Jacob Bernoulli

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A Gunawan S Alexander - One of the best experts on this subject based on the ideXlab platform.

  • HUBUNGAN DERET BERTINGKAT BERDASARKAN BILANGAN EULERIAN DENGAN OPERATOR BEDA
    Binus University, 2011
    Co-Authors: A Gunawan S Alexander
    Abstract:

    Deret bertingkat yang didefinisikan sebagai: �������������� … m n j j j j i a a n i m m Σ i Σ ΣΣi = = = 2 1 1 1 1 merupakan generalisasi dari Deret Pangkat Tetap (the sum of powers), yang solusi tertutupnya telah ditemukan secara empiris oleh Jacob Bernoulli pada tahun 1731. Makalah ini mencari hubungan antara deret bertingkat dengan operator beda. Untuk melihat hubungan ini, diberikan contoh-contoh untuk kasus m=1,2 dan α=1,2

  • HUBUNGAN DERET BERTINGKAT BERDASAR BILANGAN EULERIAN DENGAN OPERATOR BEDA
    Binus University, 2011
    Co-Authors: A Gunawan S Alexander
    Abstract:

    Deret Bertingkat yang didefinisikan sebagai: 1442443 K m n j j j j i a a n i m m Σ i Σ ΣΣi = = = 2 1 1 1 1 merupakan generalisasi dari Deret Pangkat Tetap (the sum of powers), yang secara empiris solusi tertutupnya telah ditemukan oleh Jacob Bernoulli pada tahun 1731. Dalam makalah ini, akan dicari hubungan antara Deret Bertingkat dengan Operator Beda. Untuk melihat hubungan ini, diberikan contoh-contoh untuk kasus m=1,2 dan α=1,

  • SOLUSI DERET PANGKAT TETAP DENGAN FUNGSI PEMBANGKIT
    Binus University, 2010
    Co-Authors: A Gunawan S Alexander
    Abstract:

    Makalah ini membahas mengenai Deret Pangkat Tetap a n i i Σ =1 , yang secara empiris solusi tertutupnya telah ditemukan oleh Jacob Bernoulli pada tahun 1731 dalam The Art of Conjecture. Dalam paper ini, akan dicari solusi tertutup dari Deret Pangkat Tetap ini dengan menggunakan Fungsi Pembangkit. Dengan mempelajari cara penurunan solusi tertutup dari Deret Pangkat Tetap, Fungsi Pembangkit ini dapat digunakan untuk memecahkan bentuk-bentuk Deret lain yang lebih umum

Alexander Agung Santoso Gunawan - One of the best experts on this subject based on the ideXlab platform.

Edith Dudley Sylla - One of the best experts on this subject based on the ideXlab platform.

  • Tercentenary of Ars Conjectandi (1713) Jacob Bernoulli and the Founding of Mathematical Probability
    2015
    Co-Authors: Edith Dudley Sylla
    Abstract:

    Jacob Bernoulli worked for many years on the manuscript of his book Ars Conjectandi, but it was incomplete when he died in 1705 at age 50. Only in 1713 was it published as he had left it. By then Pierre Rémond de Montmort had published his Essay d’analyse sur les jeux de hazard (1708), Jacob’s nephew, Nicholas Bernoulli, had written a master’s thesis on the use of the art of conjecture in law (1709), and Abraham De Moivre had published “De Mensura Sortis, seu de Probabilitate Eventuum in Ludis a Casu Fortuito Pendentibus ” (1712). Nevertheless, Ars Conjectandi deserves to be considered the founding document of mathematical probability, for reasons explained in this paper. By the “art of conjecturing ” Bernoulli meant an approach by which one could choose more appropriate, safer, more carefully considered, and, in a word, more probable actions in matters in which complete certainty is impossible. He believed that his proof of a new fundamental theorem – later called the weak law of large numbers – showed that the mathematics of games of chance could be extended to a wide range civil, moral, and economic problems. Gottfried Wilhelm Leibniz boasted that Bernoulli had taken up the mathematics of probability at his urging. Abraham De Moivre pursued the project that Bernoulli had begun, at the same time shifting the central meaning of probability to relative frequency. Key words: conjecture, Abraham De Moivre, G. W. Leibniz, weak law of large numbers. The origin of the frequentist theory of probability goes back to the question of whether one can compute the long-range frequency of some event E from known frequencies of some related events A, B,.... C. With an unavoidable degree of oversimplification, one might say that the theory of probability started in 1713, with the publication of the book Ars Conjectandi, by Jacob Bernoulli. Jerzy Nyman (1976, 152) 1. Introduction an

