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

Inventor claims in adiabatic system - mechanics, Inventor claims in adiabat...

Inventor claims in adiabatic system: On e inventor claims that 2 kg of air supplied to magic tube at 4 bar and 20°C and the two equal mass streams at 1 bar are produced, one

Elastomers, define elastomer.explain in details?

define elastomer.explain in details?

Illustrate the future trends in automobile, Short answer Type. a) Writ...

Short answer Type. a) Write the difference Between Dry clutch and Wet ? b) What is difference Between Chasis and Frame? c) Illustrate the Future trends in Automobile

Governor, Use of hartung governor

Use of hartung governor

Dryness fraction, how do you differentiate between wet steam and dry steam?...

how do you differentiate between wet steam and dry steam?

Determine the heat addition, Describe carburetion. What are the basic diffe...

Describe carburetion. What are the basic different air-fuel mixture on which an engine can be operated ? Write a short note on sterling cycle. In an engine working on inlet pres

Calculate the vertical anchoring forces, A converging elbow (see Figure 4) ...

A converging elbow (see Figure 4) turns water through an angle of 135 o in a vertical plane. The flow cross-section diameter is 400 mm at the elbow inlet, section (1), and 200 mm

CNC Machining, how to determine proper the depth of cut for the tool if the...

how to determine proper the depth of cut for the tool if the drill is made of HSS and the work piece is made of alluminume alloy?

What is the density of plastic, Plastics are the common term for a wide ran...

Plastics are the common term for a wide range of synthetic or semi synthetic polymerization products. There are many dissimilar plastics; all have their own density!

Cantilever beam stress, Dear Engineer! I have an aluminum tube(6061) fixed...

Dear Engineer! I have an aluminum tube(6061) fixed at one end (Cantilever Beam). The length is 180” and the load on the other end is 150 lbs. Question: What size of tubes I s

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