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

The velocity distribution in the gap is linear, A 10 kg block slides down a...

A 10 kg block slides down a smooth inclined surface as shown in Figure. Show the terminal velocity of the block if the 0.1 mm gap among the block and the surface have SAE30 oil at

Carbon fibers, 3. The tensile modulus of elasticity of a unidirectional car...

3. The tensile modulus of elasticity of a unidirectional carbon-fiber-reinforced-plastic composite material that contains 64 percent by volume of carbon fibers and is stresssed und

Relations Among Load, 5. Calculate and draw the Shear force and Bending mom...

5. Calculate and draw the Shear force and Bending moment diagrams for the loaded beam and determine the maximum moment M and its location x from left end

Cantilever beam stress, Dear Engineer! I have an aluminum tube(6061) fixed...

Dear Engineer! I have an aluminum tube(6061) fixed at one end (Cantilever Beam). The length is 180” and the load on the other end is 150 lbs. Question: What size of tubes I s

Plastic material and rigid plastic material, Plastic material and rigid pla...

Plastic material and rigid plastic material: For the plastic material, there is stress at which plastic deformation begins. A rigid plastic material is one in which the ela

Determine the eigen values, Determine the eigen values and eigen vectors of...

Determine the eigen values and eigen vectors of the matrix

Show the types of changes in project, Q. Show the types of Changes in proje...

Q. Show the types of Changes in project? During the development and execution of a project, the following changes can occur:  Scope of work changes  Cost deviation

Determine the force and stress, The space truss is supported by a ball-and-...

The space truss is supported by a ball-and-socket joint at D and short links at C and E. Determine the force and stress in each member and state if the members are buckle or

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