  • Tercentenary of Ars Conjectandi (1713) Jacob Bernoulli and the Founding of Mathematical Probability
    International Statistical Review, 2014
    Co-Authors: Edith Dudley Sylla
    Abstract:

    type="main" xml:id="insr12050-abs-0001"> The Tercentenary of the publication of Jacob Bernoulli's Ars Conjectandi (The Art of Conjecturing) provides an opportunity to look at the origins of mathematical probability from Jacob Bernoulli's point of view. Bernoulli gave a mathematically rigorous proof of what has come to be called the weak law of large numbers, relevant to discovering ratios of unknown factors through sampling. The Art of Conjecturing was a bridge between the mathematics of expectation in games of chance as found in Huygens's On Reckoning in Games of Chance and mathematical probability as found in Abraham De Moivre's The Doctrine of Chances. This paper looks at the conceptual context as well as the mathematics of Bernoulli's book.

  • Jacob Bernoulli and the Mathematics of Tennis
    Nuncius, 2013
    Co-Authors: Edith Dudley Sylla
    Abstract:

    Jacob Bernoulli’s Lettre a un Amy sur les Parties du Jeu de Paume employs the sorts of mathematical techniques that had been applied to games of chance by Pascal and Huygens to a game, now called Court Tennis or Royal Tennis, the outcomes of which depended, as he thought, not on chance but on athletic skill. He assumed that the players’ relative strengths could be determined a posteriori or by observation. Bernoulli’s work shows an alternate route by which mathematics was applied to the real world in the seventeenth century, one which did not involve Platonic conceptions of the role of mathematics, but rather the techniques of commercial arithmetic and, in particular, of algebra.

  • Mendelssohn, Wolff, and Bernoulli on Probability
    Moses Mendelssohn's Metaphysics and Aesthetics, 2011
    Co-Authors: Edith Dudley Sylla
    Abstract:

    In his “On Probability,” Moses Mendelssohn proposed to use a mathematical ­formulation of the definition of probability, found in the work of Christian Wolff to support the validity of induction (against Hume) and the view that all our actions, even including those supposed to be the result of free will, are predetermined (in agreement with Leibniz). Mendelssohn went into few of the details of mathematical probability as they had been developed by mathematicians like Jacob Bernoulli in the century before he wrote.

Patricia Radelet-de Grave - One of the best experts on this subject based on the ideXlab platform.

  • Newtonian scientists on the relation between the catenary curve and a self-supporting arch
    2012
    Co-Authors: Patricia Radelet-de Grave
    Abstract:

    In the Acta Eruditorum issue of May 1690, Jacob Bernoulli launches a challenge to the scientific community: “To find the curve shaped by a loose string freely hung from two fixed points.” And the mathematician from Basel adds: “I too assume that the string is a line which is easily flexible in all its parts.” Three men were in fact behind this challenge. Gottfried Wilhelm Leibniz, the founder of the Acta Eruditorum, who wished that the challenge might induce scientists to apply and develop the newly found calculus. Jacob Bernoulli who having read Leibniz’ article in 1687, had realized that, combined with Hooke’s law, calculus enabled specialists to treat continuous various phenomena such as flexibility of strings and elasticity of surfaces. The third man was the real inventor of the catenary problem, who also had solved it, he was Jacob’s younger brother and one time pupil, Johann Bernoulli. At that moment the brothers were still getting along; their famous quarrel was to start later.

  • The beginnings of elasticity and interaction with the development of the Calculus in Mechanics and architecture, between epistéme and téchne, ed Anna Sinopoli
    2010
    Co-Authors: Patricia Radelet-de Grave
    Abstract:

    We all know that Galileo imagined at least two problems that will later on concern elasticity, namely the problem of the hanging chain or catenaria and the fracture of the built in beam which will lead to the study of the deflection of such a beam known as elastica. The author starts the story of those problems in 1684, with the publication of two papers by Leibniz. The first one is the famous Nova methodus, where Leibniz gave the principal ideas for the differential and integral Calculus. The second paper is providing “new demonstrations on the resistance of bodies”, (Demonstrationes novae de resistentia solidorum), where he explained that before breaking, the beam is deflected. So he gave a model of deflection, using Hooke’s law of extension Leibniz’ model will give Jacob Bernoulli the possibility of applying the Calculus to the deflection of a beam.

