Threehundredandsixtysided

A threehundredandsixtysided polygon, often referred to as a 360-gon, is a closed two-dimensional shape with 360 edges and 360 vertices. It belongs to the broader class of polygons known as *n*-gons, where *n* represents the number of sides. While polygons with fewer sides, such as triangles or quadrilaterals, are common in everyday geometry, polygons with hundreds of sides are primarily theoretical constructs due to their complexity and impracticality in real-world applications.

In a regular 360-gon, all sides are of equal length, and all interior angles are equal. The sum of the interior angles of any *n*-gon is given by the formula *(n − 2) × 180°*, meaning a regular 360-gon has interior angles summing to 358 × 180° or 64,440°. Each interior angle in a regular 360-gon measures approximately 178°, approaching the shape of a circle as the number of sides increases.

Threehundredandsixtysided polygons are often used in mathematical discussions about limits and approximations. As the number of sides in a polygon increases, the shape becomes increasingly similar to a circle, illustrating the concept of a circle as a polygon with an infinite number of sides. This property is useful in calculus and geometry, particularly in studying limits and the behavior of sequences.

While constructing a perfect 360-gon is impractical due to the precision required, computer graphics and mathematical modeling can approximate such shapes for illustrative or theoretical purposes. The study of high-sided polygons also extends into fields like computer-aided design (CAD) and computational geometry, where approximations of curved surfaces are necessary.