Here yields a relative error of at most 1.061%; a value of is optimal for nearly spherical ellipsoids, with a relative error of at most 1.178%. In the "flat" limit of "c" much smaller than "a", "b", the area is approximately 2π"ab", equivalent to . The intersection of a plane and a sphere is a circle (or is reduced to a single point, or is empty). Any ellipsoid is the image of the unit sphere under some affine transformation, and any plane is the image of some other plane under the same transformation. So, because affine transformations map circles to ellipses, the intersection of a plane with an ellipsoid is an ellipse or a single point, or is empty. Obviously, spheroids contain circles. This is also true, but less obvious, for triaxial ellipsoids (see Circular section). "Given:" Ellipsoid formula_27 and the plane with equation formula_28 which have an ellipse in common. "Wanted:" Three vectors formula_29 (center) and formula_30 (conjugate vectors), such that the ellipse can be represented by the parametric equation  "Solution:" The scaling formula_32 transforms the ellipsoid onto the unit sphere formula_33 and the given plane onto the plane with equation formula_34. Let formula_35 be the Hesse normal form of the new plane and formula_36 its unit normal vector. Hence formula_37 is the "center" of the intersection circle and formula_38 its radius (see diagram). Where formula_39, let formula_40 (The plane is horizontal!) Where formula_41, let formula_42  In any case, the vectors formula_43 are orthogonal, parallel to the intersection plane and have length formula_44 (radius of the circle). Hence the intersection circle can be described by the parametric equation formula_45  The reverse scaling (see above) transforms the unit sphere back to the ellipsoid and the vectors formula_46 are mapped onto vectors formula_47, which were wanted for the parametric representation of the intersection ellipse. How to find the vertices and semi-axes of the ellipse is described in ellipse. "Example:" The diagrams show an ellipsoid with the semi-axes formula_48 which is cut by the plane formula_49  The pins-and-string construction of an ellipsoid is a transfer of the idea constructing an ellipse using two pins and a string (see diagram).