hyperplane

hyperplane的音标为["haɪpəpleɪn] ，意思是超平面。

速记技巧：可以将每个单词的字母快速地拼写出来，即“ha ip ple in”。

Hyperplane这个词的英文词源可以追溯到拉丁语和希腊语，它指的是在二维或三维空间中，一个通过所有点的直线或曲面。这个词的主要变化形式是hyper-，它是一个前缀，表示“超过，过多”的意思。

相关单词：

Hyperbolic：这个词可以指超曲面的，它是在三维空间中的一种曲面，是一种特殊的曲面形式。

Hyperboloid：这个词可以指超球面，它是在三维空间中的一种形状，类似于球面但具有更多的维度。

Hypergeometric：这个词可以指超几何的，它是一种数学理论，研究在更高维度上的几何形状和分布。

Hyperreal：这个词可以指超实数，它是一种数学概念，用于描述比实数更大的数集。

Hyperspace：这个词可以指超空间，它是空间概念的延伸，用于描述更高维度的空间。

这些词在描述高维空间和几何学方面非常有用，它们可以帮助我们更好地理解复杂数学概念。例如，超几何分布可以用于研究在多维数据中的模式和分布，而超曲面则可以用于描述在更高维度上的形状和结构。

常用短语：

1. hyperplane boundary

2. hyperplane arrangement

3. hyperplane section

4. hyperplane invariant

5. hyperplane complement

6. hyperplane duality

7. hyperplane arrangement variety

例句：

1. The boundary of a hyperplane arrangement is a smooth submanifold of the ambient space. （超平面排列的边界是嵌入在邻域中的光滑子流形。）

2. The intersection of two hyperplanes is a point or a line. （两个超平面的交集是一个点或一条线。）

3. The hyperplane section of a smooth manifold is a smooth submanifold of the same dimension. （光滑流形在超平面上的截面是同维的子流形。）

英文小作文：

Title: The Mystery of Hyperplanes

Hyperplanes play an important role in many branches of mathematics, from linear algebra to computational geometry. They are like magical tools that can cut through complex shapes and structures to reveal their inner workings.

Think of a hyperplane as a powerful knife that slices through a three-dimensional world, exposing its inner secrets. When we intersect a smooth manifold with a hyperplane, we obtain a new submanifold of the same dimension, which can be used to study the structure and properties of the original object.

Hyperplanes also provide us with tools to understand and manipulate mathematical objects in higher dimensions. They serve as boundaries, arrangements, and sections that help us gain a deeper understanding of mathematical structures and their relationships with each other.

In summary, hyperplanes are mysterious yet powerful tools that can unlock the secrets of the mathematical world. They are like magical portals that connect different dimensions and help us explore and understand the beauty and complexity of mathematical structures.