December 04, 2017 Monday
Bedtime Story
Origins of Trigonometric Sine
Last night we had left talking about the
origins of the word Sine, one of the trigonometric functions.
Europeans had found this word “jaib” in the
works of Islamic mathematicians such as Muhammad al-Khwarizmi and Al-Battani
who flourished during the Golden Era of Islam.
One of the major works of Al-Battani who
lived somewhere around 900 AD was Kitab-aj-Jiz or the Book of Astronomical
Tables.
The Europeans had actually misread the
Arabic word jyb and understandably had converted it into jaib.
Arabic mathematicians had in their turn had
transliterated this word from the Hindus who had used the Sanskrit word jiva or
jya as the term for sine.
The Sanskrit word translates into
bowstring.
If you think that is the end of the origin
of the word sine, you are mistaken.
The Hindus in their turned were inspired
from Greeks word for chord who had sued the chord function that is related to
the modern sine function.
The origin of tangent is pretty straight
forward.
Tangent comes from the Latin word tangens which means touching as
tangential line touches the circle.
Secant too has no complexity behind its
origins.
Secant comes from the Latin word secans which means “cutting” as a secant
cuts the circle.
The prefix “co-“ that is used in cosine,
cotangent and cosecant came very late in the language of mathematics, seen for
the first time in print only after 1600.
The prefix stands for complementi; thus cosine means sinus
complimenti or sine of the complimentary angle.
Mathematical tables proved to be very
useful for the rapidly industrializing European powerhouses, their utility approximating
very near to the smart phones of today.
In spite of their great utility they were
very vulnerable to errors since human computers were involved, both in the
transcription of the tables as well as in calculations.
This was noted by Babbage and since as we
saw earlier, he was already keen on mechanization of factory production, the idea
of mechanization of computation in the production of mathematical tables
followed naturally.
Let me quote a small passage from the 1953
book “Faster than Thought” written by Bertram Bowden that describes very
pertinently how the idea of mechanization of mathematical tables came into the
mind of Charles Babbage.
“In 1812 he was sitting in his room in the
Analytical Society looking at a table of logarithms, which he knew to be full
of mistakes, when the idea occurred to him of computing all tabular functions
by machinery.
The French government had produced several
tables by a new method.”
We shall continue with this idea in the
nights to come.
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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