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

Newer approaches to on-line scheduling, Newer Approaches To On-Line Schedul...

Newer Approaches To On-Line Scheduling  The on-line scheduling has established to be superior option than off-line scheduling upon the shop floor. The on-line scheduling looks

Determine the reactions at supported end, A steel dia 10 mm passes through ...

A steel dia 10 mm passes through a brass tube of internal dia 15mm and external dia is 25 mm. The bolt is tightened by a nut. The length of tube is reduced by 1.5mm and the length

I-Section, An unsymmetrical I-Section as shown in figure below. If maximum ...

An unsymmetrical I-Section as shown in figure below. If maximum bending stress is not extend more than 40MPa in the section than find out the moment which it can bear

High pressure die casting process, what is the working princile of high pre...

what is the working princile of high preesure die casting process

What is transmission system and what do you mean by a gear?, (a) What is tr...

(a) What is transmission system? Represent the main components of transmission system with the help of diagram. (b) What do you mean by terms torque, power and RPM? (c) What

Determine the angle of jet, A jet of water moving at 8 m/sec. impinges on a...

A jet of water moving at 8 m/sec. impinges on a concave-shaped vane to deflect the jet through 120 o when stationary. If the vane is moving at 5 m/sec., determine the angle of jet

What are preheat and interpass temperature, Q. What are Preheat and interpa...

Q. What are Preheat and interpass temperature? Preheat and interpass temperatures shall be in accordance with the applicable codes. Materials that require preheat for welding

Defects involving inadequate bonding, Defects Involving Inadequate Bonding ...

Defects Involving Inadequate Bonding Lack of fusion Involves lack of complete melting and fusion of some portion of the weld metal in a joint. It may occur either bet

Thermodynamic Project, ES 347 - Thermodynamics Project Assigned: 3/28/2013...

ES 347 - Thermodynamics Project Assigned: 3/28/2013 Due: 4/25/2013 Problem specification 5 kg of air is contained in a piston-cylinder device, initially at a pressure of 2MPa and a

Effect of individual alloying elements, Effect of Individual Alloying Eleme...

Effect of Individual Alloying Elements: Sulfur Sulfur is not a needed element in steel since in interferes along with hot rolling and forging resulting in hot-shortness

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