top of page

THE LOCAL PROOF

The proof presented by Manfredo Do Carmo in Differentiel Geometry of Curves and Surfaces

Screen Shot 2023-05-20 at 11.15.51 AM.png

THE GLOBAL PROOF

The proof presented by Manfredo Do Carmo in Differentiel Geometry of Curves and Surfaces

Screen Shot 2023-05-20 at 11.17.10 AM.png
Screen Shot 2023-05-20 at 11.18.16 AM.png
Screen Shot 2023-05-20 at 11.18.59 AM.png
Screen Shot 2023-05-20 at 11.19.36 AM.png
Screen Shot 2023-05-20 at 11.20.42 AM.png
Math Formulas

NOTE:

The proof uses many theorems not covered in detail yet, including the theorem of turning tangents and the Gauss Green theorem. 

bottom of page