• Title/Summary/Keyword: Bertrand's paradox

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RANDOM CHORD IN A CIRCLE AND BERTRAND'S PARADOX: NEW GENERATION METHOD, EXTREME BEHAVIOUR AND LENGTH MOMENTS

  • Vidovic, Zoran
    • Bulletin of the Korean Mathematical Society
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    • v.58 no.2
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    • pp.433-444
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    • 2021
  • In this paper a new generating procedure of a random chord is presented. This problem has its roots in the Bertrand's paradox. A study of the limit behaviour of its maximum length and the rate of convergence is conducted. In addition, moments of record values of random chord length are obtained for this case, as well as other cases of solutions of Bertrand's paradox.

A Study on Geometrical Probability Instruction through Analysis of Bertrand's Paradox (Bertrand's Paradox 의 분석을 통한 기하학적 확률에 관한 연구)

  • Cho, Cha-Mi;Park, Jong-Youll;Kang, Soon-Ja
    • School Mathematics
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    • v.10 no.2
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    • pp.181-197
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    • 2008
  • Bertrand's Paradox is known as a paradox because it produces different solutions when we apply different method. This essay analyzed diverse problem solving methods which result from no clear presenting of 'random chord'. The essay also tried to discover the difference between the mathematical calculation of three problem solvings and physical experiment in the real world. In the process for this, whether geometric statistic teaching related to measurement and integral calculus which is the basic concept of integral geometry is appropriate factor in current education curriculum based on Laplace's classical perspective was prudently discussed with its status.

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