[Graphics:Images/CurvatureMod_gr_157.gif]

The limit of  [Graphics:Images/CurvatureMod_gr_158.gif] as  [Graphics:Images/CurvatureMod_gr_159.gif] is merely [Graphics:Images/CurvatureMod_gr_160.gif],  and we have already observed that the limit in the denominator is [Graphics:Images/CurvatureMod_gr_161.gif]and both quotients in the numerator tend to  [Graphics:Images/CurvatureMod_gr_162.gif] as  [Graphics:Images/CurvatureMod_gr_163.gif] .  

Thus we have established the formula  [Graphics:Images/CurvatureMod_gr_164.gif] for the ordinate of center of the circle of curvature.

Details

[Graphics:../Images/CurvatureMod_gr_165.gif]


[Graphics:../Images/CurvatureMod_gr_166.gif]



[Graphics:../Images/CurvatureMod_gr_167.gif]

[Graphics:../Images/CurvatureMod_gr_168.gif]

 

[Graphics:../Images/CurvatureMod_gr_169.gif]



[Graphics:../Images/CurvatureMod_gr_170.gif]



[Graphics:../Images/CurvatureMod_gr_171.gif]


[Graphics:../Images/CurvatureMod_gr_172.gif]




[Graphics:../Images/CurvatureMod_gr_173.gif]


[Graphics:../Images/CurvatureMod_gr_174.gif]




[Graphics:../Images/CurvatureMod_gr_175.gif]

[Graphics:../Images/CurvatureMod_gr_176.gif]

 

[Graphics:../Images/CurvatureMod_gr_177.gif]

[Graphics:../Images/CurvatureMod_gr_178.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004