@ mu naught : yes that is why i said 'n' rectangles where n-->infinity.In integral calculus nowhere do we prove that the area is invariant (i mean irrespective of orientation of coordinate axes in the case of integration)
Thanks a Lot for the reply! by splice i mean ''slice'' into non overlapping regions.
Firstly defining the area of a rectangle as its length*breadth, and then for any general closed curve defining its area as the sum of areas of 'n',non overlapping rectangles that it can be divided into.Where...
Hello!
Quite some time ago I'd asked for help with a proof that proves that area of a closed curve is invariant i.e : its independent of the way it is spliced into.
Say we splice a closed curve into one set of rectangles with parallel sides and we then splice an identical curve with...
Suppose A travels in a spaceship and B is on earth. At the time of launch they both synchronise their clocks. When 30 secs have passed by in A's clock he reads the time in B's clock to be 40 secs.But when 30 secs have passed in B's clock A's clock shows 40 seconds. Isn't this a contradiction to...
What i meant to ask is that how is v(ba)=-v(ab) ??
In Newtonian mechanics we do this simply as we consider space to be absolute,so the vector as seen from A's origin to B's origin will be just the opposite of what it is from B's origin to A's origin(we take that for granted i guess)
So isn;t a...
In special relativity we assume relative velocity of B wrt A is the same in magnitude and opposite in direction as of velocity of A wrt B. Now doesn't this demand that the position vectors in both frames(A's and B's) are the just opposite in direction...?
I mean to ask...how can we take for...
@symbolipoint
well..it might seem very simple and very nice...but what i am saying is that area is DEFINED!Here we don't say anything about surfaces...and just by looking at the figure we CANNOT say that the area WILL be the same calculated by any means...Prove it mathematically to support...
im sorry,i still don't completely understand...isnt there still a need to prove this?
as the set HAS an rea...according to evaluation of the limit using any PARTICULAR base in the definition known to me..
I am simply using the defintion:
Area of a rectangle is defined to be l*b.
Area of any other closed figure is defined as the limit evaluated by adding areas of n rectangles the figure is subdivided into where n-->infinity
i repeatedly ask...where is the proof that both th forumulas give the same number??
you said that both of them WERE the area...but area is i had said a DEFINITION...so still it remains to prove that both numbers will be equal..
i quote wikipediaonce again.. "It remains to show that the notion...
but what is the logic behind this axiom..it can't be on the basis of pure intuition...i quote wikipedia "It remains to show that the notion of area thus defined does not depend on the way one subdivides a polygon into smaller parts"
Now how do we mathematically prove this...this is what i am...