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

Kinematics, Kinematics: We have seen the various types of motions whic...

Kinematics: We have seen the various types of motions which may be undergone by particles and rigid bodies. You may be able to understand the relationships of displacement, ve

Complaints of engine starting by repairing of motorcycle , Complaints of En...

Complaints of Engine Starting: If there is a problem related to the starting of the bike, it can be due to mechanical as well as electrical reasons. The possible reasons could be

Construction activities for plant, Construction Activities for plant Co...

Construction Activities for plant Construction activities, such as shoring and bracing of excavations, lifting and rigging activities and scaffolding need to be considered as p

Thermodynamics, klfjaljf jlas jfklsj flasj; flkjs fklja sklfj ak;lsfj lkajs...

klfjaljf jlas jfklsj flasj; flkjs fklja sklfj ak;lsfj lkajsf; kljas fkl;ajsd flk;jads fklasjdfl kjkl fjdaskl fjdsklafj ksad ,ma,v. askjlvj kljdfiojajofj adjfkldsj fkljasdf lkjads;

Conversion of pressure reading into kpa, Conve r t following reading of p...

Conve r t following reading of pressure to kPa, supposing that the barometer reads 760mm Hg. (1) 90cm Hg gauge (2) 40cm Hg vacuum (3) 1.2m H 2 O gauge Sol: Given

What are the specific issues with plant layout, Q. What are the Specific Is...

Q. What are the Specific Issues with plant Layout? There are a large number of regulations and related material that impact the operating plant. API (American Petroleum Institu

Thermodynamics: Apple Hydrocooling Unit, Design a hydrocooling unit that ca...

Design a hydrocooling unit that can cool fruits and vegetables from 30 to 5 degrees Celsius at a rate of 20,000 kg/hr under the following conditions: The unit will be of flood typ

Newtons first law, Problem: Newton's First Law Newton's First Law of Mo...

Problem: Newton's First Law Newton's First Law of Motion says that, in the absence of external forces, an object at rest stays at rest and an object in motion continues at cons

find the machine fraction, Two machining operations, A (3 minutes per part...

Two machining operations, A (3 minutes per part) and B (10 minutes per part), are performed sequentially to manufacture a part. Machines A and B produce 5% and 6% defective items,

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