The curvature of a straight line is zero. Curvature measures how much a curve deviates from being straight. Since a straight line does not bend or deviate, its curvature is zero at every point
. Mathematically, curvature is defined as the rate of change of the unit tangent vector with respect to arc length along the curve. For a straight line, the unit tangent vector is constant and does not change as you move along the line, so the derivative of the unit tangent vector is zero, resulting in zero curvature
. In summary:
- Curvature κ=0\kappa =0κ=0 for a straight line.
- This is because the direction of the tangent vector does not change along a straight line.
- Hence, a straight line is a curve with zero curvature everywhere.
