March 02, 2018 Friday
Bedtime Story
How Newton got his Hands on the Brachistochrone Problem
In short, a cycloid satisfies Snell’s Law
just the way light does, meaning it is the path of least time.
By the way, Galileo too had given a thought
to this problem even before it was posed formally by Johann Bernoulli (Johann
had proposed the problem in 1696 in the journal Acta whereas Galileo had passed
away some five decades ago in 1642).
Galileo had come to the conclusion that an
arc of a circle would be the path of shortest time to get from A to B if
gravity was the only force acting on the point object.
It is a fairly good answer though not
entirely accurate.
Circular paths are surely far better than
the intuitive answer of a straight line but it’s the cycloid path from A to B
that would get the rolling point quickest to B.
If you really care to know about the
brachistochrone problem, I recommend videos made on it by two of my favorite YouTube
channels, Vsauce and 3Blue1Brown.
It came as quite a surprise that another
favorite channel of mine Numberphile did not cover this topic though I suspect
that they may not have done so on account of the previous two channels having
already covered it and that too very comprehensively.
They are astoundingly beautiful videos
crafted with great care and utmost seriousness to make the mathematics as non-mathematical
and friendly as possible and yet keeping all the mathematical details accurate.
Now we need to get back to our story and
see whether Newton dared to take up the challenge posed by Johann Bernoulli.
It so happened that when the problem was
published in the Acta Eruditorum in June 1696, Newton was not aware of it for
six long months as he may not have got his hands on this issue of the journal.
You must remember that these were the old
days when news reached very slowly and Newton and Jacob Bernoulli were living
far apart in different countries.
When Jacob Bernoulli got no response for
the next six months that he further extended the time for response by
publishing it in a different journal called ‘programma’.
This journal ‘programma’ was a publication
of Groningen, Netherlands on January 1, 1697 by the Gregorian calendar but by
the Julian calendar that was being followed in Britain, the day of publication
was December 26, 1696.
It was when Newton got his hands on this
journal that he happened to come to know about the brachistochrone challenge and
that too some five weeks after its publication on January 29.
Newton claimed to have solved this problem
overnight and not only that but he went on to anonymously post the solution to
Johan Bernoulli.
When Johan Bernoulli received the solution,
he immediately recognized that this particular solution had to come from
Newton, one of the greatest mathematical minds of those times.
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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