  • The Problem of the Elastica treated by Jacob Bernoulli and the Further Development of this Study by Leonhard Euler
    2009
    Co-Authors: Patricia Radelet-de Grave
    Abstract:

    The article first recalls how Jacob Bernoulli began his study of elasticity with four problems, the solu- tions of which are made possible by the use of Leibniz's new differential and integral Calculus. These problems are the catenaria, the velaria, the lintearia and the elastica which gave its name to elasticity. He immediately tries to re-formulate all four problems within a single general theory. He tries to do so not only by starting with the principles of mechanics but also by starting with a variational principle or as he calls it with "isoperimetrical problems". The article then proceeds to show how Euler will, during more than forty years, try and finally suc- ceed in reaching Jacob's goal of generalization.

  • le de curvatura fornicis de Jacob Bernoulli ou l introduction des infiniment petits dans le calcul des voutes
    1995
    Co-Authors: Patricia Radelet-de Grave
    Abstract:

    Les limites et les generalisations possibles de la voute mince stable sous son propre poids n’ont pas ete comprises d’emblee. Les successeurs de Jacob Bernoulli doivent en meme temps comprendre les implications du calcul differentiel. Les difficultes rencontrees lorsque l’on veut etendre la theorie a une voute dotee d’une certaine epaisseur en temoignent

Gerd Gigerenzer - One of the best experts on this subject based on the ideXlab platform.

  • Intuitions about sample size; The empirical law of large numbers
    1997
    Co-Authors: Peter Sedlmeier, Gerd Gigerenzer
    Abstract:

    According to Jacob Bernoulli, even the “stupidest man ” knows that the larger one’s sample of observations, the more confidence one can have in being close to the truth about the phenomenon ob-served. Two-and-a-half centuries later, psychologists empirically tested people’s intuitions about sample size. One group of such studies found participants attentive to sample size; another found participants ignoring it. We suggest an explanation for a substantial part of these inconsistent findings. We propose the hypothesis that human intuition conforms to the “empirical law of large numbers ” and distinguish between two kinds of tasks—one that can be solved by this intuition (frequency distributions) and one for which it is not sufficient (sampling distributions). A review of the literature reveals that this distinc-tion can explain a substantial part of the apparently inconsistent results. Key Words: sample size; law of large numbers; sampling distribution; frequency distribution. Jacob Bernoulli, who formulated the first version of the law of large numbers, asserted in a letter to Leibniz that “even the stupidest man knows by some instinct of nature per se and by no previ-ous instruction ” that the greater the number of confirming observations, the surer the conjecture (Gigerenzer et al., 1989, p. 29). Two-and-a-half centuries later, psychologists began to study whether people actually take into account information about sample size in judgements of vari-ous kinds. The results turned out to be contradictory: One group of studies seemed to confirm, a second to disconfirm the “instinct of nature ” assumed by Bernoulli. In this paper, we propose an explanation that accounts for a substantial part of the contradic-tory results reported in the literature

  • Intuitions About Sample Size: The Empirical Law of Large Numbers
    Journal of Behavioral Decision Making, 1997
    Co-Authors: Peter Sedlmeier, Gerd Gigerenzer
    Abstract:

    According to Jacob Bernoulli, even the ‘stupidest man’ knows that the larger one’s sample of observations, the more confidence one can have in being close to the truth about the phenomenon observed. Two-and-a-half centuries later, psychologists empirically tested people’s intuitions about sample size. One group of such studies found participants attentive to sample size; another found participants ignoring it. We suggest an explanation for a substantial part of these inconsistent findings. We propose the hypothesis that human intuition conforms to the ‘empirical law of large numbers’ and distinguish between two kinds of tasks — one that can be solved by this intuition (frequency distributions) and one for which it is not suAcient (sampling distributions). A review of the literature reveals that this distinction can explain a substantial part of the apparently inconsistent results. * c 1997 by John Wiley & Sons, Ltd.