iMedPub Journals http://www.imedpub.com/ 2015 Vol. 1 No. 1:1 1 This article is available in: http://periodontics-prosthodontics.imedpub.com/ Periodontics and Prosthodontics: Open Access ISSN 2471-3082 Short Communication DOI: 10.21767/2471-3082.100001 Introducton The Miriam Webster online dictonary describes the catenary curve as: “the curve assumed by a cord of uniform density and cross-secton that is perfectly fexible but not capable of being stretched and that hangs freely from two fxed points”. It was frst described by MacConaill and Scher [1], who suggested that normal human dental arches conform closely to a catenary curve. Scot [2], in a paper using a catenometer on dried skulls, concluded that the lower border of the mandible more closely follows a catenary curve rather than the dental arches. Currier’s [3] study on the radiographs of 25 dental cast showed that the ellipse showed a smaller variaton than the parabola when using the facial surfaces of the maxillary teeth, while results were reversed in the mandible. Musich and Ackerman [4], in a study of 20 mandibular casts using the mesial of the mandibular frst molar as the posterior hanging points, found the catenary method more reliable than the brass wire method when estmatng the available arch perimeter. Pepe [5] used complex mathematcal formulae to delineate the maxillary and mandibular arch forms of seven children and found that the defning anatomic tooth landmarks were inaccurate. Rudge [6], in a narratve review in 1982, advised cauton “when treatng individuals to a mathematcally derived ideal and when making arch wires to specifc “ideal” shapes”. Batagel [7] evaluated the study casts of 35 children utlizing distal molar contacts and found that while the catenary curve approximated the arch forms reliably, it did not work well on square arches. Treviño [8] used glass beads atached to the buccal surfaces of mandibular teeth on 63 adolescents to estmate where the arch wires should be and found diferent forms; while the authors concluded that there was no representatve form, their Figure 2, showing the graphic representaton of the hundred and 26 curve elements appears catenary. Sicher and DuBrul [9] described the mandibular arch as parabolic and Stanton found that 25% of the arches he studied were parabolic. Merriam-Webster defnes the The Catenary Curve: A Guide to Mandibular Arch Form Abstract This artcle revisits a pre-existng geometric concept, the catenary curve, redefnes its dental applicaton and proposes it as a useful aid in visualizing the mandibular dental arch form both clinically and in CADCAM design. Keywords: Catenary curve; Parabolic curve; CAD-CAM; Artfcial tooth placement; Mandibular arch form Received: November 09, 2015; Accepted: November 17, 2015; Published: November 20, 2015 parabola as: “a plane curve generated by a point moving so that its distance from a fxed point is equal to its distance from a fxed line: the intersecton of a right circular cone with a plane parallel to an element of the cone.” Although most previous studies were performed by orthodontsts with the intent of designing arch wires, dental arch forms are undoubtedly just as important to prosthodontsts. The orthodontc literature focused on the frst molars as the fxed point, which is problematc for the restoratve dentst as they are rarely in an ideal positon and usually missing or in need of a restoraton. The retromolar pad, a commonly used, relatvely stable anatomic landmark is proposed as an optmal choice. Having three points to work with, the two fxed posterior “hang points” and the incisal edges of the mandibular central incisors, allows the visualizaton of the mandibular arch form which falls into a symmetric curve. As shown in Figure 1 (an intact dentton) and 2 (an artfcial dentton), the parabolic curve, when superimposed on the mandibular teeth, does not ft as well as the catenary curve if one utlizes the buccal cusps of the mandibular posterior teeth as a guide. What can be debated is that since the mid-retro molar pad is the suggested posterior “hang point”, and having the central fossae of the posterior teeth over the crest of the ridge is an of used anatomic landmark, then perhaps the parabolic curve would be more useful is planning the inital artfcial tooth placement? What is unarguable is that all of the buccal cusps of the natural Gary Goldstein 1 , Yash Kapadia 2 , Terry Y Lin 1 and Paul Zhivago 1 1 Department of Prosthodontcs, New York University College of Dentstry, New York, USA 2 Former Resident Advanced Educaton Program in Prosthodontcs, New York University College of Dentstry, New York, USA Corresponding author: Gary Goldstein  gary.goldstein@nyu.edu Department of Prosthodontcs, New York University College of Dentstry, 308 Second Ave, NY 10010, New York, USA. Citation : Goldstein G (2015) The Catenary Curve: A Guide to Mandibular Arch Form. Periodon Prosthodon 1: 1.