(A chat conversation with my best friend Saumeet, one of the few people who is rather patient with me being mathematically-challenged...or is it?)
From my Gtalk Window:
Saumeet: acha ek triangle imagine karo
me: Hmmm...
Saumeet: fir ek square imagine karo
me: Hmmm...
Saumeet: phir ek regular pentagon
and so on
sides badhaate hue jaao
number of sides
hexagon, septagon, octagon
and so on
100 sides
1000 sides
what is the shape becoming more and more like?
me: bada
the shape is becoming more and more bada
Saumeet: arre, can you see the shape converging to a circle?
me: yeah yeah....circle it is...
Saumeet: infinitely many
right?
me: If u insist :-S
Saumeet: just the way a triangle is three st lines one after the other.
me: Where are we going... :-/
Saumeet: Point being every curve is a sum total of st. lines
isliye saare curves ke slopes bhi hote hain
which point towards direction of the tangent
me: Hmmm...
Saumeet: to basically, through triangle inequality, we can prove that a st line from A to B is the shortest path from A to B, instead of, following a path of any set of st lines
And since, a curve is just a set of infinite number of infinetesimally small st lines, so, a st line from A to B is also the shortest path when compared to any curve from A to B
which means that a st line from A to B is the shortest path from A to B
me: Which is quite straightforward observation in real life?
Sent at 8:07 PM on Wednesday
Saumeet: Hmmm...
4 comments:
A taste of reality -
Saumeet: to basically, through triangle inequality, we can prove that a st line from A to B is the shortest path from A to B, instead of, following a path of any set of st lines
And since, a curve is just a set of infinite number of infinetesimally small st lines, so, a st line from A to B is also the shortest path when compared to any curve from A to B
which means that a st line from A to B is the shortest path from A to B
which is quite straightforward observation in real life
Abhilasha: :P
^Nice try. The fact that it says "Saumeet" instead of "me" validates the tweaking ;)
:-o yeh kya tha?? It increased my hatred 4 maths :P
Saumeet refers to himself in the third person and google knows it.
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