August 18, 2018 Saturday
Bedtime Story
The Elements of Perspective
Last night we had to move on to the
mathematics of perspective because there exists a link in what Felix Klein
proposed to reconcile two geometries and in the mathematics related to the art
of perspective.
Everybody should be familiar with the word
perspective or what it implies but many of us would not be accurately able to
define it.
Or perhaps you may give a hint of your understanding
but may not exactly be able to characterize the definition completely.
So what exactly is meant by perspective
when it comes to graphical art (we can leave aside the mathematics for the time
being)?
Well, you see that our retina on which the
image of the world is created is a two dimensional plane (if you ignore the
manifold nature of it by ignoring the cellular level irregularities) whereas
the world around is at the minimum three-dimensional (at least that much is
sufficient for our selfish genes to play out their games).
So when the image of the surrounding falls
on our retinas, two things happen to the objects that are lying at variable
distances:
One, the objects that are at the distance
become smaller than the ones which are closer (of course, their relative sizes
also play a role).
Secondly, the objects are subjected to
foreshortening.
Now this is an interesting word.
What is this foreshortening?
Foreshortening is a visual phenomenon
wherein the change in objects’ dimensions varies in a disparate way.
There is a greater shortening of the
object’s dimensions along the line of the site than across the line of site
(the key words in this sentence being ‘along’ and ‘across’.
It is interesting that the men who took in
interest in the arts and paintings during the Italian Renaissance were never
just painters or architects, but also mathematicians and geometers as well.
They took a great deal of interest in the
optical geometry of linear perspective, an idea that again most of you would be
vaguely familiar with without being accurately able to describe what it actually
is.
So let try to understand this old idea of
linear perspective.
One of the core essentials of any
perspective art is the concept of a horizon line that is paced on the image
directly opposite the viewer’s eye.
This horizon line actually represents the
Earth’s horizon which is the apparent line that separates the earth from the
sky.
In relation to perspective drawing, the
factual earth’s curvature is totally set aside and any theoretical line onto
which a given horizontal plane converges when projected onto the picture plane
is deemed to be the horizon.
We are currently considering the horizon
only from the artists’ perspective and not from the point of view of a
physicist or an astronomer which is both interesting and fun but we can leave
it aside for now.
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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