Namespaces
Variants
Actions

Difference between revisions of "User:Richard Pinch/sandbox-12"

From Encyclopedia of Mathematics
Jump to: navigation, search
(Start article: Elastic modulus)
(more)
Line 30: Line 30:
 
The ratio of longitudinal extension to lateral compression when an elastic substance is put under tension.
 
The ratio of longitudinal extension to lateral compression when an elastic substance is put under tension.
  
See: [[Elasticity, mathematical theory of]].
+
See: [[Elasticity, mathematical theory of]]; [[Lamé constants]].
  
 
====References====
 
====References====
Line 40: Line 40:
 
The ratio of longitudinal extension to force applied per unit area when an elastic substance is put under tension.
 
The ratio of longitudinal extension to force applied per unit area when an elastic substance is put under tension.
  
See: [[Elasticity, mathematical theory of]].
+
See: [[Elasticity, mathematical theory of]]; [[Lamé constants]].
  
 
====References====
 
====References====
 
* Horace Lamb, "Statics", Cambridge University Press (1960)
 
* Horace Lamb, "Statics", Cambridge University Press (1960)

Revision as of 17:37, 28 December 2017

Dyck path

A lattice path on the square lattice from the origin $(0,0)$ to some point $(n,n)$ consisting of $2n$ steps of the form $N : (x,y) \rightarrow (x,y+1)$ and $E : (x,y) \rightarrow (x+1,y)$ with the property that the path never passes below the line $y=x$.

The number of Dyck paths of length $2n$ is given by the $n$-th Catalan number $$ C_n = \frac{1}{n+1}\binom{2n}{n} \ . $$

References

Catalan number

The $n$-th Catalan number $$ C_n = \frac{1}{n+1}\binom{2n}{n} \ . $$ The generating function is given by $$ \sum_{n=1}^\infty C_n z^n = \frac{1-\sqrt{1-4z}}{2z} \ . $$ The Catalan numbers appear in the enumeration of a number of combinatorially defined object:

References

Poisson ratio

The ratio of longitudinal extension to lateral compression when an elastic substance is put under tension.

See: Elasticity, mathematical theory of; Lamé constants.

References

  • Horace Lamb, "Statics", Cambridge University Press (1960)

Elastic modulus

Young's modulus

The ratio of longitudinal extension to force applied per unit area when an elastic substance is put under tension.

See: Elasticity, mathematical theory of; Lamé constants.

References

  • Horace Lamb, "Statics", Cambridge University Press (1960)
How to Cite This Entry:
Richard Pinch/sandbox-12. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Richard_Pinch/sandbox-12&oldid=42633