Lesson 7: Solution to Diophantus Riddle (VI)

March 17, 2012

This is the translation of the epitaph into Spanish:

” Aquí fueron sepultados los restos de Diofanto. La infancia de Diofanto duró 1/6 de su vida, 1/12 en la adolescencia, cuando la barba cubrió su cara, Después de 1/7 de su vida contrajo nupcias. Luego de cinco años de casado nació su primer hijo. El hijo vivió ½ de la vida de su padre, su padre buscó consuelo en los números pero no lo logró y murió cuatro años después que él.”

Let x be the age of Diophantus. If we translate the epitaph into Algebra:

x/6 +x/12 +x/7 +5 +x/2 +4 = x
14x/84 +7x/84 +12x/84 +420/84 +42x/84 +336/84= 84x
14x +7x +12x +420 +42x +336= 84x
14x +7x +12x +42x -84x= -420 -336
-9x = -756
x = -756/-9 =  84  years old.


Then we have that Diophantus was born about 200 and died about 284.

Thanks  Lidia for your effort!


One comment

  1. Hi Monica, we´re Alba and Esther and we can´t leave a comment about the Thales´s story in its place so we are going to put it here:
    When the shadow is in the stick, it forms a rectangle triangle from the piramid´s height to the stick. Next, the stick´s shadow forms a rectangle triangle similar to the other one.
    And if you Know the stick´s height you can know the piramid´s height. All of these is made possible by the application of similarity in triangles.

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