title: Maxillary arch perimeter prediction using Ramanujan's equation for the ellipse.
abstract: BACKGROUND
  The prediction of arch perimeter gained when expanding the arch or proclining the anterior incisors is particularly important in the decision of tooth extraction vs nonextraction therapy for orthodontic treatment.
  
  
  METHODS
  Correlation of the measured perimeter of the maxillary dental arch and the calculated perimeter applying Ramanujan's equation for the perimeter of an ellipse was evaluated with 30 diagnostic casts of untreated maxillary dental arches. Both linear and circumferential measurements were made directly on the midbuccal surface of these maxillary arches.
  
  
  RESULTS
  Ramanujan's equation had a high level of correlation when comparing the measured perimeter of the maxillary dental arch and the calculated perimeter with the 0.01 level (1.2% error) using a 2-tailed t test. The results were applied to Ramanujan's equation to predict maxillary arch perimeter gained by expansion or proclination of the incisors.
  
  
  CONCLUSIONS
  The ellipse is an accurate geometric model of the maxillary arch form. The average amounts of maxillary arch perimeter gained were 0.73 mm per millimeter of intermolar expansion and 1.66 mm per millimeter of incisor protrusion.
authors: Program director, Division of Orthodontics and Dentofacial Orthopedics, Department of Dentistry, Maimonides Medical Center, Brooklyn, NY. Electronic address: dchung@maimonidesmed.org.
authors: David D
authors: DD
authors: Chung
authors: Private practice, Vancouver, Wash.
authors: Richard
authors: R
authors: Wolfgramm
mesh_terms: D000293:Adolescent; D000328:Adult; D000465:Algorithms; D002508:Cephalometry / Q000706:statistics & numerical data; D002648:Child; D003724:Dental Arch / Q000033:anatomy & histology*; D005260:Female; D005544:Forecasting; D006801:Humans; D007180:Incisor / Q000033:anatomy & histology; D008297:Male; D008437:Maxilla / Q000033:anatomy & histology*; D003765:Models, Dental; D008963:Molar / Q000033:anatomy & histology; D009811:Odontometry / Q000706:statistics & numerical data; D009971:Orthodontics, Corrective; D010347:Patient Care Planning; D014081:Tooth Extraction / Q000706:statistics & numerical data; D055815:Young Adult