dihedral angle

简明释义

二面角

英英释义

例句

1.In molecular chemistry, the dihedral angle 二面角 can affect the properties of a compound.

在分子化学中，dihedral angle 二面角 会影响化合物的性质。

2.In geometry, the dihedral angle 二面角 between two planes is crucial for determining the shape of polyhedra.

在几何学中，两个平面之间的dihedral angle 二面角 对于确定多面体的形状至关重要。

3.When constructing a model, it is important to measure the dihedral angle 二面角 accurately to ensure stability.

在构建模型时，准确测量dihedral angle 二面角 是确保稳定性的重要因素。

4.The dihedral angle 二面角 of a tetrahedron is essential for understanding its geometry.

四面体的dihedral angle 二面角 对理解其几何形状至关重要。

5.The dihedral angle 二面角 in a cube is always 90 degrees.

立方体中的dihedral angle 二面角 总是90度。

作文

The concept of a dihedral angle is fundamental in both geometry and various fields of science, including chemistry and physics. A dihedral angle, defined as the angle between two intersecting planes, plays a crucial role in understanding the three-dimensional structure of molecules and the spatial arrangement of atoms. In simpler terms, it can be visualized as the angle formed when two flat surfaces meet along a common edge. This geometric property is not only essential for mathematicians but also for chemists who study molecular shapes and interactions. In chemistry, the dihedral angle helps describe the conformation of molecules. For instance, in organic compounds, the arrangement of atoms around a central bond can significantly affect the compound's reactivity and properties. The staggered and eclipsed conformations of ethane, which are determined by its dihedral angle, illustrate this concept well. When the hydrogen atoms on adjacent carbon atoms are positioned as far apart as possible, the dihedral angle is at 60 degrees, resulting in a staggered conformation that is more stable. In contrast, when these atoms are aligned directly behind one another, the dihedral angle becomes 0 degrees, leading to an eclipsed conformation that is less stable due to increased steric hindrance.Understanding dihedral angles is also important in the field of materials science. The mechanical properties of materials can be influenced by the angles between their molecular chains. For example, polymers with specific dihedral angles may exhibit enhanced flexibility or strength, which can be critical for applications in engineering and manufacturing. Researchers often manipulate these angles during the synthesis of new materials to achieve desired characteristics.In the realm of architecture and design, the dihedral angle is equally significant. Architects must consider the angles between walls and roofs to ensure structural integrity and aesthetic appeal. The interplay of dihedral angles in the design of buildings can create visually stunning effects while also impacting the functionality of the space. For example, the angles at which light enters a room can affect the overall ambiance and energy efficiency.Moreover, the mathematical study of dihedral angles extends into higher dimensions, where they help define the relationships between various geometric shapes. In polyhedra, the dihedral angles between faces can influence the shape's volume and surface area, making it a key consideration in various mathematical problems and proofs.In conclusion, the dihedral angle is a vital concept that transcends multiple disciplines, from chemistry to architecture. Its implications are far-reaching, affecting everything from molecular stability to the structural integrity of buildings. By understanding and applying the principles of dihedral angles, scientists, engineers, and architects can innovate and create more effective solutions in their respective fields. As we continue to explore the intricacies of geometry and its applications, the dihedral angle will undoubtedly remain a topic of great importance and interest.

二面角的概念在几何学以及包括化学和物理学在内的多个科学领域中都是基础性的。二面角被定义为两个相交平面之间的角度，它在理解分子的三维结构和原子的空间排列方面起着至关重要的作用。简单来说，它可以被视为当两个平面相遇时形成的角度。这一几何属性不仅对数学家至关重要，对研究分子形状和相互作用的化学家同样重要。在化学中，二面角有助于描述分子的构象。例如，在有机化合物中，围绕中心键的原子排列会显著影响该化合物的反应性和特性。乙烷的交错构象和重叠构象很好地说明了这一概念。当相邻碳原子上的氢原子尽可能远离彼此时，二面角为60度，形成更稳定的交错构象。相反，当这些原子直接对齐时，二面角为0度，导致不太稳定的重叠构象，因为增加了立体阻碍。理解二面角在材料科学领域也同样重要。材料的机械性能可能受到其分子链之间角度的影响。例如，具有特定二面角的聚合物可能表现出增强的柔韧性或强度，这对工程和制造中的应用至关重要。研究人员经常在新材料的合成过程中操纵这些角度，以实现所需的特性。在建筑和设计领域，二面角同样重要。建筑师必须考虑墙壁和屋顶之间的角度，以确保结构的完整性和美学吸引力。建筑设计中二面角的相互作用可以创造出视觉上令人惊叹的效果，同时影响空间的功能性。例如，光线进入房间的角度可以影响整体氛围和能效。此外，二面角的数学研究扩展到更高的维度，在那里它们帮助定义各种几何形状之间的关系。在多面体中，面之间的二面角可以影响形状的体积和表面积，使其成为各种数学问题和证明中的关键考虑因素。总之，二面角是一个跨越多个学科的重要概念，从化学到建筑，其影响深远，涉及从分子稳定性到建筑结构完整性的方方面面。通过理解和应用二面角的原理，科学家、工程师和建筑师可以在各自的领域中创新并创造出更有效的解决方案。随着我们继续探索几何学及其应用的复杂性，二面角无疑将继续成为一个重要且引人关注的话题。