A mathematical analysis of Monson's spherical theory and its clinical implications
Author(s):
Article Type:
Research/Original Article (دارای رتبه معتبر)
Abstract:
Statement of Problem: The need to subject Monsons spherical theory to further mathematical investigation is imperative in view of its clinical importance in dental occlusion.
2. Monsons sphere is made up of four regular tetrahedrons (Monsons pyramids).
3. The radius of Monsons sphere is greater than the radius of circumsphere of Monsons pyramid.
Purpose
The main goal of this study was to test the following hypotheses:1. Monsons pyramid is the 3D unifying geometric figure for Bonwills, Spees, Monsons, and Halls theories of occlusion.2. Monsons sphere is made up of four regular tetrahedrons (Monsons pyramids).
3. The radius of Monsons sphere is greater than the radius of circumsphere of Monsons pyramid.
Materials And Method
Bonwills 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 Bonwills triangle was 10cm. A regular tetrahedron was constructed from Bonwills 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 students 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
Monsons pyramid was established as the unifying 3D geometric figure for the analyzed geometric models of occlusion. Monsons sphere is made up of four Monsons pyramids while the radius of Monsons sphere is also found to be greater than the radius of circumsphere of Monsons 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 patients bicondylar distance.Keywords:
Language:
English
Published:
Journal of Craniomaxillofacial Research, Volume:5 Issue: 1, Winter 2018
Pages:
468 to 478
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