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

Motion of connected bodies, when 2 bodies are connected by a string show ...

when 2 bodies are connected by a string show the direction of acceleration

Motorcycle pulls to one side motorcycle problem, If Motorcycle Pulls to One...

If Motorcycle Pulls to One Side Causes of Problem Remedy Misaligned shock Absorber Front and rear wheels are not alig

Injection molding, what are the finishing operation of telephone outer body...

what are the finishing operation of telephone outer body after injection molding

Hierarchical system structure, Ask question #Minimum 100 words awrite short...

Ask question #Minimum 100 words awrite short note on the the hierarchical system structure involving various level

Iterature review, I have literature review and the title is "the effect of...

I have literature review and the title is "the effect of fluid cooling on the performance of building integrated photovoltaic thermal systems. Using some BIPVT prototypes measure

Find maximum torque which can be transmitted by belt drive, Find maximum to...

Find maximum torque which can be transmitted by belt drive: A belt is stretched over the two identical pulleys having diameter D meter. The initial tension in belt throughout

Draw a single point cutting tool, Draw a single point cutting tool and defi...

Draw a single point cutting tool and define its various parts. Also describe the standard anglesof this cutting tool.

Ultrasonic welding, ULTRASONIC WELDING This is a solid state welding p...

ULTRASONIC WELDING This is a solid state welding process for joining similar or dissimilar metals by application of high frequency vibratory energy to work pieces held togethe

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