Related papers: Triangles, Fractales and Spaghetti
We study a Fermi-Pasta-Ulam-like chain with realistic potentials, which models a unidimensional solid in contact with heat baths at some temperature. We formulate an explicit analytical expression for the probability density of bonding…
This paper introduced a way of fractal to solve the problem of taking count of the integer partitions, furthermore, using the method in this paper some recurrence equations concerning the integer partitions can be deduced, including the…
The statistical physics approach to the number partioning problem, a classical NP-hard problem, is both simple and rewarding. Very basic notions and methods from statistical mechanics are enough to obtain analytical results for the phase…
"No two rainbows are the same. Neither are two packs of Skittles. Enjoy an odd mix!". Using an interpretation via spatial random walks, we quantify the probability that two randomly selected packs of Skittles candy are identical and…
In this article (it's only in italian, but I'm translating it) I will try to solve some questions about a mathematical problem that my friend Patrizio Frederic, a researcher in statistics at the University of Modena, proposed to me. Given…
Charles L. Dodgson, also known as Lewis Carroll, in his book "Pillow problems" from 1893 asked for the likelihood of a random triangle to be obtuse. Clearly, the answer to Dodgson's question depends strongly on the assumed random…
We introduce series-triangular graph embeddings and show how to partition point sets with them. This result is then used to improve the upper bound on the number of Steiner points needed to obtain compatible triangulations of point sets.…
We discuss the formation of stochastic fractals and multifractals using the kinetic equation of fragmentation approach. We also discuss the potential application of this sequential breaking and attempt to explain how nature creats fractals.
We consider two division problems on narrow strips of square and hexagonal lattices. In both cases we compute the bivariate enumerating sequences and the corresponding generating functions, which allowed us to determine the asymptotic…
A triangle decomposition of a graph is a partition of its edges into triangles. A fractional triangle decomposition of a graph is an assignment of a non-negative weight to each of its triangles such that the sum of the weights of the…
The conditions determining that two triangles are congruent play a basic role in planimetry. By comparing not congruent triangles with respect to given sets of corresponding elements it is important to discover if they have any common…
The problem of searching for a model-based scene interpretation is analyzed within a probabilistic framework. Object models are formulated as generative models for range data of the scene. A new statistical criterion, the truncated object…
We formulate the statistics of the discrete multicomponent fragmentation event using a methodology borrowed from statistical mechanics. We generate the ensemble of all feasible distributions that can be formed when a single integer…
We establish properties of a new type of fractal which has partial self similarity at all scales. For any collection of iterated functions systems with an associated probability distribution and any positive integer V there is a…
Various semantics for studying the square of opposition and the hexagon of opposition have been proposed recently. We interpret sentences by imprecise (set-valued) probability assessments on a finite sequence of conditional events. We…
The multifractal spectrum of various three-dimensional representations of Packed Swiss Cheese cosmologies in open, closed, and flat spaces are measured, and it is determined that the curvature of the space does not alter the associated…
This paper deals with the history of the following problem: "Can an arbitrary rectangle be dissected into 3 non-rectangular congruent regions?" We present a new elementary proof that the answer is indeed no.
The equilibrium distributions of the different pasta geometries and their linear sizes are calculated from the mean field Gibbs energy functional in symmetric nuclear matter at finite temperature. The average sizes and shapes coincide…
Santal\'o calculated the measures for all positions of a moving line segment in which it lies inside a fixed circle and intersects this circle in one or two points. From these measures he concluded hitting probabilities for a line segment…
The Three Gap Theorem states that for any $\alpha \in \mathbb{R}$ and $N \in \mathbb{N}$, the fractional parts of $\{ 0\alpha, 1\alpha, \dots, (N - 1)\alpha \}$ partition the unit circle into gaps of at most three distinct lengths. We prove…