The Holographic Universe and Pi = 4 in Kinematics!

[MarkE]

At least sarkeizen has a legitimate rebuttal and is contributing to this thread, unlike yourself. 

Gravock

LOL, are you still trying to convince anyone that you are serious?  You lost that battle a long time ago.

[gravityblock]

LOL.  You do realize don't you that now that you say that the geometry is non-Euclidean you are stuck both with stating what geometry system is represented and why under that geometry Mathis' taxi cab path has any validity?

I never said the geometry in the diagram is all non-euclidean as you wrongly assert.  At its simplest, traditional taxicab geometry changes the Euclidean distance formula to the metric proposed by Herman Minkowski where the distance between two points (x₁,y₁) and (x₂,y₂) is d_t = |x₂ - x₁| + |y₂ - y₁|

The idea behind this distance formula is that the distance between two points is not measured on a straight line, but on horizontal and vertical lines.  This definition leaves other geometric features such as points, lines, and angles as Euclidean. Until 1996, this was the form in which the geometry was investigated, discussed, and used. It was around this time that Thompson and Kaya independently began research into angles that natively belong to taxicab geometry thus launching investigations into a purer form of taxicab geometry.

Traditionally, taxicab geometry has included elements that are not native to the geometry. The primary example is Euclidean angles. Since angles are defined as arc length along a circle and the taxicab circle is quite different than the Euclidean circle, native taxicab angles are not Euclidean. Pure taxicab geometry uses angles that are native and natural to the geometry.

Gravock

[TinselKoala]

So now you are doing plagiarism, too? You'd think you could at least rephrase your stolen excerpts.

http://taxicabgeometry.net/general/definitions.html

[gravityblock]

So now you are doing plagiarism, too? You'd think you could at least rephrase your stolen excerpts.

http://taxicabgeometry.net/general/definitions.html

fair use
noun
noun: fair use; plural noun: fair uses

    (in US copyright law) the doctrine that brief excerpts of copyright material may, under certain circumstances, be quoted verbatim for purposes such as criticism, news reporting, teaching, and research, without the need for permission from or payment to the copyright holder.

I don't have the time nor the energy to rephrase the excerpts that is being used for teaching and research purposes.  The excerpts are not stolen and falls under fair use, and is not plagiarism as you wrongly asserted.  Also, the formula of d_t = |x₂ - x₁| + |y₂ - y₁| is an in-line image on the website, and I choose not to copy this image, but to type it out.   I find it interesting how you throw plagiarism at me for exposing your deliberate misdirection in one of your previous posts.  You have now exposed your immaturity and how you are a very vindictive person.  Also, this is totally off-topic, and is not a mathematical or scientific rebuttal in any sense.

Gravock

[MarkE]

I never said the geometry in the diagram is all non-euclidean as you wrongly assert.  At its simplest, traditional taxicab geometry changes the Euclidean distance formula to the metric proposed by Herman Minkowski where the distance between two points (x₁,y₁) and (x₂,y₂) is d_t = |x₂ - x₁| + |y₂ - y₁|

The idea behind this distance formula is that the distance between two points is not measured on a straight line, but on horizontal and vertical lines.  This definition leaves other geometric features such as points, lines, and angles as Euclidean. Until 1996, this was the form in which the geometry was investigated, discussed, and used. It was around this time that Thompson and Kaya independently began research into angles that natively belong to taxicab geometry thus launching investigations into a purer form of taxicab geometry.

Traditionally, taxicab geometry has included elements that are not native to the geometry. The primary example is Euclidean angles. Since angles are defined as arc length along a circle and the taxicab circle is quite different than the Euclidean circle, native taxicab angles are not Euclidean. Pure taxicab geometry uses angles that are native and natural to the geometry.

Gravock

LOL.  You wish to propose a system of plane geometry that cannot distinguish the length between paths taken directly between two points and paths taken circuitously around to travel between those points to describe ... wait for it ... the distance along of the direct paths.  Have your pants exploded yet?