A regular polygon is a special type of polygon with two important properties. First, it is equilateral, meaning all sides have the same length. Second, it is equiangular, meaning all interior angles are equal. Examples include triangles, squares, pentagons, hexagons, and octagons.
正多边形是几何学中的重要概念。它是指所有边长相等、所有内角相等的多边形。正多边形具有完美的对称性，从中心向各个顶点画线段，这些线段长度都相等，称为外接圆半径。
正多边形具有三个基本性质。首先是边长相等，我们可以看到每条边都标记为s，表示长度相同。其次是内角相等，比如正方形的四个内角都是90度。最后是对称性，正多边形既有旋转对称性，也有轴对称性。
在日常生活中，我们经常遇到各种正多边形。正三角形有3条相等的边，正方形有4条相等的边，正五边形有5条相等的边，正六边形有6条相等的边，正八边形有8条相等的边。边数越多的正多边形看起来越接近圆形。
正多边形的内角有固定的计算公式。内角和等于n减2乘以180度，其中n是边数。每个内角的度数等于内角和除以边数。以正五边形为例，内角和是540度，每个内角是108度。
正多边形在现实生活中有广泛的应用。在建筑设计中，我们可以看到蜂窝状的正六边形结构，这种设计既美观又节省材料。在工程技术中，螺母通常采用正六边形设计。在艺术创作和自然界中，正多边形的对称美也随处可见。
Regular polygons demonstrate the fundamental properties of equal sides and equal angles. A triangle has three equal sides and three 60-degree angles. A square has four equal sides and four 90-degree angles. A pentagon has five equal sides and five 108-degree angles. As the number of sides increases, each interior angle becomes larger, and the polygon approaches the shape of a circle.
Regular polygons have a fixed formula for calculating interior angles. The sum of all interior angles equals n minus 2, multiplied by 180 degrees, where n is the number of sides. Each interior angle equals this sum divided by n. For example, a pentagon has an interior angle sum of 540 degrees, so each angle measures 108 degrees.
Regular polygons have countless applications in our daily lives. In architecture, hexagonal honeycomb patterns are used for their strength and efficiency. In engineering, octagonal shapes are common in nuts, bolts, and gears. Artists use regular polygons to create beautiful symmetric patterns. Even in nature, we see regular polygons in snowflakes and crystal structures, demonstrating the fundamental importance of these geometric forms.