Curve Equations

Consider a curve defined by its radius and central angle. The tangent distance is the distance from the point of intersection to the curve's start or end point.

This tangent length depends on the curve's radius and the central angle, with its relationship defined through geometric analysis.

The length of the chord is the straight line connecting the curve's start and endpoints. This length is derived by visualizing the curve's endpoints as forming a triangle with the center, where the curve's radius serves as its sides.

The relationship between this triangle's angle and base gives the length of the chord.

The middle ordinate describes the maximum perpendicular distance between the straight connecting line and the curve itself.

This value is determined by examining the curve's depth relative to the connecting chord, using the relationship between the curve's radius and its offset at the midpoint.

The curve's total length is directly proportional to the central angle. It is calculated by understanding how the curve's angular extent relates to its radius, offering a measure of the arc's physical span.