Ramanujan's equation for calculation of Maxillary Arch perimeter

Published: 1 July 2020| Version 2 | DOI: 10.17632/ryc5y6c7k7.2
gowri sankar singaraju,
, praveen Reddy Jn


The data consists of calculated Maxillary Arch perimetre based on Ramanujan's equation of ellipsoid. The equation gives us the perimeter of the elliptical model that is fitted to the Maxillary arch. It requires measurement semi Major axis 'a' and semiminor axis 'b'. The equation is a complex mathematical expression. This mathematical expression is converted into a formula for automated data entry in excel sheet. The calculated arch perimetre(CP) derived mathematically is compared with the measured arch perimetre(MP) on the models manually. The Intermolar molar width(IMW), Inter Canine Width(ICW) , and Inter Molar width perpendicular were also measured. All these measurements can have an effect on the maxillary arch perimeter. The relationship between CP, MP and other parameters was assessed in three different classes of malocclusion. These models class I, Class II, Class III were selected based on certain cephalometric criteria. The distobuccal cusp of the second molar was marked. The midpoint between the central incisors is also marked. The horizontal distance between the left and right second molars at the cuspal points provides the IMW. The perpendicular distance from the midpoint of IMW line to the central point of incisors ( IMW Per) provides us the arch length. It also indicates the arch length that can be increased or decreased with the proclination or retroclination of the Central Incisors. The arch perimeter can be increased for gaining space during the correction of malocclusion by non-extraction means. The perimeter can be either increased by Increase in IMW or IMW per. The amount of space that can be gained is accurately derived by this mathematical expression.


Steps to reproduce

1. class I, class II class III models based on cephalometric criteria 2. identification of the midpoint of central incisor, Distobuccal cusp of the second molar 3. measurement of the IMW and IMW per equivalent to 'a'- semi major axis and 2'b'- twice the minor axis. 4. enter this values in the column with formula derived for perimeter of elliptical model. The half of this value denotes the Maxillary Arch perimeter that is calculated arch perimeter 5. The measured arch perimeter can be measured directly on the model with the help of a brass wire and the steel wire


Narayana Dental College


Algebraic Algorithm, Compliance in Orthodontics, Orthodontic Treatment Planning, Dental Biomechanics