hyperbola

简明释义

英[haɪˈpɜːbələ]美[haɪˈpɜːrbələ]

n. [数] 双曲线

复 数 h y p e r b o l a s 或 h y p e r b o l a e

英英释义

单词用法

同义词

反义词

例句

1.It is indicated that the stress-strain relationship under the excitation of vertical and torsional vibration can be characterized with a hyperbola curve.

试验结果表明，煤灰土在纵向和扭转振动时的动应力-应变关系均满足双曲线关系。

2.The demand curve is thus an equilateral hyperbola.

因此需求曲线是等轴双曲线。

3.Firstly, it turns up that the hyperbola-structured narrative line of War and Peace makes itself clearly on the advance of time, the process of history and the representation of theme.

首先，《战争与和平》呈现出一种双曲线式的叙事线条，使得故事的时间推进、历史进程和主题呈现很明晰。

4.Hyperbola from Four Points.

由四点作双曲线。

5.In order to simplify the procedure, we use the arc which radius is the radius of the larger circular cylinder to replace the hyperbola.

有时，为了简化作图，往往采用以大圆柱半径为半径的圆弧代替双曲线近似画出。

6.Greek mathematician who first defined the conic sections called the parabola, hyperbola, and ellipse.

阿普罗涅斯：古希腊数学家，他最早定义了称为抛物线、双曲线和椭圆的圆锥形部分。

7.And visually what we're accomplishing is somehow to take the hyperbola, and take a point on the hyperbola, and figure out some tangent line.

从视觉上看，我们要做的是，想办法，在这个反函数，在反函数上取一个点，设法找出切线。

8.The graph of a hyperbola consists of two separate curves that open away from each other.

一个 双曲线 的图形由两个分开的曲线组成，这些曲线彼此远离。

9.In conic sections, a hyperbola is one of the four types, along with circles, ellipses, and parabolas.

在圆锥曲线中，双曲线 是四种类型之一，其他类型包括圆、椭圆和抛物线。

10.The equation of a standard hyperbola is usually written in the form (x²/a²) - (y²/b²) = 1.

标准 双曲线 的方程通常写成 (x²/a²) - (y²/b²) = 1 的形式。

11.In mathematics, a hyperbola is defined as the set of all points where the difference of the distances to two fixed points is constant.

在数学中，双曲线 被定义为所有点的集合，这些点到两个固定点的距离差是恒定的。

12.In physics, the trajectory of certain objects can be modeled using a hyperbola.

在物理学中，某些物体的轨迹可以用 双曲线 来建模。

作文

The concept of a hyperbola is fundamental in the field of mathematics, particularly in geometry and algebra. A hyperbola is defined as a type of conic section that appears when a plane intersects both nappes of a double cone. This fascinating shape can be visualized as two separate curves that mirror each other, opening either horizontally or vertically. The standard equation of a hyperbola can be expressed in the form (x²/a²) - (y²/b²) = 1 for a horizontally opening hyperbola, or (y²/a²) - (x²/b²) = 1 for a vertically opening hyperbola. Here, 'a' and 'b' are constants that determine the shape and size of the hyperbola.Understanding hyperbolas goes beyond their geometric representation; they also have practical applications in various fields. For instance, in physics, the paths of certain celestial bodies can be modeled using hyperbolas. When an object travels fast enough to escape the gravitational pull of a planet, its trajectory can often describe a hyperbola. This characteristic makes hyperbolas essential in astrodynamics and space exploration.In addition to their applications in physics, hyperbolas have significant implications in engineering and architecture. Structures that require precise angles and measurements often utilize the principles of hyperbolas to ensure stability and strength. For example, in the design of bridges and arches, engineers might use the properties of a hyperbola to distribute weight evenly and enhance the durability of the structure.Moreover, hyperbolas appear in various technologies, including satellite dishes and antennas. The reflective properties of a hyperbola allow signals to be focused on a single point, optimizing communication and data transmission. This principle is crucial in modern telecommunications, where efficient signal processing is paramount.In mathematics education, students often encounter hyperbolas in their studies of conic sections. Learning about hyperbolas not only helps students understand advanced mathematical concepts but also encourages critical thinking and problem-solving skills. By exploring the properties and equations associated with hyperbolas, students gain insights into the beauty and complexity of mathematics.Furthermore, hyperbolas can be found in the world of art and design. Artists and architects often draw inspiration from geometric shapes, including hyperbolas, to create visually appealing works. The elegance of a hyperbola can be seen in various artistic expressions, from sculptures to paintings, showcasing the intersection of mathematics and creativity.In conclusion, the hyperbola is more than just a mathematical concept; it embodies a rich tapestry of applications across different disciplines. Whether in science, engineering, education, or art, hyperbolas serve as a reminder of the interconnectedness of knowledge and the importance of understanding mathematical principles in our everyday lives. By appreciating the significance of hyperbolas, we can foster a deeper appreciation for the beauty of mathematics and its relevance in shaping our world.

在数学领域，双曲线的概念是基础，尤其是在几何和代数中。双曲线被定义为一种圆锥曲线，当一个平面与双圆锥的两个部分相交时出现。这种迷人的形状可以想象成两个彼此镜像的独立曲线，水平或垂直打开。双曲线的标准方程可以用形式 (x²/a²) - (y²/b²) = 1 表示，表示水平打开的双曲线，或者 (y²/a²) - (x²/b²) = 1 表示垂直打开的双曲线。这里的 'a' 和 'b' 是常数，决定了双曲线的形状和大小。理解双曲线不仅仅局限于它们的几何表现；它们在各个领域也有实际应用。例如，在物理学中，某些天体的路径可以用双曲线建模。当一个物体以足够快的速度逃离行星的引力时，它的轨迹往往可以描述为一条双曲线。这一特性使得双曲线在天体动力学和太空探索中至关重要。除了在物理学中的应用，双曲线在工程和建筑中也具有重要意义。需要精确角度和测量的结构通常利用双曲线的原理，以确保稳定性和强度。例如，在桥梁和拱门的设计中，工程师可能会使用双曲线的性质来均匀分配重量，并增强结构的耐久性。此外，双曲线出现在各种技术中，包括卫星天线和天线。双曲线的反射特性使信号能够集中在一个点上，优化通信和数据传输。这一原理在现代电信中至关重要，因为高效的信号处理是重中之重。在数学教育中，学生们经常在圆锥曲线的学习中遇到双曲线。了解双曲线不仅帮助学生理解高级数学概念，还鼓励批判性思维和解决问题的能力。通过探索与双曲线相关的性质和方程，学生们能够深入了解数学的美和复杂性。此外，双曲线还可以在艺术和设计的世界中找到。艺术家和建筑师经常从几何形状中汲取灵感，包括双曲线，以创造视觉上吸引人的作品。双曲线的优雅可以在各种艺术表达中看到，从雕塑到绘画，展示了数学与创造力的交汇。总之，双曲线不仅仅是一个数学概念；它在不同学科之间编织了一幅丰富的应用图景。无论是在科学、工程、教育还是艺术中，双曲线都提醒我们知识的相互联系，以及理解数学原理在我们日常生活中的重要性。通过欣赏双曲线的重要性，我们可以培养对数学之美及其在塑造我们世界中的相关性的更深刻的欣赏。