The Holographic Universe and Pi = 4 in Kinematics!

[MarkE]

According to your definition in the bold portion above, the square does inscribe a circular path within.  Also, a circular path is a real physical circle with a time variable according to your definition.  So, according to your logic and definitions, this circular path inscribed by the rotation of the square by 1/4 has a time element?

Gravock

Read the words again.  Take whatever time that you like.

Take any object with one or more points that are at a fixed distance from the center, and rotate that object about its center.  The points remaining a fixed distance from the center by definition follow the same circular path.  The path between those points around the original shape has nothing to do with the rotation of that object.

There is no such thing as a "physical circle" distinct from a circle.  A circle is a plane geometry object.  It has no time dependency.  Be my guest and find any academic citation that states that a circle has a time element.

Do you understand the difference between a path and motion along a path?

[gravityblock]

Read the words again.  Take whatever time that you like.

There is no such thing as a "physical circle" distinct from a circle.  A circle is a plane geometry object.  It has no time dependency.  Be my guest and find any academic citation that states that a circle has a time element.

Do you understand the difference between a path and motion along a path?

In a "physical circle", the motion itself forms the path from the perimeter and the path is formed over a period of time, while the path itself is not formed by a single point or center.  The path of a physical circle forms a single point, the center.  In other words, it is not an instantaneous circle, thus it has both a time element and a path to measure.  In an abstract geometrical circle, the perimeter is formed from a single point that has no time period, the center, and is without motion, and both the center and the perimeter of the abstract circle is formed instantaneously without a time element and has no path to measure.  A physical circle and an abstract circle are the inverse of each other.

Gravock

[gravityblock]

@Gravityblock
MarkE is correct in his diagram about the measurements of a geometric timeless circle (in his diagram the string comes up short) but he is incorrect about a circular path traversed by a massive object. 
In the latter the time to complete one revolution is 4 times longer than the time to traverse the diameter by velocity whose magnitude is equal to tangential velocity.
If you let him conflate the static situation with the dynamic one, he will be successful in refuting your postulate.

MarkE is trying to use plane geometry, which has left the time element out in it's current form, in order to measure a physical circle that does have a time element.  He tells me I can't use the Manhattan path to measure Pi = 4 in a physical circle because the Manhattan path has no time element, which I disagree with when the points are at the planck scale.  However, he is doing what he said I couldn't do in plane geometry.  The summation of his own logic and his own definitions are conflicted and contradictory to each other in every way.

Gravock

[MarkE]

In a "physical circle",

This is an invention of yours.

the motion itself forms the path

Motion follows a path.  The path can be in one two or three dimensions.  The motion is fully time dependent.  The geometry of the path is itself timeless.  The geometry does not change, before, during or after the motion of the object that traverses it. When the path followed conforms to the plane geometry shape known as a circle, then the path is circular.  When the path followed violates any of the constraints of the plane geometry shape known as a circle, then the path is not circular.  The path that some object follows does not redefine plane geometry.

from the perimeter and the path is formed over a period of time, while the path itself is not formed by a single point or center.  The path of a physical circle forms a single point, the center.  In other words, it is not an instantaneous circle, thus it has both a time element and a path to measure. 

This is your silly invention.

In an abstract geometrical circle,

This is another invention of yours.  There is no such thing as either a "physical circle" or an "abstract geometrical circle" distinct from the plane geometry shape known as a "circle".

the perimeter is formed from a single point that has no time period, the center, and is without motion, and both the center and the perimeter of the abstract circle is formed instantaneously without a time element and has no path to measure.  A physical circle and an abstract circle are the inverse of each other.

Gravock

[TinselKoala]

What's the matter, too much actual math? Did you "Pi=4" claimants not notice that I have proven you wrong, YET AGAIN, using a real physical circle with time element involved?

Earth's orbital radius = about 149.6 million km. Duration of one full orbit is of course one sidereal year, 365.256 days or about 31,558,118 seconds.
(wikipedia).

The tangential velocity of the Earth in its orbit is 29814 meters per second, derived from v²=GMs/r.

Now let us calculate.
The circumference of the orbit (assuming pi = 3.1416 and a circular orbit) is 2 x pi x 149.6 million km, or about 939.97 million km.

The tangential speed computed from the radius and the conventional value of pi is therefore 939.97 million km / 31,558,118 seconds or about 29785 meters/second.

The diameter of the orbit is about 299.2 million km. Traversing this distance at the tangential velocity of 29814 m/sec will therefore take about 10035553 seconds. Four times that is 40,142,212 seconds... but a year is only 31,558,118 seconds.  Curiously.... 10035553 x  3.1416 = about 31,527,693 seconds.... nearly exactly the number of seconds in a sidereal year.

Conclusion.....  The value of pi, for the real figure of the Earth's orbit, taking TIME and velocity into account, must be very close to 3.1416, and not close at all to 4.

Please feel free to show a working that demonstrates otherwise.