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

Show application to gyroscope, Q. Show Application to Gyroscope? A fibe...

Q. Show Application to Gyroscope? A fiber optic Gyroscope is used to detect the mechanical rotation of the interference of light. Two beams travel along the fiver in opposite d

Mechanics of materials, how to find bending moment diagram of cantilever be...

how to find bending moment diagram of cantilever beam.any formula

What are the need of a surface condensing, (a) What are the need of a surfa...

(a) What are the need of a surface condensing ? Write disadvantages and advantages of Jet condenser and surface condenser. (b) A surface condenser is designed to handle 10000 Kg

Von-mises stress and strain distributions, Consider a pressure vessel as sh...

Consider a pressure vessel as shown in the figure. The cylinder has a longitudinal axis of rotational symmetry and is also symmetric with respect to a plane passing through it

Telescopic hydraulic fork , Telescopic Hydraulic Fork: This type of suspen...

Telescopic Hydraulic Fork: This type of suspension system is used to serve for front part of motorcycle. Figure (Front Suspension Fork) shows detailed view of front fork assembly.

Select a flat belt drive, It is essential to select a flat belt drive for a...

It is essential to select a flat belt drive for a compressor running at 720 r.p.m which is driven by a 25kW, 1440 r.p.m. motor. Space is available for a distance of 3m. The belt is

Working of lacashire boiler, Working of lacashire boiler: WORKIN G: ...

Working of lacashire boiler: WORKIN G: Water is filled through feed check valve. On burning fuel over grate, the hot gasses are produced which move in flue gas tubes.

Arc initiation-touch start-high frequency start, ARC INITIATION Touch...

ARC INITIATION Touch Start With the power supply energised and the shielding gas flowing through the cup, the torch is lowered toward the workpiece until the tungsten electr

Explain straight line mechanism, a) Illustrate with the help of neat sketch...

a) Illustrate with the help of neat sketch any three straight line mechanism. b) Describe Degree of Freedom and prove the relation for Grumbler's equation.

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