February 27, 2018 Tuesday
Bedtime Story
The Brachistochrone Challenge
The brachistochrone problem was posed with
the hope or rather the conviction that only the true originator of calculus
would be able to offer its solution using infinitesimal calculus (there are
multiple ways to arrive at the solution of this problem).
Before I state the brachistochrone problem,
let us first understand what this word means.
Brachistochrone is a compounded word that
comes from two ancient Greek words brakhistos which means shortest and khronos
which means time.
So the word simply means shortest time and
the problem would The Shortest Time Problem.
So now if you wish you can even forget that
complex Greek word and simply think this as The Shortest Time Problem and that
will perhaps take away 90% of your fear and trepidation.
Also now the problem should begin to sound
more understandable.
Brachistochrone curve is a familiar concept
to most mathematicians and physicists as a curve of fastest descent of a
frictionless ball between point A and a lower point B lying on a single plane
with point B lying not directly below A.
But that information is going ahead of the
story and you can forget that last sentence for time being.
Now let us go back to Jacob Bernoulli and
see how he framed the problem in the journal.
“I, Johann Bernoulli, address the most
brilliant mathematicians in the world.
Nothing is more interesting to intelligent
people than an honest, challenging problem, whose possible solution will bestow
fame and remain as a lasting monument.
Following the example set by Pascal, de
Fermat, etc., I hope to gain the gratitude of the whole scientific community by
placing before the finest mathematicians of our time a problem which will test
their methods and the strength of their intellect.
If someone communicates to the solution of
the proposed problem, I shall publicly declare him worthy of praise.”
With this he stated with utmost pithy the
problem:
“Given two points A and B in a vertical
plane, what is the curve traced out by a point acted on only by gravity, which
starts at A and reaches B in the shortest time.”
Many mathematical problems are very
difficult to state.
Take for example Riemann Hypothesis; most
average apes would not be even to properly even state the hypothesis even after
having it being explained to them by masters.
In his 2003 book “Prime Obsession: Bernhard
Riemann and the Greatest Unsolved Problem in Mathematics” the author who is
himself a mathematician John Derbyshire took great pains and devoted several
chapters in merely introducing to the authors what exactly the Riemann Hypothesis
states.
The very first three terms “Riemann zeta
function” of the hypothesis are so heavily loaded that one gets to know them, albeit
only amateurishly, only by the end of the book.
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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