December 02, 2016 Friday
Bedtime Story
Translation, Rotation & Reflection
Translation, Rotation & Reflection
Translation in geometry can be best described as one-to-one
correspondence between all the sets of points on a plane.
In other words, every point of a translated object shifts in the
space by same given distance and direction.
Rotation in geometry is seen as motion in space that preserves at
least one point.
So besides this one point, all the rest turn around it by a fixed
angle.
To mathematicians, rotation is also seen as a mapping function.
Reflection is mapping of an Euclidean space to itself along a set
of fixed points that can be either an axis or a plane.
Another term that is introduced in Euclidean space is the word
affine.
Euclidean space is seen as an affine space rather than a vector
space.
Affine space makes the ideas of absolute distance, angles and
origins archaic and irrelevant keeping in prominence the notions of parallelism
and displacement.
There is no canonical (unique) choice where the origin should be.
This was a very brief and limited introduction on the idea of Euclidean
space that actually is an endless subject.
Cantor using his idea of 1-to-1 correspondence came upon a very
astonishing result.
He was trying out some very bizarre thought experiments.
For one, he tried to find out whether there could exist 1-to-1
correspondence between a unit square (a square with side of length 1 unit) and
a unit line (line of length 1 unit).
In attempting this, he ended up in finding a proof for a most stupefying
fact.
That there exists a 1-to-1 correspondence between all the points
on a unit line and all the points possible in an n-dimensional space!
He shot a letter to Dedekind in 1877 telling him about this
remarkable finding:
“I see it, but I don’t believe it!”
Stay tuned to the voice of an average story storytelling chimpanzee
or login at http://panarrans.blogspot.in/
Good night and my fellow cousin ape.
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, may I
suggest this large collection of Kids Songs:
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