On Buffon’s Problem for a Lattice and its Deformations
نویسندگان
چکیده
We consider the Buffon’s problem for the lattice Rα,a which has the fundamental cell composed by the union of octagon, with all sides of lengths a and the angles (π − α) and ( 2 + α) with α ∈ ] 0, π 2 [ , and of the square with side of length a (see Fig. 1). We determine the probability of intersection of a body test needle of length l, l < a. For α = π 4 we also give the estimate of this probability for the cases, when the segment is non-small with respect to Rπ 4 ,a (see [1], [2]). MSC 2000: 60D05, 52A22
منابع مشابه
Solutions of Buffon’s problems in the 19 century
The Buffon’s needle problem is a well known problem of geometric probability. But Buffon formulated and solved also other problems in this topic. We recall them and their solutions by Buffon, Laplace, Todhunter, Lamé and Barbier.
متن کاملA Modification on Applied Element Method for Linear Analysis of Structures in the Range of Small and Large Deformations Based on Energy Concept
In this paper, the formulation of a modified applied element method for linear analysis of structures in the range of small and large deformations is expressed. To calculate deformations in the structure, the minimum total potential energy principle is used. This method estimates the linear behavior of the structure in the range of small and large deformations, with a very good accuracy and low...
متن کاملFour different types of a single drop dripping down a hole under gravity by lattice Boltzmann method
In this paper the dynamic of a droplet on a surface with a hole is investigated under gravitational effect by using lattice Boltzmann method. Incompressible two-phase flow with high density ratio proposed by Lee is considered. Cahn’s theory is used to observe the wettability of the surface in contact with liquid and gas phases. Several parameters such as contact angle, surface tension and gravi...
متن کاملOn the design and security of a lattice-based threshold secret sharing scheme
In this paper, we introduce a method of threshold secret sharing scheme (TSSS) in which secret reconstruction is based on Babai's nearest plane algorithm. In order to supply secure public channels for transmitting shares to parties, we need to ensure that there are no quantum threats to these channels. A solution to this problem can be utilization of lattice-based cryptosystems for these channe...
متن کاملTREE AUTOMATA BASED ON COMPLETE RESIDUATED LATTICE-VALUED LOGIC: REDUCTION ALGORITHM AND DECISION PROBLEMS
In this paper, at first we define the concepts of response function and accessible states of a complete residuated lattice-valued (for simplicity we write $mathcal{L}$-valued) tree automaton with a threshold $c.$ Then, related to these concepts, we prove some lemmas and theorems that are applied in considering some decision problems such as finiteness-value and emptiness-value of recognizable t...
متن کامل