Encyclopedia > Surface (physics)

  Article Content

Surface (physics)

In Physics, a surface is a set of elements with pairwise measured distance d, satisfying the following properties:

  • For any two distinct elements A and B there are elements X and Y such that
    • d( Y, A ) < d( X, A ) < d( B, A ),
    • d( Y, X ) < d( X, A ),
    • d( Y, X ) < d( X, B ),
    • d( Y, B ) < d( X, B ),
    • d( Y, B ) < d( B, A ); and

  • for any four distinct elements A, B, C, and Q, which satisfy d( Q, A ) < d( C, B ) < d( C, A ) < d( B, A ) < d( C, A ) + d( C, B ), holds
    • either Vol( A, B, C, Q ) = 0, or
    • there exist elements J and K with d( K, A ) < d( J, A ) < d( C, A ) < d( J, A ) + d( K, A )
such that for all elements T with d( T, A ) < d( K, A ) holds
Vol( A, J, K, T ) / Area( A, J, K ) ≤ ½ Vol( A, B, C, Q ) / Area( A, B, C ).

Here Vol(), as a function of four elements, denotes the Volume of the corresponding 3-simplex (i.e. tetrahedron), expressed in terms of the six distance values (pairwise) between these four elements by Tartaglia's formula; and Area() , as a function of three elements, denotes the Area of the corresponding 2-simplex (i.e. triangle), expressed in terms of the three distance values (measured pairwise) between these three elements by Heron's formula.

In topology as applicable to physics, a surface is a topological space which satisfies for any three elements:



All Wikipedia text is available under the terms of the GNU Free Documentation License

 
  Search Encyclopedia

Search over one million articles, find something about almost anything!
 
 
  
  Featured Article
North Haven, New York

... 30.9% of all households are made up of individuals and 18.1% have someone living alone who is 65 years of age or older. The average household size is 2.20 and the average ...

 
 
 
This page was created in 30.5 ms