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

What do you mean by stage discharge relationship, Q. What do you mean by St...

Q. What do you mean by Stage Discharge Relationship? Regular recording of discharges over a period of time is essential for estimation of water resources of river basins and su

Circulation pumps, Are the types of pumps selected (base mounted, in-line)?...

Are the types of pumps selected (base mounted, in-line)? Locate pump on discharge side of boiler. Flexible connector used. Valving indicated, isolation valve on suction and dis

Determine maximum shearing stress in shaft, Determine maximum shearing stre...

Determine maximum shearing stress in shaft:   A propeller shaft 100 mm in the diameter, is 45 m long, transmits 10 MW at 80 rotation per minute. Determine maximum shearing str

Piston and piston rings - part of combustion engine, Piston and Piston Ring...

Piston and Piston Rings - Part of combustion engine: Piston: The piston reciprocates within cylinder and transmits force exerted by expanding gases to crank by means of conn

Fracture toughness of material of plate, Fracture toughness of material of ...

Fracture toughness of material of plate: A large thin plate carrying a crack of 70 mm at its centre is subjected to fluctuating stress cycle perpendicular to crack. s max = 7

QFD chart and engineering specifications, Deliverables: A QFD chart, sh...

Deliverables: A QFD chart, showing the relationships between the customer requirements and the engineering specifications. (Refer to the Ullman QFD chart posted on My

Difference between components and resolved parts, D i f fe r enc e be...

D i f fe r enc e between components and resolved parts: 1. When the force is resolved into two parts along the two mutually perpendicular directions, the parts along th

Short circuiting transfer, Short Circuiting Transfer The short circuiti...

Short Circuiting Transfer The short circuiting transfer  occurs when the welding current and the arc voltage is low. Metal is transferred from the electrode to the work only wh

Batteries and alternative sources of energy, state six typical application ...

state six typical application of primary cells

Aspects of scheduling , Aspects Of Scheduling  The difficulty is a mod...

Aspects Of Scheduling  The difficulty is a modification of a flexible manufacturing cell at ABB's plant for the manufacturing of turbocharger in Baden, Switzerland. The difficu