 Universal parabolic constant

The Universal Parabolic Constant, often denoted by the symbol \( p \), is a mathematical constant defined as the ratio of the length of a parabola's arc segment to the length of its vertical projection. More specifically, for a parabola described by the equation \( y = x^2 \), the constant is derived from the comparison between the arc length of the curve and the distance along the vertical from the origin to a given point on the parabola.