- #1
labinojha
- 12
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Hi. This post is about general topology and is Euler's second formula . Can you people help me by finding a proof for V-E+F=2-2p. ![Smile :smile: :smile:](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
Where,
p=genus of the surface.
F=number of regions the surface is partitioned into.
V=number of vertices.
E=number of arcs.
I'm currently reading this proof from a book 'Introduction to Modern Mathematics' by S.M Maskey(you won't be finding this book in the internet, we don't have a system of buying books from the internet in our country and most of the people are too lazy to make it into an ebook.And these books are just dumbed down(to simle english) versions of other good books ).Thus, this book has vague descriptions regarding the proving process.![Mad :mad: :mad:](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
The proof here talks about considering spheres with p handles and removing them again.and i am not understanding the process written herein this book.
Any links of this proof will be appreciated, or we could discuss .![Approve :approve: :approve:](https://www.physicsforums.com/styles/physicsforums/xenforo/smilies/oldschool/approve.gif)
Where,
p=genus of the surface.
F=number of regions the surface is partitioned into.
V=number of vertices.
E=number of arcs.
I'm currently reading this proof from a book 'Introduction to Modern Mathematics' by S.M Maskey(you won't be finding this book in the internet, we don't have a system of buying books from the internet in our country and most of the people are too lazy to make it into an ebook.And these books are just dumbed down(to simle english) versions of other good books ).Thus, this book has vague descriptions regarding the proving process.
The proof here talks about considering spheres with p handles and removing them again.and i am not understanding the process written herein this book.
Any links of this proof will be appreciated, or we could discuss .
![Approve :approve: :approve:](https://www.physicsforums.com/styles/physicsforums/xenforo/smilies/oldschool/approve.gif)