March 14, 2017 Tuesday
Bedtime Story
al-Khwarizmi Used Only Words, Bereft of Any Symbolism
Further al-Khwarizmi says:
“Halve the roots; moiety is fifty and half”.
We would use our notation of quadratic equation here.
Let the root of the equation be p and q.
Then (p + q)/2 = 50 + ½
Then he says:
“Multiply this by itself, it is two thousand five hundred and
fifty and a quarter”.
((P + q)/2)2 = (50 + ½)2 = 2550 + 1/4
Then he says:
“Subtract from this one hundred; the remainder is two thousand
four hundred and a fifty and a quarter.”
2550 + ¼ - 100 = 2450 + ¼
“Extract the root from this; it is forty nine and a half”
√(2550+¼ - 100) = 50.5 + ½
- 50 ~ 49 ½
“Subtract this from the moiety of the roots, which is fifty and a
half. There remains one and this is one of the two parts”.
50 1/2 - 49 1/2 = 1
The entire algebraic operation if you notice was conducted in
words.
There is not a single iota of notation, either modern or
primitive, used anywhere.
And so it remained for a long time that way even till the time of
Vieta in 1600.
Vieta was not even aware of the symbol for multiplication or the
symbol for equality (=).
So frustrated was he with the algebraic notations that hardly
existed or barely were used that he wrote these harsh words to express his
feelings of distraught:
“These things which are new are wont in the beginning to be set
forth rudely and formlessly and must then be polished and perfected in
succeeding centuries.
Behold, the art which I present is new, but in truth so told, so
spoiled and defiled by the barbarians, that I considered it necessary, in order
to introduce an entirely new form into it, to think out and publish a new
vocabulary, having gotten rid of all its pseudo-technical terms…”
Vieta laid down the principle that the quantities that would be in
an equation must be homogenous.
His algebra had operations taking place on letters and the final
result was obtained by simple replacement.
This forms the basis of the contemporary algebraic method.
With Vieta, finally letters became a norm to be used as algebraic
variables.
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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