I have this thought that circle in 'real' is not a closed figure. We all know that 'pi' is irrational.And integers are nodes in a 'monstrous' line of real numbers. Irrational numbers are non-terminating i.e. to whatever lower scales you go and try to measure, there is still something left (so are repeating decimals).
Lets say in a Cartesian plane we start at a point (x0 ,y0), x0 = 0.0000000.... and y0 = 0.000000... and draw a circle ( let the center be (2.000000....., 0.00000000...) ). If its perimeter itself is non-terminating how are we closing circle at (x0 ,y0) again. i.e. even though how much you draw shouldn't there be even more to draw to close that circle?
(Perimeter = 2*pi*radius, and 'pi' is irrational => perimeter is irrational or non-terminating)
The same problem occurs also when
a) repeating decimals are present,
b) In isosceles right angled triangle, where hypotenuse has Sqrt(2),
Is this problem related anyhow to Achilles-tortoise problem? ( I don't see any-- the reason is that, here a infinite series is not converging 'miraculously' to a finite value instead we have a irrational value to realize)
Am I going wrong somewhere?