Under “Discrete” I refer to the acceptance in Engineering [ and not only ] of π in the Form of :

4 /{SQRT[ Golden Ratio ]},
which is associated, indissolubly, with Microcosmos and Macrocosmos .

The proposed π keeps its “Irrational” form in powers and roots unchanged.

As it is difficult to anticipate truth of the many π values, obtained “Diachronically” by searching various theoretical methods [ without a controlling feedback to each method used- e.g for the cube root of 2 ( Unsolved Theorem by Ruler and Compass), theoretically we obtain 1.25992105 and, as a feedback check, find that the cube of this is 2], it is proposed, here, that one experimental method could be reassuring, as is the testing of a designed equipment for its efficiency [ say that of a high speed rotating engine mechanism], using the proposed value of π, against the standard one in use.

Photo 1
Condition of Three Concentric Circle in Common Ratio [ 4/π].
Simulation of an Engineering Equivalent of an Epicyclic Gear Train in same ratio.

Photo 2

Top figure:
Δx , Δy and Δθ, detected discrepancies

Bottom figure:
No discrepancies

Photo 3
Complying Theoretical Proof

Video

MICROCOSMOS Geometrically Related to the MACROCOSMOS “ Nested Circles, Squares, Triangles” Quadrature of the Circle, Compass and Ruler - NOVEL CONCEPT - via “The Quadrature Triangle” CONFIGURATION EXHIBITNG MAXIMUM SYMMETRY For Value of π = 4 / [SQRT(Phi)] = 3.14460551..

The work presented relates to author's recent book:
Treatise on Circle – Generator Polyhedron
Harmony and Disharmony Condition of Three Concentric Circles in Common Ratio.
ISBN 978 – 618 – 83169 – 0 - 4], National Library of Greece-, 04/05/2017, by Panagiotis Ch. Stefanides.

http://www.stefanides.gr/pdf/2017/Treatise_on_Circle-Generator_Polyhedron.pdf

© Copyright, Eur Ing Panagiotis Chr. Stefanides BSc(Eng)Lon(Hons) MSc(Eng)NTUA TCG CEng MIET