Two new concepts, the generalized support function and restricted chord function, both referring to a convex set, were introduced in [1]. General formulae to yield the kinematic measure of a segment of fixed length in...Two new concepts, the generalized support function and restricted chord function, both referring to a convex set, were introduced in [1]. General formulae to yield the kinematic measure of a segment of fixed length in a convex set were established based on these concepts. In this article , using the partial intersection method, we consider the generalized Buffon problem for three kinds of lattices. We determine the probability of intersection of a body test needle of length l, l a.展开更多
Buffon’s needle experiment was originally devised to get the value of π. With the advent of computers, Buffon’s needle algorithm has been used pedagogically as an example of Monte Carlo methods in introduction clas...Buffon’s needle experiment was originally devised to get the value of π. With the advent of computers, Buffon’s needle algorithm has been used pedagogically as an example of Monte Carlo methods in introduction classes, and there are many Buffon’s needle algorithm implementations available on the internet. However, for the calculation of π, the exact value of π is used in the programs for Buffon’s needle angle sampling, and hence the example is not demonstrated correctly. This brief note presents a random angle sampling algorithm for the Buffon’s needle. We then compare the Buffon’s needle and Hit-and-Miss integration algorithms using Monte Carlo laboriousness comparison, and find that the Hit-and-Miss algorithm is superior.展开更多
Father Joseph-Adrien Lelarge de Lignac was born in Poitiers （France） in the year 1697. He died in Paris in 1762. In 1731, he was ordained priest and he became an oratorian the following year. His Letters to an Ameri...Father Joseph-Adrien Lelarge de Lignac was born in Poitiers （France） in the year 1697. He died in Paris in 1762. In 1731, he was ordained priest and he became an oratorian the following year. His Letters to an American is an attempt to refute Buffon and Condillac; this book was prepared in collaboration with Rraumur （J. Roger, P. Charbonnat）. Here, we present some elements of the correspondence between Lignac and Rraumur which show a scientific dialogue about 1736-1748 and we try to bring some foundations of the thought of Lignac to light. Between empiricism and ontology, Lignac stands up for scientific questions being subject to literal reading of the Bible. But Lignac is also the first one to perceive a way of thinking in Buffon Natural History （T. Hoquet）. According to him, the thought of Buffon is a deviation in an order of knowledge, because Natural History would especially be based on observation and experiment. So in this paper, we emphasize two original sources in the thought of Father de Lignac： Malebranche philosophy and his collaboration with Reaumur.展开更多
文摘Two new concepts, the generalized support function and restricted chord function, both referring to a convex set, were introduced in [1]. General formulae to yield the kinematic measure of a segment of fixed length in a convex set were established based on these concepts. In this article , using the partial intersection method, we consider the generalized Buffon problem for three kinds of lattices. We determine the probability of intersection of a body test needle of length l, l a.
文摘Buffon’s needle experiment was originally devised to get the value of π. With the advent of computers, Buffon’s needle algorithm has been used pedagogically as an example of Monte Carlo methods in introduction classes, and there are many Buffon’s needle algorithm implementations available on the internet. However, for the calculation of π, the exact value of π is used in the programs for Buffon’s needle angle sampling, and hence the example is not demonstrated correctly. This brief note presents a random angle sampling algorithm for the Buffon’s needle. We then compare the Buffon’s needle and Hit-and-Miss integration algorithms using Monte Carlo laboriousness comparison, and find that the Hit-and-Miss algorithm is superior.
文摘Father Joseph-Adrien Lelarge de Lignac was born in Poitiers （France） in the year 1697. He died in Paris in 1762. In 1731, he was ordained priest and he became an oratorian the following year. His Letters to an American is an attempt to refute Buffon and Condillac; this book was prepared in collaboration with Rraumur （J. Roger, P. Charbonnat）. Here, we present some elements of the correspondence between Lignac and Rraumur which show a scientific dialogue about 1736-1748 and we try to bring some foundations of the thought of Lignac to light. Between empiricism and ontology, Lignac stands up for scientific questions being subject to literal reading of the Bible. But Lignac is also the first one to perceive a way of thinking in Buffon Natural History （T. Hoquet）. According to him, the thought of Buffon is a deviation in an order of knowledge, because Natural History would especially be based on observation and experiment. So in this paper, we emphasize two original sources in the thought of Father de Lignac： Malebranche philosophy and his collaboration with Reaumur.
