Let $\Re _{1}\left( a,b\right) $ be a regular lattice with the fundamental cell a rectangle with sides $a,b$, let $\Re _{2}\left( a,b,\varpi \right) $ be a regular lattice with the fundamental cell a parallelogram with sides $a,b$ and angle $\varpi $ and let $\Re_{3}\left( a,b,c\right) $ be a regular lattice with the fundamental cell $C_{0}^{\left( 3\right) }$ as in fig. 7. In this paper we compute the probability that a random rectangle $r$ of constant side $l,m$ intersects a side of the lattice. In particular when the rectangle $r$ becomes a segment of lenght $l$, $\left( m=0\right) $ we obtain the Laplace probability.
Some extensions of the Laplace problem
CARISTI, Giuseppe;
2011-01-01
Abstract
Let $\Re _{1}\left( a,b\right) $ be a regular lattice with the fundamental cell a rectangle with sides $a,b$, let $\Re _{2}\left( a,b,\varpi \right) $ be a regular lattice with the fundamental cell a parallelogram with sides $a,b$ and angle $\varpi $ and let $\Re_{3}\left( a,b,c\right) $ be a regular lattice with the fundamental cell $C_{0}^{\left( 3\right) }$ as in fig. 7. In this paper we compute the probability that a random rectangle $r$ of constant side $l,m$ intersects a side of the lattice. In particular when the rectangle $r$ becomes a segment of lenght $l$, $\left( m=0\right) $ we obtain the Laplace probability.File in questo prodotto:
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