The Holographic Universe and Pi = 4 in Kinematics!

[MarkE]

Again, your post is not a scientific argument.

Gravock

LOL, I've covered why the squares method taken to its limit converges on the area but not the circumference.  And your scientific counterargument was?

[gravityblock]

LOL, I've covered why the squares method taken to its limit converges on the area but not the circumference.  And your scientific counterargument was?

Look up Planck's constant - matter/energy is quantized. A circle is theoretical, there's no perfect circle in nature anywhere.  A real circle with a time variable is quantized at the planck scale with a zig-zag or rectilinear circumference, just as you find with the square in the squares method.  This is how there is a convergence on the rectilinear circumference at the planck scale. 

Edit:  Also, in step two of the squaring method, we can see there are four points of the square which converge on the rectilinear circumference of the circle.  In each successive step of the squaring method, more and more points converge exponentially.  At the planck scale, all points will have converged on the rectilinear circumference of the circle.

Gravock

[verpies]

In order to establish a circular path, a continuous acceleration must be centripetal:  orthogonal to the instant velocity which directs it to the center of a circle.

I was away today and regrettably I could not participate in the ongoing discussion about circular motion.

I just saw the statement above made by MarkE and I disagree with him that a centripetal force directed at the center of the circle depicted in Diag.4 will result in circular path without violating Newton's 1^st law.
This is because an orthogonal force & acceleration cannot change any velocity component that is perpendicular to it.

This problem is germane to the discussion about Pi in kinematic circles and I invite everyone to discuss it before we return to the Pi issue.

I remind everyone that Newton 1^st law pertains to the innate vector of motion as well to any components of that motion.
Please study the diagram attached below *

And let's keep the discussion civil and scientific.  It is OK to call attention to a Straw Man when one sees it but please do not immediately assume that it is constructed maliciously.  It can be a result of misunderstanding.
Since not everyone reading this discussion might be familiar with the names of these debating fallacies please link them to their definitions at RationalWiki.org


P.S.
@TinselKoala
You might find this paper about Taxicab geometry enjoyable.

@TinselKoala, @MileHigh, @Farmhand
I guarantee that the problem of circular motion illustrated here will bring you many minutes (or hours) of intellectual enjoyment even if you are a practical guy that prefers knobs and molten solder.  I welcome you to disagree with me since you make a good opponent.

Please begin by stating whether in your opinion Diag.3 or Diag.4 or Diag.5 correctly depicts reality.

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Legend to the diagram below ( its hi-res version is here ) :
V_T(t₀): Tangential velocity at time t_0.
V_║(t₁) : Velocity at the time t₁ that is parallel to the tangential velocity at the previous time (t₀).
V_┴(t₁) : Velocity that is perpendicular to the velocity V_║(t₁) at the time t₁.

Example statements:
│V_T(t₀)│= │V_T(t₁)│= │V_T(t₂)│= etc... : A statement meaning that the magnitude of all tangential velocities is equal in all times t₀, t_1, t₂, etc...
V_║(t₁) ║ V_T(t₀): A statement meaning that velocity V_║(t₁) is parallel to velocity V_T(t₀).
V_║(t₁) < V_T(t₀): A statement meaning that the velocity V_║(t₁) is smaller than the velocity V_T(t₀).

[MarkE]

Look up Planck's constant - matter/energy is quantized. A circle is theoretical, there's no perfect circle in nature anywhere.  A real circle with a time variable is quantized at the planck scale with a zig-zag or rectilinear circumference, just as you find with the square in the squares method.  This is how there is a convergence on the rectilinear circumference at the planck scale. 

Edit:  Also, in step two of the squaring method, we can see there are four points of the square which converge on the rectilinear circumference of the circle.  In each successive step of the squaring method, more and more points converge exponentially.  At the planck scale, all points will have converged on the rectilinear circumference of the circle.

Gravock

Look up limits.  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.  It does not make the path a better approximation of the circumference. Y * X/X is still Y even for very large and very small values of X.

[MarkE]

I was away today and regrettably I could not participate in the ongoing discussion about circular motion.

I just saw the statement above made by MarkE and I disagree with him that a centripetal force directed at the center of the circle depicted in Diag.4 will result in circular path without violating Newton's 1^st law.
This is because an orthogonal force & acceleration cannot change any velocity component that is perpendicular to it.

Wrong and wrong.  This is basic calculus and physics.

This problem is germane to the discussion about Pi in kinematic circles and I invite everyone to discuss it before we return to the Pi issue.

I remind everyone that Newton 1^st law pertains to the innate vector of motion as well to any components of that motion.
Please study the diagram attached below *

And let's keep the discussion civil and scientific.  It is OK to call attention to a Straw Man when one sees it but please do not immediately assume that it is constructed maliciously.  It can be a result of misunderstanding.
Since not everyone reading this discussion might be familiar with the names of these debating fallacies please link them to their definitions at RationalWiki.org


P.S.
@TinselKoala
You might find this paper about Taxicab geometry enjoyable.

@TinselKoala, @MileHigh, @Farmhand
I guarantee that the problem of circular motion illustrated here will bring you many minutes (or hours) of intellectual enjoyment even if you are a practical guy that prefers knobs and molten solder.  I welcome you to disagree with me since you make a good opponent.

Please begin by stating whether in your opinion Diag.3 or Diag.4 or Diag.5 depict reality.

------------------------------------------------------------------------------------------------------------------------------------------------------

Legend to the diagram below ( its hi-res version is here ) :
V_T(t₀): Tangential velocity at time interval t_0.
V_║(t₁) : Velocity at the time interval t₁ that is parallel to the tangential velocity at the previous time interval (t₀).
V_┴(t₁) : Velocity that is perpendicular to the velocity V_║(t₁) at the time interval t₁.

Example statements:
│V_T(t₀)│= │V_T(t₁)│= │V_T(t₂)│= etc... : A statement meaning that the magnitude of all tangential velocities is equal in all time intervals t₀, t_1, t₂, etc...
V_║(t₁) ║ V_T(t₀): A statement meaning that velocity V_║(t₁) is parallel to velocity V_T(t₀).
V_║(t₁) < V_T(t₀): A statement meaning that the velocity V_║(t₁) is smaller than the velocity V_T(t₀).

Invented math and physics yield nonsense answers.