March 14, 2017 Tuesday
Bedtime Story
Using these two operations, al-Khwarizmi was able to solve the
linear and quadratic equations by reducing any problem to the following six
forms (where a, b and c are positive integers):
Squares equal root ax2 = bx
Squares equal number ax2 = b
Roots equal number bx = c
Squares and roots equal number ax2 + bx = c
Squares and number equal roots ax2 + c = bx
Roots and number equal squares bx + c = ax2
These unforgettable and legendary terms are found in the
mathematical treatise written by al-Khwarizmi in around 830 AD.
The book is called:
The Compendious Book on Calculation by Completion and Balancing
It is interesting to have a glimpse of its Arabic version too as
some of the names would seem very familiar to the Hindus both of the past as of
the present.
“Al-kitab al-mukhtasar fi
hisab al-jabr wa’l-muqabala”
The other book that this great legend wrote and which in turn
would inspire Fibonacci 400 years later to write Liber Abaci and Modus Indorum
was:
“On the Calculation with
Hindu Numerals”.
Yet even this great genius had not invented the algebraic notation
and mainly used words like your average storytelling chimpanzee.
Let me give you an example how al-Khwarizmi stated his problems
and the answers.
Question:
“If someone say you divide ten into two parts, multiply the one by
itself, it will be equal to the other taken eighty one times”.
His answer comes as follows:
“You say, ten less thing, multiplied by itself, is a hundred plus
a square less twenty things, and this is equal to 81 things.”
Today we would depict that “thing” with the unknown x.
It seems quite remarkable that even as late as 850 AD, a long way
since the human apes had left Africa and discovered civilization, the notion of
using x for an unknown variable had not been invented.
And the above sentences will be transformed to the following
equation.
100 + x2 – 20x = 81x
Then he says:
“Separate the twenty things from a hundred and a square and then
add them to eighty-one.
It will then be a hundred plus a square, which is equal to hundred
and one roots.”
This will be written as:
100 + x2 = 101x
Stay tuned to the voice of an average story storytelling
chimpanzee or login at http://panarrans.blogspot.in/
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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