Girolamo Cardano

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Girolamo Cardano
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Girolamo Cardano

• - Was an illegitimate child.
• - Cardan was outspoken and not well liked.
• This I recongnise as unique and outstanding
  amongst my faults- the habit, which I persist in,
  of preferring to say above all things what I know
  to be displeasing to the ears of my hearers. I am
  aware of this, yet I keep it up wilfully, in no
  way ignorant of how many enemies it makes for
  me.
• - In 1545 Cardan published Ars Magna his greatest
  work.
• - Besides Algebra he made great contributions in
  probability, hydrodynamics, mechanics and
  geology.

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(Continued)

• He had a passion for chess, dice and cards which
  lead to Liber de Ludo Aleae
• His early ideas of how to win at gambling made
  way for probability for Fermat and Pascal

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Ars Magna
Cardano's Ars Magna, the first great Latin
treatise devoted solely to algebra, appeared at
Nuremberg in 1545 and set forth the theory of
algebraic equations so far as it was then known.
It includes the solution of the cubic, which he
seems to have secured from Tartaglia under pledge
of secrecy and then dishonorably to have
published, and the solution of the biquadratic
which had been discovered by his pupil Ferrari.
Ferraris formula was believed to be absurd to
take a quantity to the fourth power, given that
there are only three dimensions.
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Cubic Equation

• -The hint for the cubic had been provided by
  Tartaglia, but
• Tartaglia could not provide solutions for all the
  other
• forms that the cubic might require
• -There was no cubic at the time, but thirteen
  cubics
• -Cardan was the first to acknowledge negavtive
  roots
• -He also was the pioneer to show a cubic could
  have three
• roots
• -Rafael Bombelli was the first to accept
  imaginary numbers
• -Bombelli had the idea that complex values of the
  radicals might be related much as the radicals
  themselves

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Formulas

• To obtain roots
• P b-a2/3
• Q -(2a3/27-ab/3c)
• Find roots by canceling the x2
• Xy-(a/3)

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Cubic Problems
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1.X3 20x 6x233 2.X3 64 6x2 24x 3.X3
27x 6x2 58
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References

• Book
• www.webguru.com/biography-girolamo-cardano.htm
• www.lib.virginia.edu/science/parshall/cardano.html
  
• www.stetson.edu/edfriedma/periodictable/html/Cd.h
  tml