雙曲抛物面的意思、翻譯和例句

是什麼意思

「雙曲抛物面」是一種二次曲面,其數學方程式通常為 z = (x^2/a^2) - (y^2/b^2),其中 a 和 b 是常數。這種曲面在數學、物理和工程學中有著廣泛的應用,特別是在描述某些類型的拋物線和雙曲線的形狀時。它具有特殊的幾何性質,並且在光學、建築結構以及其他科學領域中經常被用來設計和分析。

依照不同程度的英文解釋

  1. A specific type of surface in geometry.
  2. A shape formed by curves in three dimensions.
  3. A surface that looks like a bowl or a saddle.
  4. A surface created by moving a parabola along a straight line.
  5. A surface that has properties of both hyperbolas and parabolas.
  6. A type of surface that can be described mathematically with specific equations.
  7. A geometric figure that combines features of parabolic and hyperbolic shapes.
  8. A mathematical surface that is utilized in various scientific applications.
  9. A complex surface that is defined by specific quadratic equations in three-dimensional space.
  10. A unique geometric surface that is formed by the intersection of certain curves.

相關英文單字或片語的差別與用法

1:Hyperbolic Paraboloid

用法:

這是雙曲抛物面的正式名稱,常用於數學和工程學中。它的形狀像一個馬鞍,並且具有兩個不同的曲率方向。在建築設計中,這種形狀常被用來創造美觀且結構穩定的屋頂或其他結構。

例句及翻譯:

例句 1:

這座建築的屋頂設計採用了雙曲抛物面,展現出獨特的美感。

The roof design of this building features a hyperbolic paraboloid, showcasing a unique aesthetic.

例句 2:

工程師們利用雙曲抛物面來設計強度更高的結構。

Engineers use hyperbolic paraboloids to design structures with greater strength.

例句 3:

在數學課上,我們學習了雙曲抛物面的性質和應用。

In math class, we studied the properties and applications of hyperbolic paraboloids.

2:Saddle Surface

用法:

這是雙曲抛物面的另一種描述方式,因為它的形狀類似於馬鞍。這種表面在數學中具有重要性,因為它是最基本的非平坦表面之一。它的幾何特性使其在物理學和工程學中有著廣泛的應用。

例句及翻譯:

例句 1:

這個模型展示了馬鞍面(雙曲抛物面)的幾何特性。

This model demonstrates the geometric properties of a saddle surface (hyperbolic paraboloid).

例句 2:

馬鞍面在機械設計中常被用來分析應力分佈。

Saddle surfaces are often used in mechanical design to analyze stress distribution.

例句 3:

數學家們對馬鞍面的研究促進了對非線性系統的理解。

Research on saddle surfaces by mathematicians has advanced the understanding of nonlinear systems.