Determining shapes and dimensions of dental arches for the use of straight-wire arches in lingual technique

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4296656/

The curve of dental arch in normal occlusion
https://www.aaup.edu/sites/default/files/Publications/40-The...

Dentition
The upper dental arch is housed in the alveolar arch of the premaxillae and maxillae. The lower dental arch is housed in the alveolar arches of the two halves of the mandible which in higher primates are always fused on the midline. The shape of the dental arches ranges from rectangular to semicircular or U-shaped depending on the species and/or sex of the animal. Dentition is usually described by quadrants of the mouth: right and left maxillary (upper) and right and left mandibular (lower) quadrants. Four classes of teeth (Butler, 1978) are evident in each quadrant of higher primates (Figure 4.6). From anterior (midline) to posterior these are incisor, canine, premolar, and molar (James, 1960; Marshall, 1933; Swindler, 2002).
https://www.sciencedirect.com/topics/veterinary-science-and-...

Several attempts have been made to defne an “ideal” arch form taking into cognizance the fact that dental arch is symmetric in nature and can be represented by an algebraic or geometric formula [1].
Te ideal lower arch form has been described as a slightly modifed equilateral triangle with the base representing the intercondylar width; the six anterior teeth are arranged on the arc of a circle, and the radius is equivalent to the width of canines and incisors combined [2, 3]. Other suggested arch forms include semi-ellipse [4], parabolic [5], and catenary form [6–8]. Other authors have suggested diferent forms for upper and lower arches; with the upper arch taking the form of an ellipse, and the lower arch a parabola [9].
https://bmcoralhealth.biomedcentral.com/track/pdf/10.1186/s1...