Appendix-2 : Development of the exterior triangle of a Golden-Section-Pyramid

see further Appendix-3 for the development of the internal triangle.

The development of the exterior triangle TBC of a golden-section pyramid (figure below) produces similar trapeziums.

The fig. A2-1 shows the successive “phases”.

Further expansions are in table below:

Ci(Bi + 1) Bi(Ci + 1) Ci(Bi + 2)

The multiplication factor for the lines is:

Square root 5 / Phi = 1,38196601 this +/- = square root 6 / Pi and +/- = 1/square root ( 1 el ).

Four first phases are in figure, next in table.

Magnitude Pi is the big diagonal of phase 4.

Our attention may be brought to some special relations between Pi (3,1416), Phi (1,618034 ) , and the number 6.

We can see that for the diagonal B4C5 we have 3,141132 deviating only 0,0149 of 3,1416.

Further B1C1 equals 0,7861513 deviating 0,0956% from Pi / 4.

A diagonal B6C7 equals 5,999028 deviating 0,01619 from 6.

Application of the rulings of Pythagoras on the external triangle gives the expression:

Square root 5 = Phi + (1/PHI)

If we replace square root 5 by 2 Phi – 1, because Phi = ( 1 + square root 5) / 2 , we get again the golden-section comparison:

Phi / 1 = 1 / (Phi – 1 ).

We see that the exterior triangle give the positive roots Phi and 1 / Phi, while the solution of the internal triangle gives as well Phi and –1/Phi.

Click : see further Appendix-3 for the development of the internal triangle.

For a more complete abstract about a golden section pyramid : see also Phi, Cheops and our Sun and Planet System, out of book 3, Hidden Analogic, click to : Cheopsmodel

Remark of Prof. Michael Joyce: schema below shows also the development of the trapeziums

Initially we may think the trapezium is developed from the one shown inside the pyramid, and of course  later realise this is not the case - it develops from the actual triangle.

 The multiplication factor for the lines is:

 Square root 5 / Phi = 1,38196601 this +/- = square root (  6 / Pi )   and +/- = 1/square root ( 1 el ). 

Line multiplier 1,38196601 also closely equates to ( 4 x 11 x pi ) / 100 or ( 1,3823007)

Four first phases are in figure, next in table.

 Magnitude Pi is the big diagonal of phase 4.

+

For links to the website of Prof. Michael Joyce , chemistry , UK,

Website on ancient and new metaphysical geometry and numerology ,

With extended studies and comments on the works of Prof. Kris Thijs :

click on : Website of Prof. Michael Joyce :

for The Biblical book of Nummbers

click on Cheops Covenant Codes

for The Universal Pyramid structure

click on PYRAMID-the UNIVERSAL STRUCTURE

for The Solar System

click on Thijs on The Universal Pyramidal Structure

for Bifurcation and constant "e"

click on Thijs on The Universal Pyramidal Structure (continued)

for Saturn and Planck's constant

click on Ark of the Covenant, Saturn Effect, Precession and Planck's constant

For next appendix click on appendix 3

For appendix overview, click Appendix 1 – 32 The Secret Language of God

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Explanations are taken over in translated form from Het Geheimschrift van God ( The Sacred Language of God)

of Professor Kris Thijs, with the written authorization of Editor Guido Maes Millennium Productions Belgium, documents still under copy rights.