The derivative of a quintic function is a quartic function. The standard forms for elliptic integrals involved the square roots of cubic and quartic polynomials. There exist more complicated algebraic solutions for cubic equations and quartic equations. Some cubic and quartic equations can be solved using trigonometry or hyperbolic functions. Eigenvalues of the Klein quartic have been calculated to varying degrees of accuracy. There are also formulas for the cubic and quartic equations. For a different parametrization and resulting quartic, see Lawrence. Intersections between spheres, cylinders, or other quadrics can be found using quartic equations. Here are examples of other geometric problems whose solution involves solving a quartic equation. Finding the distance of closest approach of two ellipses involves solving a quartic equation. The Higgs mechanism is based on a symmetry-breaking scalar field potential, such as the quartic. It has 60 vertices and 120 edges, and is a quartic graph Archimedean graph. He also acknowledges that it was Ferrari who found a way of solving quartic equations. This is an important aspect of the solutions of the differential equation for quartic potentials. The mass of the lightest Higgs boson is set by the Higgs "quartic coupling".