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

Calculate the magnitude and position of the balance mass, The four masses m...

The four masses m1, m2, m3 and m4 having their radii of rotation as 200mm, 250mm, 150mm, 250mm and 300mm are 200kg, 300kg,240kg and 260kg in magnitude respectively. The angles betw

Maximum bending moment, Maximum Bending Moment: The SF changes sign at...

Maximum Bending Moment: The SF changes sign at A, among A and B and at B. Let a section XX at a distance x from the end C as illustrated in Figure SF at section XX, F x

Third gear position - shifting of gear, Third Gear Position: When gea...

Third Gear Position: When gear M3 on the main shaft is in mesh with gear C3 on the counter shaft then this is known as third gear position. The fixed gear M3 rotates with mai

Short life cycle demand uncertainty - risk management, how I can formulate ...

how I can formulate mathematically the risk management in demand uncertainty of short life cycle product.

Cyclone dip tube length calculation., how can we calcute the length of dip ...

how can we calcute the length of dip tube and what are its effects on cyclone efficiency if we change its length

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