Data Set For Computation Of Maxillary Arch Perimeter With Ramanujan's Equation For Ellipse In Different Skeletal...

Every practicing orthodontist today is aware of the importance of considering arch form in the attainment of a functional orthodontic correction [1]. Arch perimeter or circumference prediction is an essential component when Tooth Size Arch Length Discrepancy (TSALD) is estimated. Arch perimeter is the distance from mesial contact of the permanent molar on one side to the mesial contact of the permanent molar on the other side, with the line connecting the buccal/incisor tip points in the intervening teeth. This is most evident when seeking to resolve dental crowding or arch-length discrepancy (ALD) [2]. The shape of the arch form of maxillary and mandible resembles that of the various geometric forms such as including ellipse, parabola, hyperbola, and catenary curve [3], [4], [5], [6]. Ellipse is the best form that fits the shape of the Maxillary arch [1,2]. The mathematical equation formulated by Srinivasan Ramanujan in 1914 for widely considered to be the most accurate for calculation of the circumference of an ellipse is [7]. The computation of the circumference of the ellipse by this equation requires two values- 'a' and 'b,' the semi-major and semi-minor axis [half of the major axis and minor axis of the ellipse] respectively [8]. The perimeter (P) of an ellipse is given by the formulae; = π(a+b){1+(3h/(10-√(4-3h))}; where h=(a-b)²/(a+b)² and calculated Maxillary arch perimeter (CP) =1/2 P. This necessitates a complex series of steps, and to overcome this, a statistical formula is developed by algorithm steps for mathematical equation where perimeter can be directly obtained by just two inputs 'a' and 'b' in excel sheet. We correlated this calculated arch perimeter (CP) with directly measured perimeter (MP) and marginal difference estimated in three different classes of malocclusion.