If the sphere is described by a parametric representation  one gets Clelia curves, if the angles are connected by the equation Special cases are: Viviani's curve (formula_40) and spherical spirals (formula_41). In navigation, a rhumb line or loxodrome is an arc crossing all meridians of longitude at the same angle. A rhumb line is not a spherical spiral. There is no simple connection between the angles formula_16 and formula_43. If a sphere is intersected by another surface, there may be more complicated spherical curves. The intersection of the sphere with equation formula_44 and the cylinder with equation formula_45 is not just one or two circles. It is the solution of the non linear system of equations   A sphere is uniquely determined by four points that are not coplanar. More generally, a sphere is uniquely determined by four conditions such as passing through a point, being tangent to a plane, etc. This property is analogous to the property that three non-collinear points determine a unique circle in a plane. Consequently, a sphere is uniquely determined by (that is, passes through) a circle and a point not in the plane of that circle. By examining the common solutions of the equations of two spheres, it can be seen that two spheres intersect in a circle and the plane containing that circle is called the radical plane of the intersecting spheres. Although the radical plane is a real plane, the circle may be imaginary (the spheres have no real point in common) or consist of a single point (the spheres are tangent at that point). The angle between two spheres at a real point of intersection is the dihedral angle determined by the tangent planes to the spheres at that point. Two spheres intersect at the same angle at all points of their circle of intersection. They intersect at right angles (are orthogonal) if and only if the square of the distance between their centers is equal to the sum of the squares of their radii. If and are the equations of two distinct spheres then is also the equation of a sphere for arbitrary values of the parameters and . The set of all spheres satisfying this equation is called a pencil of spheres determined by the original two spheres. In this definition a sphere is allowed to be a plane (infinite radius, center at infinity) and if both the original spheres are planes then all the spheres of the pencil are planes, otherwise there is only one plane (the radical plane) in the pencil.