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

Types of stresses, Types of stresses: In general stress is divided in ...

Types of stresses: In general stress is divided in to three group as: various types of stresses may be classified as: 1. Simple or direct stress (Tension, Compressi

Shear force and bending moment, question no 2,page no 84 of strenght of mat...

question no 2,page no 84 of strenght of materials by G H Ryder

Overbridges - fly-overs and underpasses, Overbridges, Fly-Overs And Underpa...

Overbridges, Fly-Overs And Underpasses: Railway Over-bridges Railway Over-bridges (ROB) are structures constructed to enable the road traffic to go over the railway t

Axis inclain to vp and parallel to hp., draw the projection of hexagonal pr...

draw the projection of hexagonal prism of base side 20mm & axis length 50mm. when it is lying on the ground on one of its rectangular phase and axis is inclained 35 degree to vp. s

Theory of mechanics , analyze a six bar linkage to get the position, veloci...

analyze a six bar linkage to get the position, velocity and acceleration

Explain bevel gear generating process, Explain Bevel Gear Generating Proces...

Explain Bevel Gear Generating Process? The fundamental of bevel gear generating process involves the rolling of a bevel gear blank on a crown wheel. The crown wheel is a bevel

Explain the concept of cell-decomposition, Cell-decomposition In cell-d...

Cell-decomposition In cell-decomposition, an object can be represented as the sum of cells into which it can be decomposed. Each cell-decomposition system defines a set of prim

Chemistry, what is law of chemical combinations?

what is law of chemical combinations?

Determine the moment of forces, Determine the moment of forces: The si...

Determine the moment of forces: The side of a square ABCD is 1.60 m long .Four forces equal to 6, 5, 4 and 8 N acts respectively along with the line CB, BA, DA, DB. Determine

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