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

Explain classification of welding processes, Classification Of Welding Proc...

Classification Of Welding Processes The classificated depending upon the nature of heat source and its movement resulting in spot, seam or zonal welds; or on the extent of heat

Violation of clausius statement - thermodynamics, Equivalen t of Kelvin Pl...

Equivalen t of Kelvin Plank and Clausius statement: The Kelvin plank and clausius statements of the second law and are equivalent in all the respect. The equivalence of state

Connecting rod, how to design a steel connecting rod using minimum weight a...

how to design a steel connecting rod using minimum weight and thickness?

Thermodynamic process - thermodynamics, Thermodynamic process - Thermodynam...

Thermodynamic process - Thermodynamics: Thermodynamic system undergoes changes because of the energy and mass interactions. Thermodynamic state of system changes because of th

Thin uniform wire bent - centre of gravity, Thin uniform wire bent - centre...

Thin uniform wire bent - centre of gravity: Find out the C. G. of the thin uniform wire bent into shape ABC as illustrated in Figure. Solution Assume G be the loc

Estimate the tempreture measured by thermocouples, An experiment to determi...

An experiment to determine the convection coefficient associated with airflow over the surface of a thick stainless steel casting involves insertion of thermocouples in the casting

Legal aspects of entrepreneurship development , Legal Aspect :  Few simple ...

Legal Aspect :  Few simple steps to take care of legal aspects of setting up a business are to register your unit with concerned organisation, check out the labour laws that would

Write Your Message!

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