The Holographic Universe and Pi = 4 in Kinematics!

[MarkE]

But we are not discussing abstract timeless plane geometry.  You are assertions about Pi are correct in abstract time geometry.

Circles are basic constructs of plane geometry.  [/quote]
We are not discussing abstract geometry, we are discussing real physical problems from the start.  [/quote]Citing the rantings of internet cranks as reference "papers" hardly seems like a discussion of anything real.

This link you posted refers to an article describing a physical circle, created by real forces acting on a real mass.  There is no avoiding the time variables in this one.

Here we go back to your special pleadings of "abstract" and "physical" circles.  Until such time as you can actually delineate what it is that makes a circle:  "physical", distinct from textbook circles, and still qualifies them as circles, you might as well say "brominsmores".

That article states:
"Note that in both cases, Δv points to the center of the circle reflecting that the acceleration is also directed towards the center of the circle"
..but it is just an empty assertion. 
That article does not prove that the acceleration vector and force that causes the circle lays on a line that passes through the center of the circle.

So you assert.  Read it again.

That article correctly subtracts two tangent velocity vectors.  On my diagram that is V_T(t₀) - V_T(t₁) but it fails to prove that the result of this subtraction lays on a line that passes through the center of the circle.
What proof did you or that article give that the acceleration/force vector lays on such line?  What proof did you or that article give that the acceleration/force vectors do not lay on the dashed lines depicted on the diagram below that does not pass through the center ?

Let's see your vector math that can actually hold an object on a circular path while the accelerating force does not point radially through the center of that circle.  Be sure that whatever "circle" you use satisfies the requirements: a closed path where all points on the circumference are equidistant from the center.

[verpies]

Here we go:  A special pleading to "circles" that are not "circles" except when you two want them to be circles. 
...
Neither you nor Gravityblock have established that your special "circles" are in fact circles

I was clear from the first post about the difference between abstract circles and physical circles.
Are you claiming that the circle in that article you quoted is not a circle?

Yet they fail tests for basic properties of circles.

They don't.
Your argument that Pi=3.14 defines a circle instead of the circle defining the Pi is putting the cart before the horse and it is a fallacy.  But I thank you for sensitizing me to this line of argument reversal.  I will be ready for it with other opponents.

Until such time as you can actually delineate what it is that makes a circle:  "physical", distinct from textbook circles, and still qualifies them as circles, you might as well say "brominsmores".

A circle is a set of equidistant points on a spatial plane from the center of the circle.  The difference between an abstract and physical circle is whether these points have time coordinates or not.  Physical circles do and those coordinates are not the same.  Time is hard to diagram and most likely that's why you are confused about the distinction.

Citing the rantings of internet cranks as reference "papers" hardly seems like a discussion of anything real.

That paper is relevant because it discusses the approach of the chord to the arc in real physical circles at the limit.
Attack author's arguments not the author.  We are beyond burning Brunos and the likes of him.

LOL, now you don't believe first semester calculus.

Actually I don't thing that's applicable in case of physical circles. 

You are free at any time to as you say use actual facts to argue your specious and silly case.

Mathis proves that the chord does not approach the arc at the limit in kinematic circles quite exhaustively with rigorous arguments.  I shouldn't have to repost his paper here - a link should be sufficient.
If you are resorting to ridiculing his rigorous analysis instead of refuting his arguments, that means that you have run out of ammunition.

[MarkE]

MarkE,

The plot of a convergent sequence {a_n} is shown in blue in the illustration below. Visually we can see the sequence is converging to the limit 0 as n increases.  Similarly, we can see the exponentially larger quantity of smaller squares in each successive squaring method is converging while the path length does not change.

Gravock

Which does absolutely nothing for getting the path traveled following orthogonal segments to better approximate the path length of the circumference.

[gravityblock]

Which does absolutely nothing for getting the path traveled following orthogonal segments to better approximate the path length of the circumference.

The path length isn't changing as it converges, and we can visually see this, so this is the exact path length of the circumference.  The "better" approximation you speak of simply doesn't exist as you wrongly assert.

Gravock

[MarkE]

I was clear from the first post about the difference between abstract circles and physical circles.

Really?  What is that difference?  What qualifies a "physical circle" to be a circle and what properties may it have that are different than an "abstract circle"?

Are you claiming that the circle in that article you quoted is not a circle?

You are off in the bushes again.

Your argument that Pi=3.14 defines a circle instead of the circle defining the Pi is putting the cart before the horse and it is a fallacy.  But I thank you for sensitizing me to this line of argument reversal.  I will be ready for it with other opponents.

Slay those men of straw.  I have stated clearly that Pi is defined as the ratio of a circle's circumference to its diameter, and the mutual claim you make with GravityLock that the ratio is numerically equal to four is patently false.

A circle is a set of equidistant points on a plane from the center of the circle.  The difference between an abstract and physical circle is whether these points have time coordinates or not.  Physical circles do and those coordinates are not the same.

"Those coordinates" are not the same as what?  A plane has two axes.  A circle is a construct of plane geometry.  Be sure that your "physical circle" conforms to those requirements.

Time is hard to diagram and most likely that's why you are confused about the distinction.

Again, a circle is a construct of plane geometry.  There are only two dimensions.  If you cannot draw it on a piece of paper then it isn't plane geometry.

The paper is relevant because it discusses the approach of the chord to the arc in real physical circles at the limit.

The paper's premise is utter and total BS.  Mathis introduces the line RBD which never appears in Lemma VI.  Lemma VI declares that as B approaches A that the angle subtended between B-A-D approaches zero.  This is visibly obvious.  As B approaches A, B rises to A and the line between B and A comes closer and closer to being parallel with the line between A and D.  Ergo in the limit the slope of the line between A and B becomes tangent to the circle, parallel to the line between A and D and the subtended angle:  B-A-D goes to zero.  Ergo the cited article is in error.

Attack author's arguments not the author.  We are beyond burning Brunos and the likes of him.