nephroid

简明释义

英[ˈnefrɔɪd]美[ˈnefrɔɪd]

adj. 肾形的

英英释义

单词用法

同义词

反义词

例句

1.Construct rotating nephroid and three-cusped epicycloid while remaining orthogonal to each other.

作旋转的肾脏线和旋转的三瓣外摆线，且彼此维持正交。

2.Construct rotating nephroid and three-cusped epicycloid while remaining orthogonal to each other.

作旋转的肾脏线和旋转的三瓣外摆线，且彼此维持正交。

3.Doctors often use the term nephroid when discussing kidney shapes in medical imaging.

医生在讨论医学影像中的肾脏形状时常用术语nephroid。

4.The shape of the kidney can be described as a nephroid, which means resembling a kidney.

肾脏的形状可以描述为nephroid，这意味着类似于肾脏。

5.In art, some sculptures take on a nephroid form, mimicking the organic shapes found in nature.

在艺术中，一些雕塑呈现出nephroid的形状，模仿自然界中的有机形状。

6.The mathematician illustrated a nephroid curve on the board to explain its properties.

数学家在黑板上展示了一个nephroid曲线来解释其特性。

7.In geometry, a nephroid is a specific type of curve that resembles the outline of a kidney.

在几何学中，nephroid是一种特定类型的曲线，类似于肾脏的轮廓。

作文

The beauty of mathematics often lies in its ability to describe complex shapes and forms using simple equations. One such fascinating shape is the nephroid, a curve that has intrigued mathematicians and artists alike. The term nephroid comes from the Greek word 'nephros,' meaning kidney, which aptly describes the kidney-like shape of this curve. The nephroid can be defined as a specific type of epicycloid, formed by the path traced by a point on the circumference of a smaller circle as it rolls around the outside of a larger fixed circle. This rolling motion creates a smooth, flowing curve that resembles the contours of a kidney bean.To better understand the nephroid, we can look at its mathematical properties. The equation for the nephroid in polar coordinates is given by r(θ) = a(1 + cos(θ)), where 'a' is a constant that determines the size of the curve. When plotted, the nephroid exhibits a unique symmetry and can be seen to have two distinct lobes, making it visually striking. This symmetry is not only aesthetically pleasing but also holds significance in various fields of science and engineering.In nature, we can observe forms similar to the nephroid in the shapes of certain flowers, leaves, and even the outlines of some fruits. These natural occurrences of the nephroid shape highlight the interconnectedness of mathematics and the natural world. Artists have also drawn inspiration from the nephroid, utilizing its graceful curves in their works to convey movement and fluidity.The exploration of the nephroid extends beyond pure mathematics; it has applications in physics, particularly in the study of waves and oscillations. The principles underlying the formation of the nephroid can be applied to understand various phenomena, such as sound waves and light patterns. This demonstrates how a seemingly simple mathematical concept can have profound implications across different disciplines.Furthermore, the nephroid serves as an excellent example for students learning about curves and their properties. By studying the nephroid, students can gain insights into the concepts of curvature, symmetry, and the relationship between geometry and algebra. Engaging with such shapes can foster a deeper appreciation for mathematics, encouraging learners to see it not just as abstract numbers and formulas, but as a language that describes the world around us.In conclusion, the nephroid is more than just a mathematical curiosity; it is a bridge connecting mathematics, nature, art, and science. Its unique shape and properties invite exploration and inspire creativity. Whether one encounters the nephroid in a classroom, a piece of artwork, or a botanical garden, it serves as a reminder of the beauty and complexity inherent in both mathematics and the world we inhabit.

数学的美在于它能够用简单的方程描述复杂的形状和形式。其中一个迷人的形状是nephroid，这个曲线吸引了数学家和艺术家的兴趣。nephroid一词来源于希腊语单词'nephros'，意为肾脏，这恰如其分地描述了这个曲线的肾脏状形状。nephroid可以被定义为一种特定类型的外接圆，由一个较小的圆周围滚动时，一个点所描绘的路径形成。这种滚动运动创建了一个平滑流畅的曲线，类似于肾豆的轮廓。为了更好地理解nephroid，我们可以看看它的数学性质。nephroid在极坐标中的方程为r(θ) = a(1 + cos(θ))，其中'a'是一个常数，决定了曲线的大小。当绘制时，nephroid展现出独特的对称性，并且可以看到它有两个明显的叶瓣，使其在视觉上引人注目。这种对称性不仅令人愉悦，还在科学和工程的各个领域具有重要意义。在自然界中，我们可以观察到与nephroid相似的形状出现在某些花朵、叶子，甚至一些水果的轮廓中。这些自然界中出现的nephroid形状突显了数学与自然世界之间的相互联系。艺术家们也从nephroid中汲取灵感，利用其优雅的曲线在作品中传达运动和流动感。对nephroid的探索超越了纯数学，它在物理学中也有应用，特别是在波动和振荡的研究中。形成nephroid的原理可以应用于理解各种现象，如声波和光模式。这表明一个看似简单的数学概念可以在不同学科中产生深远的影响。此外，nephroid作为学生学习曲线及其属性的优秀示例。通过研究nephroid，学生可以深入了解曲率、对称性以及几何与代数之间的关系。参与这样的形状可以培养对数学的更深层次的欣赏，鼓励学习者将其视为描述我们周围世界的语言，而不仅仅是抽象的数字和公式。总之，nephroid不仅仅是一个数学奇观；它是连接数学、自然、艺术和科学的桥梁。它独特的形状和属性邀请探索并激发创造力。无论一个人在教室、艺术作品还是植物园中遇到nephroid，它都提醒我们数学和我们所居住的世界中固有的美和复杂性。