A mathematical analysis of the relationship between Schneider's method and Weine's method for the measurement of root canal curvature / 实用口腔医学杂志

ABSTRACT

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.