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Please use this identifier to cite or link to this item: http://acervodigital.unesp.br/handle/unesp/360786
Title: 
Relatively prime numbers and zeta(2)
Author(s): 
Arik, Okay
Language: 
eng
Description: 
  • Prime Numbers
  • Two integers are relatively prime if they share no common positive factors (divisors) except 1. In the graphic the points have integer x and y coordinates. If an integer pair consists of relatively prime numbers, no other such point lies on the line between the origin and this point. With no expansion, the distribution of relatively prime pairs is shown and their density (or probability) is expressed as p. When this distribution is expanded by s, their density is reduced by the square of s. Because there is no intersection between the expansion sets, the individual densities can be summed to obtain the overall density, which is 1. Therefore p is obtained as [1+(1/4)+(1/9)+...]^(-1), which is equal to 6/(pi)^2
  • Componente Curricular::Ensino Fundamental::Séries Finais::Matemática
Issue Date: 
  • 2008
  • 20-Sep-2008
  • 20-Sep-2008
  • 20-Sep-2008
  • 11-Sep-2008
Keywords: 
  • Prime Numbers
  • Greek Mathematics
  • Number Theory
  • Educação Básica::Ensino Fundamental Final::Matemática::Aritmética
Notes: 
Show relatively prime numbers and zeta
Credits: 
This demonstration needs the "MathematicaPlayer.exe" to run. Found in http://objetoseducacionais2.mec.gov.br/handle/mec/4737
Source: 
http://objetoseducacionais2.mec.gov.br/handle/mec/5615
URI: 
http://acervodigital.unesp.br/handle/unesp/360786
Rights: 
Demonstration freeware using Mathematica Player
Type: 
outro
Appears in Collections:MEC - Objetos Educacionais (BIOE) - OE

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