Objective:To study the mathematical relation between the measurements of root canal curvature obtained by Schneider's method(?_S) and Weine's method(?_W).Methods:The axis of a curved root canal was simplified by an arc (whose radius was r and central angle ?) and 2 tangent line segments (whose lengths were l_1 and l_2),the relation of ?_S and ?_W was studied with the help of mathematical analysis according to the different ways of determining the measured angles on the simplified axis.The graphs of the function were analysed.Results:The following formulas were proved:(1)tan?_S=(1-cos?_W+ ksin?_W)/(sin?_W+kcos?_W),k=l_2/r;(2)?_W/2≦?_S≦?_W.If ?_W was in the interval [0,?],a proximate linear correlation existed between ?_S and ?_W.Conclusion:There is a complex function between the 2 angles(?_S and ?_W) measured by Schneider's method and Weine's method,the ratio of the length of the apical straight part to the radius of the canal curvature is an important factor determining the different values of ?_S and ?_W.

Objective:To analyze the wall thickness of C-shaped canals in permanent mandibular second molars.Methods:40 ex-tracted permanent mandibular second molars with C-shaped root were collected from native Chinese and were scanned by micro-CT scan-ner.The specimens were reconstructed three-dimensionally by software Mimics 10.01.The roots were sliced from cemento-enamel junc-tion (CEJ)to apex with 1 mm intervals.The cross-sectional root canal configurations were classified into 5 types according to the Fan's Classification.The minimum buccal wall thickness (MBWT),minimum lingual wall thickness(MLWT)and their locations,as well as the wall thickness at the mesial and distal reference sites were detected.Two-way ANOVA and post hoc LSD-t tests were used to com-pare the mean thickness at 4 sides.Results:Among 370 cross-sections of 40 C-shaped roots,C1,C2 and C3 canals were observed on 126(34.1%),46 (12.4%)and 160 (43.2%)sections respectively.Except at the 10 mm level,the mean MLWT was always lower than MBWT;and the MLWT and MBWT were always lower than the wall thickness at the mesial and distal reference sites.The differ-ence was statistically significant (P <0.05)along the root length above the 12 mm level.The MBWT of the C2 and C3 canals was more likely located at the mesial region,and the MBWT of the C1 and the MLWT of C1,C2 and C3 was more frequently located at the center region.Conclusion:The lingual wall of C-shaped canal in mandibualr second molars was the thinnest zone among four sides,and care should be taken during root canal instrumentation and post space preparation to avoid perforation.