circumscribed polygon

简明释义

外切多边形

英英释义

例句

1.The architect designed the building to fit within a circumscribed polygon, ensuring that it maximizes the use of space.

建筑师设计了这座建筑，使其适合于一个外接多边形内，确保最大化空间的使用。

2.To calculate the area of a circumscribed polygon, you can use the formula involving the radius of the circumscribed circle.

要计算外接多边形的面积，可以使用涉及外接圆半径的公式。

3.In geometry class, we learned that a circumscribed polygon is a polygon that can be drawn around a circle, touching it at all vertices.

在几何课上，我们了解到外接多边形是一个可以画在圆周上的多边形，所有顶点都与圆相切。

4.In computer graphics, a circumscribed polygon can help in rendering shapes more efficiently.

在计算机图形学中，外接多边形可以帮助更高效地渲染形状。

5.The mathematician explained how a circumscribed polygon relates to its inscribed circle.

数学家解释了外接多边形与其内切圆之间的关系。

作文

In the realm of geometry, understanding various shapes and their properties is crucial for students and professionals alike. One important concept that often comes up in discussions about polygons is the idea of a circumscribed polygon. A circumscribed polygon is a polygon that is drawn around a circle, meaning that all its vertices touch the circumference of the circle. This unique relationship between the polygon and the circle offers a variety of interesting properties and applications that are worth exploring.To understand the significance of a circumscribed polygon, we must first consider the characteristics of the circle it is associated with. The circle serves as the boundary within which the polygon resides, and the center of the circle is also the center of the polygon when it is regular. For instance, if we take a regular hexagon, it can be inscribed in a circle such that each of its six vertices touches the circle. In this case, the hexagon is a perfect example of a circumscribed polygon.One of the most fascinating aspects of circumscribed polygons is their relationship with the radius of the circle. The distance from the center of the circle to any vertex of the circumscribed polygon is constant, equal to the radius of the circle. This property allows for the calculation of various measurements related to the polygon, including its area and perimeter. For example, the area of a regular circumscribed polygon can be calculated using the formula that incorporates the radius of the circle and the number of sides of the polygon.Moreover, circumscribed polygons are not limited to regular shapes. Irregular polygons can also be circumscribed around a circle, although the calculations and properties may differ. The concept of circumscription is essential in many fields, including architecture, engineering, and computer graphics, where precise measurements and relationships between shapes are necessary.In practical applications, circumscribed polygons can be seen in various designs and structures. For instance, in the design of roundabouts or circular parks, planners often use circumscribed polygons to ensure that pathways or roads are evenly distributed around a central point. This not only enhances aesthetic appeal but also improves functionality by allowing for smoother traffic flow.Furthermore, the study of circumscribed polygons extends into the realm of trigonometry. The angles formed at the vertices of the polygon can be analyzed using trigonometric functions, leading to deeper insights into the relationships between different shapes and their properties. This interplay between geometry and trigonometry exemplifies the interconnected nature of mathematical concepts.In conclusion, the concept of a circumscribed polygon is a fundamental aspect of geometry that provides valuable insights into the relationships between shapes. Whether in academic studies or real-world applications, understanding circumscribed polygons enhances our ability to analyze and create complex designs. As we continue to explore the world of geometry, the knowledge of circumscribed polygons will undoubtedly remain a vital tool in our mathematical toolkit.

在几何学领域，理解各种形状及其特性对学生和专业人士来说至关重要。一个常常在多边形讨论中出现的重要概念是外接多边形的概念。外接多边形是指一个多边形被画在一个圆周上，这意味着它的所有顶点都触及圆的周长。这个多边形与圆之间的独特关系提供了多种有趣的性质和应用，值得深入探讨。要理解外接多边形的重要性，我们首先必须考虑与之相关的圆的特性。圆作为多边形所处的边界，而圆的中心也是当多边形为正多边形时的多边形中心。例如，如果我们取一个正六边形，它可以被画在一个圆内，使得它的六个顶点都触及这个圆。在这种情况下，六边形就是外接多边形的完美例子。外接多边形最迷人的方面之一是它与圆半径之间的关系。从圆心到外接多边形任何顶点的距离是恒定的，等于圆的半径。这个特性允许我们计算与多边形相关的各种测量，包括面积和周长。例如，正外接多边形的面积可以通过包含圆的半径和多边形边数的公式来计算。此外，外接多边形并不限于规则形状。不规则多边形也可以被外接到一个圆周上，尽管计算和性质可能会有所不同。外接的概念在许多领域中都是必不可少的，包括建筑、工程和计算机图形学，在这些领域中，精确的测量和形状之间的关系是必要的。在实际应用中，外接多边形可以在各种设计和结构中看到。例如，在环形交叉口或圆形公园的设计中，规划者通常使用外接多边形来确保路径或道路均匀分布在中央点周围。这不仅增强了美学吸引力，还通过允许更平滑的交通流动来改善功能性。此外，外接多边形的研究扩展到了三角学的领域。多边形顶点形成的角度可以使用三角函数进行分析，从而深入了解不同形状及其性质之间的关系。这种几何与三角学之间的相互作用体现了数学概念的相互关联性。总之，外接多边形的概念是几何学的一个基本方面，为我们提供了关于形状之间关系的宝贵见解。无论是在学术研究还是现实世界的应用中，理解外接多边形都增强了我们分析和创造复杂设计的能力。随着我们继续探索几何学的世界，外接多边形的知识无疑将继续成为我们数学工具箱中的重要工具。