January 01, 2017 Sunday
Bedtime Story
Naming All Points on and in the Sphere
Naming each and every infinite point of our hypothetical sphere is
equivalent to creating an infinite mathematical set.
This can be conveniently done using four letters for the chief
cardinal directions.
Up U (all points starting with U can be colored
red)
Down D (all points starting
with D can be colored green)
Right R (they can be colored light blue)
Left L (and these violet)
Starting Points (pink)
Poles (yellow)
The starting point will be the origin for each particular set.
The set of sphere with infinite points that we are creating will
also have a center and two fixed poles.
The nearest points from the origin can then be labeled as RR, LL,
UU, DD but not RL or UD or DU since such a manipulation returns you to the
original location.
Then you can further have UUU, DDD, RRR, LLL,
UUR, DDR, RRU, LLU…and so on.
You get the idea I think.
The similarity of this to the hyper-Oxford dictionary is distinctly
perceptible.
You also get the idea that these will be uncountably huge number
of such points.
Physically it is an impossible feat to carry out but
mathematically one can.
Now we are going to repeat this exercise taking another point on
the surface as origin and generate such discrete uncountably infinite points.
After doing so, we are going to repeat this taking every possible
point on the sphere as origin.
Once this is done (theoretically), every point of the sphere has
been labelled.
Having done that mammoth task, we have to consider the poles that
do NOT change.
Now from these mammoth sets of points, we are going to separate
out all the up points, all the down points, all the left points and all the
right points along with every single origin and every single pole.
Remember that we had given a unique color for each of them, because
of which we would eventually land up with 6 spheres.
It will look somewhat like this as animated by Vsauce in one of his
video.
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.
A colored visual representation of all the labelled points on and inside the sphere (Copyright Vsauce1 and Michael Stevens)
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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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