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        riddles >> general problem-solving / chatting / whatever >> Story: Tartaglia, Cardan, and Cubic Equations
        
(Message started by: william wu on May 15th, 2003, 7:57pm)
Title: Story: Tartaglia, Cardan, and Cubic Equations
Post by william wu on May 15th, 2003, 7:57pm
The fascinating story of the mathematician Tartaglia, and his feud with Cardano and Ferrari over revealing the secrets to solving cubic equations algebraically:

http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Tartaglia.html



The article refers to a poem which Tartaglia writes to convey the secrets to Cardan in an encrypted form; this poem is reprinted below:

   When the cube and the things together
   Are equal to some discrete number, 1
   Find two other numbers differing in this one.
   Then you will keep this as a habit
   That their product shall always be equal
   Exactly to the cube of a third of the things. 2
   The remainder then as a general rule
   Of their cube roots subtracted
   Will be equal to your principal thing. 3
   
   - Tartaglia, March 1539

   Footnotes:
   1 Solve x3 + cx = d
   2 Find u, v such that u - v = d and uv = (c/3)3
   3 Then x = 3u - 3v


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