bolradius

Bolradius refers to the radius of a circle that circumscribes a regular polygon. In simpler terms, imagine drawing a circle that passes through every vertex of a regular polygon. The distance from the center of that circle to any of the polygon's vertices is the bolradius. This concept is particularly relevant in geometry and trigonometry. For a regular n-sided polygon with side length 's', the bolradius 'R' can be calculated using the formula R = s / (2 * sin(pi/n)). This formula is derived by considering the isosceles triangle formed by two adjacent vertices of the polygon and the center of the circumscribing circle. The angle at the center of this triangle is 360/n degrees, or 2*pi/n radians. Bisecting this angle creates two right-angled triangles, allowing the use of trigonometric relationships to solve for R. The bolradius is always greater than or equal to half the apothem (the radius of the inscribed circle). When the polygon becomes very large, approaching a circle, the bolradius essentially becomes the radius of that circle.