August 02, 2018 Thursday
Bedtime Story
Lodovico Ferrari and Solution to the Depressed Quartic
Last night after starting with Lodovico
Ferrari, I had turned towards his master and teacher Gerolamo Cardano whose
real life story appealed to me personally since he too was a physician.
To be a renowned physician and an
accomplished mathematician and a writer (his Ars Magna is a majestic accomplishment
of the early Renaissance) is indeed praiseworthy.
Cardano is one of the few gamblers I know
who chronically lived on the brink of poverty and the only think that kept him
afloat was his mastery over the art of gambling and chess.
He even went on to write a book on gambling
which at its core was a treatise on the mathematics of chance and probability
using dice throwing as a means to understand these difficult concepts.
This book even had a chapter devoted to
methods of effective cheating in some of the prevailing games used in gambling
those days.
Cardano wrote in his autobiography that
Kings of Denmark and France and the Queen of Scotland tried to lure him as
their personal physicians but he declined.
Thanks to his fabulous practice of medicine
he left the mathematics teaching position of Rome in 1536 with his recommendation
to the post for his student Ferrari who then was mere 14 years old.
It is said that Cardano correctly predicated
his own death by committing suicide on the very same day that he had predicted
his death (pretty cool divining technique that I feel I should try on myself
too).
Ferrari took up the position of mathematics
after Cardano resigned from it and recommending his pupil.
From the age of 14 till the age of 42
Ferrari taught mathematics in Milan after which he finally retired and when on
to live with his sisters.
Story has it that he died there soon after
poisoned by his sisters with arsenic.
Let us see the solution the Ferrari offered
for the quartic polynomial.
Just like Scipione del Ferro, Ferrari too
tackled only the depressed quartic equation of the form:
y4 + py2 + qy + r = 0
The above equation he rewrote as
(y2 + p/2)2 = -qy – r
+ p2/4
Then Ferrari introduced a variable m in the
left-hand side
(y2 + p/2 + m)2 = 2my2
– qy +m2 + mp + p2/4 - r
Whatever be the value of m, the equivalence
of the equation to the original one does not change
Now this m can have any arbitrary value, we
can choose such a value so as to get an equation in which the value of the
right hand side would be 0.
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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