center of the torus, is the radius of the tube. Angle represents rotation around the tube, whereas represents rotation around the torus' axis of revolution. is known as the "major radius" and is known as the "minor radius". The ratio divided by is known as the "aspect ratio". The typical doughnut confectionery has an aspect ratio of about 3 to 2. An implicit equation in Cartesian coordinates for a torus radially symmetric about the -axis is or the solution of , where Algebraically eliminating the square root gives a quartic equation, The three classes of standard tori correspond to the three possible aspect ratios between and : When , the surface will be the familiar ring torus or anchor ring. corresponds to the horn torus, which in effect is a torus with no "hole". describes the self-intersecting spindle torus; its inner shell is a lemon and its outer shell is an apple When , the torus degenerates to the sphere. When , the interior of this torus is diffeomorphic (and, hence, homeomorphic) to a product of a Euclidean open disk and a circle. The volume of this solid torus and the surface area of its torus are easily computed using Pappus's centroid theorem, giving: These formulas are the same as for a cylinder of length and radius , obtained from cutting the tube along the plane of a small circle, and unrolling it by straightening out (rectifying) the line running around the center of the tube. The losses in surface area and volume on the inner side of the tube exactly cancel out the gains on the outer side. Expressing the surface area and the volume by the distance of an outermost point on the surface of the torus to the center, and the distance of an innermost point to the center (so that and ), yields As a torus is the product of two circles, a modified version of the spherical coordinate system is sometimes used. In traditional spherical coordinates there are three measures, , the distance from the center of the coordinate system, and and , angles measured from the center point. As a torus has, effectively, two center points, the centerpoints of the angles are moved; measures the same angle as it does in the spherical system, but is known as the "toroidal" direction. The center point of is moved to the center of , and is