In mathematics, degree is defined as the power to which any variable of an algebraic expression is raised. For example, if the variable x is raised to the second power as x² then this single algebraic term is said to be a second degree expression. On the other hand, the expression x²y²z² is said to be a sixth degree term. Similarly, the expression xyis of the second degree. However, the inverse variation xy=kwhere k is the constant of variation is equivalently the simplest rational function. Therefore, by this definition the simplest rational function is always a second degree function. Moreover, every second degree function should have two solutions. However, the rational equation xy=x-y is an exception. On the contrary, it satisfies solutions of dual operations of both multiplication and subtraction. The algorithmic advantage of second degree rational given by 4xy=P-3-6x-2y is its ability to determine the primality of odd positive integer P. It is a prime if and only if there are no simultaneous integer solutions of both x and y. Equivalently, prime P can never be represented by an integer pair (x,y) of a given Cartesian coordinate system.

In a deeper mathematical sense, the subtlety of second degree rational having dual solutions, especially among conic sections, is unique for all hyperbolas. It is directly associated with the corresponding derivatives. The derivative of xy=kfor k positive unity is dy/dx=-1/x², implying two x’s with the same absolute value indicating negative slopes for the entire domain between negative and positive infinity. On the other hand, if k is negative unity then the slope is positive everywhere. Furthermore, since a given space-time event on a hyperbolic surface has infinite parallels with respect to a given worldline, it has the biggest advantage over Euclidean or Riemannian topology for representing the true space-time geometry of the physical universe. Consequently, the derivative given above indicates a general covariance with the inverse square law of forces for electrostatics, magnetostatics, as well as Newton’s gravity.