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Please use this identifier to cite or link to this item: http://acervodigital.unesp.br/handle/unesp/369926
Title: 
Enumerating pythagorean triangles
Author(s): 
Rangel-Mondragon, Jaime
Language: 
eng
Description: 
  • Ensino Médio::Matemática
  • There is a one-to-one correspondence between positive rational numbers q less than 1 and points with positive rational coordinates (x,y) on the unit circle. This correspondence is achieved by joining the point (-1,0) with (0,q) and extending the line to intersect the unit circle at (x,y) as shown in this Demonstration. As any integral solution of the equation a²+b²=c² corresponding to a Pythagorean triangle can be put in the form (a/c)²+(b/c)²=1, we can associate Pythagorean triangles with points with positive rational coordinates on the unit circle. This Demonstration shows the n^(th) rational number and its associated n^(th) Pythagorean triangle. By varying n, can you find the only Pythagorean triangle with a side equal to 2009 that exists in the given range? Alas, the first rational with a part equal to 2009 is 30/2009 and it occurs at n=154876, too far out of our range n<1000
Issue Date: 
  • 18-Mar-2013
  • 18-Mar-2013
  • 18-Mar-2013
  • 2010
  • 14-Apr-2010
Publisher: 
Wolfram demonstrations project
Keywords: 
  • Educação Básica::Ensino Médio::Matemática::Geometria
  • Geometria
Notes: 
Enumerar os triângulos pitagóricos com coordenadas racionais positivas, em uma circunferência unitária. Esta demonstração mostra que para valores muito grandes ou muito pequenos de n, pode-se obter triângulos relacionados a estes valores, chamados n-ésimos triângulos
Credits: 
This demonstration needs the "MathematicaPlayer.exe" to run. Find it in http://objetoseducacionais2.mec.gov.br/handle/mec/4737
Source: 
http://objetoseducacionais2.mec.gov.br/handle/mec/22912
URI: 
http://acervodigital.unesp.br/handle/unesp/369926
Rights: 
Demonstration freeware using MathematicaPlayer
Type: 
outro
Appears in Collections:MEC - Objetos Educacionais (BIOE) - OE

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