degree of convexity

简明释义

凸起程度

英英释义

例句

1.The graphic designer adjusted the degree of convexity 凸性程度 in the logo to create a more dynamic look.

平面设计师调整了标志的degree of convexity 凸性程度以创造更具动态感的外观。

2.In finance, the degree of convexity 凸性程度 of a bond can indicate its sensitivity to interest rate changes.

在金融中，债券的degree of convexity 凸性程度可以指示其对利率变化的敏感性。

3.The engineer measured the degree of convexity 凸性程度 of the road curvature for safety assessments.

工程师测量了道路曲率的degree of convexity 凸性程度以进行安全评估。

4.The architect assessed the degree of convexity 凸性程度 of the building's design to ensure it met aesthetic standards.

建筑师评估了建筑设计的degree of convexity 凸性程度，以确保其符合美学标准。

5.A higher degree of convexity 凸性程度 in a function may indicate a greater potential for optimization.

函数中的更高degree of convexity 凸性程度可能表明更大的优化潜力。

作文

The concept of degree of convexity plays a significant role in various fields, including mathematics, economics, and even design. To understand this term, it is essential to first grasp what convexity means. In simple terms, a shape is considered convex if, for any two points within the shape, the line segment connecting them lies entirely within the shape. This property can be observed in everyday objects, such as a ball or a lens. The degree of convexity refers to how pronounced this curvature is. A higher degree of convexity indicates a more rounded shape, while a lower degree suggests a flatter form.In mathematics, particularly in optimization problems, the degree of convexity is crucial. Convex functions are those where a line segment connecting any two points on the graph of the function lies above or on the graph itself. This property ensures that any local minimum is also a global minimum, making these functions easier to analyze and optimize. For instance, in economics, utility functions often exhibit convexity, which reflects diminishing marginal returns. Here, the degree of convexity helps economists understand consumer behavior and make predictions about market trends.In design and architecture, the degree of convexity influences aesthetics and functionality. Curved surfaces can enhance the visual appeal of a structure, but they also affect light reflection and structural integrity. Architects must carefully consider the degree of convexity when designing buildings to ensure that they are both beautiful and practical. For example, the Sydney Opera House features a highly convex design that not only captivates viewers but also serves specific acoustic purposes.Moreover, in the realm of technology, especially in computer graphics and modeling, the degree of convexity is vital for rendering shapes accurately. When creating 3D models, designers often manipulate the degree of convexity to achieve desired effects. A model with a high degree of convexity will appear smooth and organic, while a lower degree might give it a more angular and mechanical look.Understanding the degree of convexity extends beyond theoretical applications; it has practical implications in everyday life. For example, consider the design of ergonomic furniture. The degree of convexity in a chair's backrest can significantly impact comfort and support. A chair with an optimal degree of convexity will conform to the natural curve of the spine, promoting better posture and reducing discomfort during prolonged use.In conclusion, the degree of convexity is a multifaceted concept that permeates various domains, from mathematics and economics to design and technology. Its importance cannot be overstated, as it not only aids in theoretical understanding but also influences practical applications in our daily lives. By appreciating the nuances of the degree of convexity, we can enhance our comprehension of the world around us and apply this knowledge to improve both functionality and aesthetics in numerous fields.

“凸性程度”这一概念在数学、经济学甚至设计等多个领域中起着重要作用。要理解这个术语，首先需要掌握凸性意味着什么。简单来说，如果在一个形状内的任意两点之间连接的线段完全位于该形状内部，则该形状被认为是凸的。这一特性可以在日常物体中观察到，例如球体或透镜。“凸性程度”指的是这种曲率的明显程度。较高的“凸性程度”表示形状更为圆润，而较低的程度则表明形状较平坦。在数学中，特别是在优化问题中，“凸性程度”至关重要。凸函数是指连接函数图上任意两点的线段始终位于图形之上或与图形重合的函数。这一特性确保了任何局部最小值也是全局最小值，从而使这些函数更易于分析和优化。例如，在经济学中，效用函数通常表现出凸性，反映了边际收益递减。在这里，“凸性程度”帮助经济学家理解消费者行为并预测市场趋势。在设计和建筑中，“凸性程度”影响着美学和功能性。曲面可以增强结构的视觉吸引力，但它们也会影响光线的反射和结构的完整性。建筑师在设计建筑时必须仔细考虑“凸性程度”，以确保建筑既美观又实用。例如，悉尼歌剧院的设计高度凸出，不仅吸引观众，还具有特定的声学目的。此外，在技术领域，尤其是在计算机图形和建模中，“凸性程度”对于准确渲染形状至关重要。在创建3D模型时，设计师经常操控“凸性程度”以实现所需效果。具有较高“凸性程度”的模型将显得光滑且有机，而较低的程度可能使其呈现出更为角度分明和机械化的外观。理解“凸性程度”超越了理论应用，它在我们的日常生活中具有实际意义。例如，考虑人体工程学家具的设计。椅背的“凸性程度”对舒适度和支撑性有显著影响。具有最佳“凸性程度”的椅子将符合脊柱的自然曲线，促进更好的姿势，并减少长时间使用时的不适感。总之，“凸性程度”是一个多方面的概念，渗透到数学、经济学、设计和技术等多个领域。其重要性不容小觑，因为它不仅有助于理论理解，还影响我们日常生活中的实际应用。通过欣赏“凸性程度”的细微差别，我们可以增强对周围世界的理解，并将这一知识应用于改善多个领域的功能性和美学。