Illustrate the euler-poincare formula, Mechanical Engineering

Assignment Help:

The Euler-Poincare Formula 

The Euler-Poincaré formula describes the relationship of the number of vertices, the number of edges and the number of faces of a manifold. It has been generalized to include potholes and holes that penetrate the solid. To state the Euler-Poincaré formula, we need the following definitions :

  • V : the number of vertices
  • E : the number of edges
  • F : the number of faces
  • G : the number of holes that penetrate the solid, usually referred to as genus in topology
  • S : the number of shells. A shell is an internal void of a solid. A shell is bounded by a 2-manifold surface, which can have its own genus value. Note that the solid itself is counted as a shell. Therefore, the value for S is at least 1.
  • L : the number of loops, all outer and inner loops of faces are counted.

Then, the Euler-Poincaré formula is the following :

                                   V - E + F - (L - F) - 2 (S - G) = 0  

 


Related Discussions:- Illustrate the euler-poincare formula

Total decrease in length - hollow cast iron cylinder, Total decrease in len...

Total decrease in length: Q: A hollow cast iron cylinder 4 m long, 300 mm is the outer diameter, and thickness of metal 50 mm is subjected to central load on top when standin

Motorcycle repairing, In MOTORCYCLE REPAIRING we have gone through various ...

In MOTORCYCLE REPAIRING we have gone through various complaints related to engine starting, problem related to gear, clutch, etc. and their possible reasons of trouble making. The

Petrol-general safety tips , Petrol: Work in a well-ventilated area. Keep ...

Petrol: Work in a well-ventilated area. Keep flames or sparks away from the work area or where petrol is stored.

Describe polythionic acid corrosion, Q. Describe Polythionic Acid Corrosion...

Q. Describe Polythionic Acid Corrosion? Although it is not typically thought of as high temperature corrosion, polythionic acid stress corrosion cracking occurs in areas where

Seam welding-selection of parameters, Seam Welding-Selection of parameters ...

Seam Welding-Selection of parameters The selection of parameters for seam welding depends mainly on: weld nugget size which is related to weld strength. probability of

Resolution of a force - mechanics, Resolution of a force: Sol.: When...

Resolution of a force: Sol.: When a force is resolved into two parts along the two mutually perpendicular directions, without changing the effects of it on the body, the par

Engine oil replacement procedure, Engine oil replacement Motorcycle i...

Engine oil replacement Motorcycle is thoroughly drained by kicking the vehicle several times. Inspect the drain bolt washer and replace if necessary. Tighten the drai

Where a and b are positive constants, Assume the production function is giv...

Assume the production function is given by the following equation (where a and b are positive constants): Q = aL+bK. What is the marginal rate of technical substitution of labor fo

Processes , example on operation sheet?

example on operation sheet?

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd