讨它的数学定义和性质。hypocycloid的基本方程可以通过参数方程推导出来，这些方程描述了曲线上点的坐标。对于由半径为r的圆在半径为R的较大圆内滚动而生成的hypocycloid，其参数方程为： x(t) = (R - r) * cos(t) + r * cos((R - r)/r * t) y(t) = (R - r) * sin(t) - r * sin((R - r)/r * t) 这里，t表示随着较小圆沿较大圆内边缘滚动而随时间变化的参数。根据R与r的比率，生成的曲线可以呈现出不同的形状。例如，当比率为2:1时，hypocycloid形成一个具有四个尖点的形状，称为“菱形”。这种具有尖点的特性使得hypocycloid在视觉上引人注目，并在数学上具有重要意义。 hypocycloid不仅仅是一个理论构造；它在现实世界的应用中也具有实际意义。一个显著的用途是设计某些类型的齿轮，称为内摆线齿轮。这些齿轮能够高效传递运动，通常用于需要平稳运动的机械系统中。hypocycloid的独特特性使得这些应用中的精度非常高，使其成为工程领域中不可或缺的工具。 除了在机械学中的应用外，hypocycloid还出现在物理学中，尤其是在波形和振荡的研究中。某些系统的行为可以使用hypocycloid进行建模，从而提供对其运动规律的深入理解。这种几何与物理之间的联系突显了数学的跨学科特性及其在我们理解自然界中的相关性。 此外，hypocycloid也吸引了艺术家和设计师的想象力。其独特的形状和对称性使其成为艺术和设计中的热门主题，常常激发出可以在各种创作表达形式中找到的图案和主题。从建筑到图形设计，hypocycloid继续影响和启发，展示了数学在视觉艺术中的美感。 总之，hypocycloid不仅仅是一个数学曲线；它体现了几何、物理和艺术之间丰富的交集。通过探索它的性质和应用，我们可以欣赏到它在理论和实践背景下的重要性。无论是在工程领域还是艺术世界，hypocycloid都提醒我们数学在日常生活中的优雅和实用性。