The Holographic Universe and Pi = 4 in Kinematics!

[verpies]

Each one of your jaunts along two edges of the approximating squares travels along one segment towards the perimeter and one away from it.    Dividing into a larger quantity of smaller squares does not change the path length. 

That was Gravityblock's whole point.  The path length does not change with finer subdivision - only area does.
You were supposed to be a good opponent and refute his observation that real physical circles have the same circumference as physical squares - not agree with Gravityblock.

BTW:  A real physical circle must be defined by some real physical process, not an abstract one.

You still have not replied directly which diagram (Diag.3 or Diag.4 or Diag.5) correctly depicts reality in this physical process, in your opinion.

[verpies]

Wrong and wrong.  This is basic calculus and physics.Invented math and physics yield nonsense answers.

Refute my statements rigorously.  Show me the error in logic or math.
An argument by assertion is not the way to do it.

First of all:  How can V_║(t₁) be smaller than the tangential velocity V_T(t₀) if the force acting on it was always perpendicular between t₀ and t₁ ?

[MarkE]

Wrong and wrong.  This is basic calculus and physics.Invented math and physics yield nonsense answers.

Refute my statements rigorously.  Show me the error in logic or math.
An argument by assertion is not the way to do it.

First of all:  How can V║(t1) be smaller than the tangential velocity VT(t0) if the force acting on it was always perpendicular between t0 and t1 ?

http://theory.uwinnipeg.ca/physics/circ/node6.html

[verpies]

Refute my statements rigorously.  Show me the error in logic or math.
An argument by assertion is not the way to do it.

First of all:  How can V║(t1) be smaller than the tangential velocity VT(t0) if the force acting on it was always perpendicular between t0 and t1 ?

http://theory.uwinnipeg.ca/physics/circ/node6.html

That theory page does not show rigorously that when "the direction of the centripetal acceleration is inwards along the radius vector"  then circular motion is produced - it just asserts it, like you.

The question how can V_║(t₁) be smaller than the tangential velocity V_T(t₀) if the force acting on it was always perpendicular between t₀ and t₁, still stands unanswered.

[MarkE]

That was Gravityblock's whole point.  The path length does not change with finer subdivision - only area does.
You were supposed to be a good opponent and refute his observation that real physical circles have the same circumference as physical squares - not agree with Gravityblock.

BTW:  A real physical circle must be defined by some real physical process, not an abstract one.

LOL, you can enjoy yourself misstating what I have said if that pleases you. 

Gravityblock's method does not reproduce the path of travel along the circumference.  The path that his method generates constantly approaches and then turns away from the circumference.  With enough and small enough square elements, his method can accurately approximate the circle's area and outline using the vertices that touch or approach the circumference.  As his method constantly turns away from the circumference it never improves its approximation of the circumference's path.  It doesn't matter how small or how many elements he uses. 

The shortest path between two points is only orthogonal line segments when one of those segments is zero length.  The distance following a Manhattan route between vertices on the circumference is therefore always greater than the straight line distance between the same vertices.