December 03, 2017 Sunday
Bedtime Story
Mathematical Tables
In the days of Babbage any mechanical
device that did computing or rather calculations was called a machine and any
human ape that performed mathematical calculations as a routine was termed a
computer.
We all who are born after World War II may
find it amusing since computer now have become so powerful, quick and
multi-faceted that only a prodigy would be given the nickname of computer.
Back then, in the days of Babbage in 1850s,
even the conceptualized mechanical calculating devices were clunky and unwieldy
and the very thought of using them would have deterred many.
In fact, the nearest thing that came close
to a computing device was the mathematical tables.
I am sure you all must have used them as
school children, these tables often found at the back of standard mathematical
text books and use of calculators was an absolute blasphemy.
Now I understand that this kind of
unreasonable diktat was simply a prolongation of historical legacy.
There were days much before the invention
of computers or even electronic calculators when the logarithmic tables greatly
enhanced the speed of performing multiplication, division and exponential
operations.
Even extraction of nth root was greatly
simplified.
All these logarithmic tables were in turn
devised purely mechanically by human computers by hand.
Mathematical tables, as I am sure you are
aware, consist of more than logarithmic tables; we all did use mathematical
tables that contained sine, cosine and tangent trigonometric functions and
their reciprocals cosecant, secant and tangent.
Sometimes the tables would be arranged in
such a manner that angles less than 45 degrees would be in one page and angle
more than that in other pages.
All this mechanical calculations appeared
very trivial to me back then simply because I was never told that for many
years until World War II, these tables and this type of mechanical calculations
were central to navigation, astronomy, science, engineering, statistics and of
course, mathematics.
We of course limited ourselves to few
“important” angles such as 90 degrees (
/2
radians), 60 degrees (
/3
radians), 30 degrees (
/6radians),
45 degrees (
/4
radians) and so on.
I think, as far as I recall, my father had
taught me to derive these values using a simple equilateral triangle of side 1
or a right angles triangle with the base and height of 1.
It is very interesting to know how these
trigonometric terms originated.
Sine comes from the Latin sinus which means
“bend” but more specifically the hanging fold of the upper part of the famous
Roman dress toga or the bosom of a garment.
The Romans in turn had chosen this word as
it was the literal translation of the Arabic word jaib that meant pocket or
fold.
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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