Tehran University of Medical SciencesJournal of Craniomaxillofacial Research2345-54895120180422A mathematical analysis of Monson’s spherical theory and its clinical implications468478ENLOTOAdolphus OdogunDepartment of Restorative Dentistry Faculty of Dentistry Lagos State University College of Medicine Ikeja, Lagos, Nigeria.. dollyloto@Outlook.com2018042120180421Statement of Problem: The need to subject Monson’s spherical theory to further mathematical investigation is imperative in view of its clinical importance in dental occlusion.Purpose: The main goal of this study was to test the following hypotheses:1. Monson’s pyramid is the 3D unifying geometric figure for Bonwill’s, Spee’s, Monson’s, and Hall’s theories of occlusion.2. Monson’s sphere is made up of four regular tetrahedrons (Monson’s pyramids).3. The radius of Monson’s sphere is greater than the radius of circumsphere of Monson’s pyramid.Materials and Method: Bonwill’s triangle was used as the basis of geometrical model for constructing other 3D objects in this study; and it was assumed that the length of each side of Bonwill’s triangle was 10cm. A regular tetrahedron was constructed from Bonwill’s triangle. Then, linear and angular parameters were calculated for the constructed tetrahedron and its associated geometric figures. The calculated values were then subjected to statistical analysis using SPSS version 20; and comparisons of parameters were made using student’s t-test.Results: It was found that the theoretical geometrical figures that were proposed and demonstrated by Bon will, Spee, Monson and Hall were interconnected geometrically by means of a 3D geometric figure known as tetrahedron.Conclusion: Monson’s pyramid was established as the unifying 3D geometric figure for the analyzed geometric models of occlusion. Monson’s sphere is made up of four Monson’s pyramids while the radius of Monson’s sphere is also found to be greater than the radius of circumsphere ofMonson’s pyramid. The clinical significance of this study is that some important linear and angular parameters, that are required in the fabrication of dentures, can be calculated from a regular tetrahedron and its associated geometric figures based on individual patient’s bicondylar distance.Keywords: Connectivity, Mathematics, Occlusion, Theory.http://jcr.tums.ac.ir/index.php/jcr/article/view/207http://jcr.tums.ac.ir/index.php/jcr/article/download/207/206