“…Most researchers have focused on the normal or ideal dental arch and have used algebraic or geometric formulae to describe it. Such geometric figures and mathematical functions, most of which enforce symmetry, include: semicircle (10), ellipse (1,11), parabola (12), hyperbola (13), catenary curve (14), the cubic spline function (15), conic sections (8,16), polynomial European Journal of Orthodontics, 2016, 202-211 doi:10.1093/ejo/cjv019 Advance Access publication 3 April 2015 functions, including the fourth-order polynomial (17,18) and the sixth-order polynomial (7,9), Euclidean distance matrices (19), Fourier series (20), and the beta function (3,9). Mixed models have also been used, such as, ellipse and parabola (21), a semicircle joined to straight segments (10) and a combination of the polynomial, parabola and hyperbolic cosine functions (22).…”