Girolamo Cardano
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Transcript of Girolamo Cardano
September 24, 1501 - September 21, 1576
GIROLAMO CARDANO
16 th Century Mathematician
Latin: Hieronymus Cardanus
Girolamo Cardano (Gerolamo),
(English: Jerome Cardan)
born on September 24, 1501 in
the city of Pavia, duchy of Milan
(Italy).
BIRTH
LIFE WITH MATHEMATICS
Cardano was the most outstanding
mathematician of his time.
Here are some of his works (books) in
Mathematics.
LIFE WITH MATHEMATICS
Practica Arithmetica et Mensurandi
Singularis (1539)
Ars Magna (1545)
Liber de Ludo Aleae (1663)
De Vita Propria
BOOKS
Practica Arithmetica et Mensurandi Singularis
(1539)
English: The Practice of Arithmetic and
Simple Mensuration
first mathematical publication
P r a c t i c a A r i t h m e t i c a e t M e n s u r a n d i S i n g u l a r i s ( 1 5 3 9 )
Ars Magna(Artis Magnæ sive
de regulis algebraicis liber
unus)(1545)
English: The Great Art; or, The Rules of Algebra
contained the solution of the cubic equation,
for which he was indebted to the Venetian
mathematician Niccolò Tartaglia, and also the
solution of the quartic equation found by
Cardano’s former servant , Lodovico Ferrari .
Ars Magna
This was probably the most important
mathematical achievement of the 16th
century.
This book contains a variety of methods for
solving polynomial equations, and anticipates
the discovery of complex numbers .
Ars Magna
He demonstrates for the first time that
solutions can be negative, irrational, and in
some cases may involve square roots of
negative numbers.
Ars Magna
In another book, Ars Magna Arithmetic ,
Cardano remarks that √(-9) is neither +3 nor
–3 but some “obscure third sort of thing”
(quaedam tertia natura abscondita ). This is
how complex numbers were announced to the
world.
Ars Magna
Liber de Ludo Aleae
(1663)
Caravaggio The Cardsharps c. 1594, oil on canvas, The Kimbell Art Museum, Fort Worth, Texas, USA.
English: The Book on Games of Chance
presents the first systematic computations of
probabilities
formulated the fundamentally important
concept of solving a probability problem by
identifying a sample space with equally likely
outcome
Liber de Ludo Aleae
When discussing the case of rolling two
symmetric dice he wrote:
. . . there are six throws with like faces, and
fifteen combinations with unlike faces, which
when doubled gives thirty, so that there are
thirty-six throws in all , . . .
Liber de Ludo Aleae
Cardano showed remarkable understanding
that the outcomes for two rolls should be taken
to be the 36 ordered pairs rather than the 21
unordered pairs.
Liber de Ludo Aleae
De Vita Propria
English: The Book of My Life
his autobiography; completed before he died
This book was an unvarnished and often
outrageous account of his character and
conduct .
Cardano displays the same unbounded
curiosity that made him a scientific pioneer.
De Vita Propria
“This I recognise 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.”
TRAGEDIESIN LIFE
Cardano's beloved son, Giambatista, confessed
that he poisoned his cuckolding wife. He was
then executed for murder (1560). Cardano
never recovered from the blow.
TRAGEDIES IN LIFE
In 1570 he was arrested on the accusation of
heresy (in part for casting the horoscope of
Jesus). After several months in jail , he was
permitted to abjure privately, but he lost his
position and the right to publish books.
TRAGEDIES IN LIFE
Cardano is reported to have correctly
predicted the exact date of his own death
but…
TRAGEDIES IN LIFE
… he committed suicide by drinking a glass
of poison on September 21, 1576 to ensure
his prediction would come true.
TRAGEDIES IN LIFE
“Quinquies exscriptus, maneat tot millibus annis.”
“I wrote it out five times, may it last
the same number of millennia.”
– final line of Ars Magna
QUOTATION
In what way/s can you
relate your life to
Cardano’s?
QUESTIONHe had been a hot tempered person, not well - l iked, a
compulsive gambler, but he st i l l stood outduring his t ime.