The Holographic Universe and Pi = 4 in Kinematics!

[gravityblock]

Or if for some reason you no longer think the terms euclidean and non-euclidean are sufficient to describe the diagram's geometry and were unable to form a sentence to communicate that.   Then please point out which features on the diagram are in a particular geometry.

Sarkeizen,

Let me play the devil's advocate for a moment, but before I do, please clarify if question 3 of the "If yes" portion is in reference to question 1 or question 2.

Thanks,

Gravock

i) If I say that this diagram: http://www.milesmathis.com/vel5.jpg showing a bunch of "steps" implies that the pythagorean theorem is false.  Do you agree with me or not?
ii) If not, then is your basis for your objection that the pythagorean theorem is not applicable to non-euclidean geometry?.  Yes or no?
iii) If yes, then clearly that diagram has to represent something in non-euclidean geometry.  Agree or disagree?

[gravityblock]

The illustration shown below (second image), courtesy of MarkE, is for a static circle with no motion or time element involved and there is no disagreement that pi = 3.14 in this case.  Now, let's give that static circle a motion where a curve is traced by a point on the rim or circumference of the circular wheel as the wheel rolls along a straight path to generate a cycloid (first image below).  The arc of a cycloid is 8r, which pi is also replaced by 4, just as in the Manahattan metric.

Gravock

[sarkeizen]

Let me play the devil's advocate for a moment, but before I do, please clarify if question 3 is in reference to question 1 or question 2.

You're going to have to be considerably more specific.  "in reference" doesn't mean anything to me other than "related".  Clearly some relation exists between all the questions since they are forming an argument.

While you're trying to gather the acumen to explain yourself.  You could try answering my question.  Which, as it happens still stands (now asked EIGHT times):  You say that the diagram contains both euclidean and non-euclidean geometry.  Which parts do you consider euclidean and which parts do you consider non-euclidean?  Again if for some reason you no longer think the terms euclidean and non-euclidean are sufficient to describe the diagram's geometry and were unable to form a sentence to communicate that.   Then please point out which features on the diagram are in a particular geometry.

[gravityblock]

You're going to have to be considerably more specific.  "in reference" doesn't mean anything to me other than "related".  Clearly some relation exists between all the questions since they are forming an argument.

iii) If yes, then clearly that diagram has to represent something in non-euclidean geometry.  Agree or disagree?

Is the bold portion in question 3 in reference to question 1 or question 2?

Gravock

[MarkE]

The illustration shown below, courtesy of MarkE, is for a static circle with no motion or time element involved and there is no disagreement that pi = 3.14 in this case.  Now, let's give that static circle a motion where a curve is traced by a point on the rim or circumference of the circular wheel as the wheel rolls along a straight line to generate a cycloid.  The arc of a cycloid is 8r, which pi is also replaced by 4, just as in the Manahattan metric.

Gravock

LOL. The path length on the rolling surface traversed as the wheel makes one complete rotation, ie maps out one circumference is identically still Pi*D, ~3.141593*D.