Complex Root Extraction—Moivre’s Theorem

2021 ◽  
pp. 31-37
Author(s):  
Jörg Kortemeyer
Keyword(s):  
Vestnik MEI ◽  
2018 ◽  
Vol 5 (5) ◽  
pp. 79-88
Author(s):  
Sergey B. Gashkov ◽  
◽  
Aleksandr B. Frolov ◽  
Elizaveta Р. Popova ◽  
◽  
...  

Oriens ◽  
1964 ◽  
Vol 17 ◽  
pp. 331
Author(s):  
H. Hermelink ◽  
Abdul-Kader Dakhel ◽  
Wasfi A. Hijab ◽  
E. S. Kennedy
Keyword(s):  

2020 ◽  
Vol 14 (1) ◽  
pp. 421-425
Author(s):  
Alfredo Iandolo ◽  
Alessandra Amato ◽  
Stefano Martina ◽  
Dina Abdel latif ◽  
Giuseppe Pantaleo

Objective: The aim of this work was to show the management of severe curvatures done with the new generation of rotating files through a safe and predictable protocol. Methods: Three clinical cases were described. A safe protocol was explained using the latest generation of rotating files for the shaping of the anatomy of complex root canals. All the cases presented 90°, 45° curvatures and/or double curvatures. Results: The instrumentation of canals increased their surface area and volume. All the cases with 90° and 45° curvatures were optimally shaped. Conclusion: With the help of rotating files in the martensitic alloy, it is possible to work safely, while avoiding the risk of file separation, even in root canals with severe curvatures, thus achieving success even in complex clinical cases.


2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Paramee Thanaruengrong ◽  
Sirinya Kulvitit ◽  
Mettachit Navachinda ◽  
Pornkawee Charoenlarp

Abstract Background Mandibular premolars demonstrate high variability in root canal morphology, especially mandibular first premolars. The purposes of this study were to determine the prevalence of root canal configurations of mandibular premolars according to Vertucci classification in a Thai population. Methods Total of 1159 CBCT images of Thai patients who received radiographic imaging at the Department of Radiology, Faculty of Dentistry, Chulalongkorn University in 2017–2018 was evaluated. The data were reported using descriptive statistics and the relationship between the prevalence of the root canal complexities and sex was analyzed using the chi-squared test. Results The most common root canal configuration was Vertucci type I, with a 63.1% and 98% prevalence in the mandibular first and second premolars, respectively. More than 98% of mandibular premolars had a single root. The prevalence of a bifurcation was 28.5% and 1.5% in the mandibular first and second premolars, respectively. The prevalence of a trifurcation was 3.2% in the mandibular first premolar. A C-shaped root canal was observed at 23.7% and 0.7% in the mandibular first and second premolars, respectively. The level of branching was mostly found at the middle 1/3 of the root. Bilateral appearance of the same root canal configuration was identified in 80.3% and 95.9% in the mandibular first and second premolars, respectively. There was no relationship between sex and the prevalence of a bifurcation, trifurcation, or C-shaped root canal. Conclusion Mandibular first premolars have more root canal complexities than mandibular second premolars. Horizontal tube shift x-ray technique, CBCT, dental operating microscope, and knowledge of root canal configurations have an important role in root canal identification in mandibular premolar with suspected complex root canal morphology.


2022 ◽  
Vol 40 ◽  
pp. 1-6
Author(s):  
Saroj Kumar Padhan ◽  
S. Gadtia

The present investigation deals with the critical study of the works of Lancaster and Traub, who have developed $n$th root extraction methods of a real number. It is found that their developed methods are equivalent and the particular cases of Halley's and Householder's methods. Again the methods presented by them are easily obtained from simple modifications of Newton's method, which is the extension of Heron's square root iteration formula. Further, the rate of convergency of their reported methods are studied.


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