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

Evaluate boiler efficiency, The following data were obtained in a boiler tr...

The following data were obtained in a boiler trail: Mass and temperature of feed water: 680 kg/hr and 20 0 C, Steam temperature and its pressure : 15bar and 300 0 C, Coal used

CIM, discuss the main components of computer aided manufacturing

discuss the main components of computer aided manufacturing

Determine the natural circular frequencies, The two-storey  frame shown in ...

The two-storey  frame shown in Figure Q4 is such  that  the self-mass may be considered to be located at the beam levels and the beams may be presumed to be rigid.  The self-mass (

What are square footings, What are square footings? SQUARE FOOTINGS ...

What are square footings? SQUARE FOOTINGS This type of footing, also termed an isolated spread footing is probably the most common, simplest and most economical of the vario

Evaluate thermal efficiency of the engine, A carnot engines performs betwee...

A carnot engines performs between two reservoirs whose difference in temperature is 200 o C. If the work output of the engine is 0.5 times the heat rejected, make evaluation for th

Determine couple - homogeneous cylinder, Determine couple - Homogeneous cyl...

Determine couple - Homogeneous cylinder: Homogeneous cylinder having weight W rests on horizontal floor in contact with wall (Fig ure given below ). If the coefficient of

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 economic order quantity, Determine the economic order quantit...

Determine the economic order quantity: Determine the economic order quantity and the reorder point. Given Annual demand (D) = 2,000 units Average daily demand (d) = 2,00

Governor, sensitivity of governors

sensitivity of governors

Coil circulation pump, Q. Coil Circulation Pump? Type of pump, vertical...

Q. Coil Circulation Pump? Type of pump, vertical in line. Locate on supply side of coil. Valving indicated, isolation valves on suction and discharge, check valves on bypass. P

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