🚀 go-pugleaf

"xxein" <xxein@comcast.net> wrote in message 
news:50c4d3b3-f2c5-4cdd-8095-1760a4851e85@i72g2000hsd.googlegroups.com...
On Jan 30, 5:30 am, Pentcho Valev <pva...@yahoo.com> wrote:
> http://hem.bredband.net/b153434/Works/Einstein.htm
> Divine Albert: "In a space which is free of gravitational fields we
> introduce a Galilean system of reference K (x, y, z, t), and also a
> system of co-ordinates K' (x', y', z', t') in uniform rotation
> relatively to K. Let the origins of both systems, as well as their
> axes of Z, permanently coincide. We shall show that for a space-time
> measurement in the system K' the above definition of the physical
> meaning of lengths and times cannot be maintained. For reasons of
> symmetry it is clear that a circle around the origin in the X, Y plane
> of K may at the same time be regarded as a circle in the X', Y' plane
> of K'. We suppose that the circumference and diameter of this circle
> have been measured with a unit measure infinitely small compared with
> the radius, and that we have the quotient of the two results. If this
> experiment were performed with a measuring-rod at rest relatively to
> the Galilean system K, the quotient would be [pi]. With a measuring-
> rod at rest relatively to K', the quotient would be greater than [pi].
> This is readily understood if we envisage the whole process of
> measuring from the "stationary" system K, and take into consideration
> that the measuring-rod applied to the periphery undergoes a Lorentzian
> contraction, while the one applied along the radius does not. Hence
> Euclidean geometry does not apply to K'."
>
> Why does Divine Albert believe that, "with a measuring-rod at rest
> relatively to K', the quotient would be greater than [pi]"? Obviously
> because "the measuring-rod applied to the periphery undergoes a
> Lorentzian contraction". Then why does the segment of the periphery,
> to which the measuring-rod is applied and which moves together with
> the measuring-rod, fail to undergo a Lorentzian contraction?
>
> In 1902, in "La Science et l'hypothese", Henri Poincare, in order to
> justify non-Euclidean geometries, presented a parabole. Bidimensional
> creatures live on a disc. The disc is heated under its center so that
> the temperature is high at the center and decreases towards the
> periphery. The creatures use rigid measuring rods in order to
> determine the geometry of their world. They know nothing about the
> heater and accordingly discover that the ratio of the circumference
> and the diameter is greater than [pi]. The creatures conclude that
> Euclidean geometry cannot be true on their disc.
>
> Pentcho Valev
> pva...@yahoo.com

xxein:  We are K' to any other observer (gravity or not).  For your
question (sans gravity) who would not be K'?  How do WE get pi?

  http://en.wikipedia.org/wiki/Computing_%CF%80