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

Applied load shall elongate the spring, Applied load shall elongate the spr...

Applied load shall elongate the spring: Design a close coiled helical spring which shall deflect 100 mm under a load of 600 N. The radius of the coil is 6 times the wire diame

Engfine, how we made parts of engine

how we made parts of engine

Consideration for centrifugal tension, Consideration: 1. From above eq...

Consideration: 1. From above equation, it is clear that centrifugal tension is not dependent of T1 and T2. It depends upon velocity of the belt. For lower belt speed (that is,

Metal transfer in co2 welding, METAL TRANSFER IN CO2 WELDING In CO 2 wel...

METAL TRANSFER IN CO2 WELDING In CO 2 welding, two distinct types of metal transfers are identified viz. short circuiting transfer and free flight globular transfer. Short Cir

Determine the velocity in a moving frame of reference, Determine the veloci...

Determine the velocity in a Moving Frame of Reference: As illustrated in Figure, a ship A moves with a velocity v A = 40 km/hour whereas ship B moves with a velocity of v B

Kinetic inversion, kinetic Inversion In a mechanism, in a kinematic cha...

kinetic Inversion In a mechanism, in a kinematic chain one of the links is fixed. One can get different mechanisms by fixing in different links in a kinematic chain. This techn

Determine magnitude of the couple, Determine magnitude of the couple: ...

Determine magnitude of the couple: A square block having each side 1.5 m is acted upon by system of forces along its sides as shown in the adjoining figure. If system reduces

Estimate elevator algorithm-closest cylinder next, Disk requests come in to...

Disk requests come in to the disk driver for cylinders 10, 22, 20, 2, 40, 6, and 38, in that order. A seek takes 6 mes per cylinder moved. How much seek time is needed for (a) F

Hardenability of steel, The hardened layer depth is the measure of harden-a...

The hardened layer depth is the measure of harden-ability. A good harden-ability will sense even thicker sections are uniformly hardened. Conversely a poor harden-ability will gene

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