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

Features of the scheme entrepreneurship development, Features of the Schem:...

Features of the Schem:  Features of the scheme are as follows : DIC is the primary registering centre. Registration is voluntary and not compulsory. Two types of

.planar mechanism, degrees of freedom of a planar mechanism

degrees of freedom of a planar mechanism

Drainage of the railway track - construction of railway line, Drainage of t...

Drainage of the Railway Track: It is necessary to keep the embankment free from water. This is done by providing side ditches, all along the edge of the embankment, and leadi

Context level data flow diagram, Context Level Data Flow Diagram In thi...

Context Level Data Flow Diagram In this section, the cell control model conversation in the former section is demonstrated by the data flow diagram as in following figure of co

Heat exchangers for plant design, Q. Heat exchangers for plant design? ...

Q. Heat exchangers for plant design? All exchangers shall be arranged to be readily dismantled for cleaning and maintenance. Cooling and heating streams generally flow against

Define the isolated and combined footings, Isolated and Combined Footings ...

Isolated and Combined Footings Individual columns are generally supported on isolated footings. A typical isolated footing is shown in Figure. This arrangement is suitable when

Evaluate the support required by body on plane, Evaluate the Support requir...

Evaluate the Support required by body on plane: A body having weight 50KN rests in limiting equilibrium on rough plane, whose slope is 30º. The plane is raised to a slope of

Objectives-computerized scheduling and control manufacturing, Objectives ...

Objectives After studying this section, you should be familiarized about: The typical job shop scheduling problem, Characteristics of computer controlled scheduling,

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