July 30, 2018 Monday
Bedtime Story
It was only somewhere in 1540 or 1550 that
two men from Mediterranean Europe, the next power house of mathematics after the
Islamic World, that the two men, one a Venetian by the name of Niccolo Fontana
Tartaglia (the stammerer) and Italian by the name of Gerolamo Cardano (an
accomplished gambler and chess player in addition to being a perpetually poor
doctor) provided to the world the general formula for the solution to cubic
equations.
Even before them, there was another Italian
mathematician by the name of Scipione del Ferro who had arrived at a solution
to what is known as depressed cubic equation or simplified cubic equation.
He never published his work because strangely
enough in those times there was this concept of public mathematical duel where
mathematicians publicly posed challenges to each other.
What is most surprising that the loser in
such public mathematical duels was vulnerable to the loss of his funding or
position in the University if he happened to occupy.
Scipione del Ferro was a lecturer in
arithmetic and geometry at the University of Bologna and because of his fear of
being challenged he kept his mathematical works private and only wrote them
down in his personal notebooks that was shared with a group of very selected
people close to him.
A general depressed cubic equation looks
something like this:
x3 + px = q
It is known exactly how del Ferro came to
his solution for the depressed cubic equation as only one note book of his had
survived that was inherited by his son-in-law who in turn had happened to share
it with Girolamo Cardano.
Cardano in his turn published the solution
in his Ars Magna or “The Great Art” in 1545.
The first edition of the book came in three
volumes and consisted of forty chapters dedicated specifically to algebra.
It was first published in 1545 and is
considered as one of the three greatest scientific work of the Renaissance
along with Nicolaus Copernicus’ ‘On the Revolutions of the Heavenly Spheres’
(1543) and Andreas Vesalius’ ‘On the fabric of the human body in seven books’
(1543).
If I were to provide you even today the
general solution of the cubic equation, you will understand why it took so many
hundreds of years before the human apes arrived at its solution.
So here goes, let me show you the solution
as addressed by Gerolamo Cardano in his book Ars Magna, but surely helped in a
major way by both Scipione del Ferro and Tartaglia.
Cardano was a gentleman and in this book
explicitly acknowledges the formula for solving the cubic equation was provided
to him by Tartaglia.
Once again it needs to be stressed that
this Cardano’s method is only applicable to the depressed cubic equation
t3 + pt + q = 0
We shall take a closer look at the
Cardano’s method of the solution to the general depressed cubic equation in the
nights to come.
Stay tuned to the voice of an average story storytelling
chimpanzee or login at http://panarrans.blogspot.com
Good night Mon Ami and my fellow cousin ape.
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Another great educator and a teacher that I am aware of is
Professor Subhashish Chattopadhyay in Bangalore, India.
While I narrate stories, Professor Subhashish an electronic
engineer and a former professor at BARC, does and teaches real mathematics and
physics.
He started the participation of Indian students at the
International Physics Olympiad.
Do visit him here:
All his books can be downloaded for free through this link:
For edutainment and English education of your children, I
recommend this large collection of Halloween Songs for Kids:
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