The QUADRATURE, pure and simple !

A) The QUADRATURE, by RULE and COMPASSES:

1) For PERIMETERS:

*DIAMETER=1(UNIT)

*SIDE of the SQUARE=

=1/sqrt(PHI)=sqrt(phi)=sin51.82729237(…)deg.=cotan51.82729237(…)deg.= =cos37.17270763(…)=tan38.17270763(…)=0.786151377(…)

2) For AREAS:

*DIAMETER=1(UNIT)

*SIDE of the SQUARE= =1/sqrt[sqrt(PHI)]=sqrt[sqrt(phi)]=cotan48.43814254(…)deg.=tan41.56185746(…)deg.=

=0.886651779(…)

@ ATTENTION, please: -The “simple” QUADRATURE of the AREAS, (as a matter of fact, by RULE and COMPASSES for 48.43814254 deg.!) is’nt possible without the previous QUADRATURE of the PERIMETERS, described in 10  STEPS/from 22 total (see, in Romanian language,  in http://quadrature.blog.com  and http://mirceamugurelserban.myforum.ro ) and by the PYRAMIDAL PATTERN <Keops/PHI> (as above : see the <LOGISTIC PYRAMID> formula in the chapter <Designs&Formulas> and other FORMULAS in the chapter <Pure inspirations>).

B) PI=4/sqrt(PHI)=4sqrt(phi)=3.144605511029693144(…)

MEASURING on the ground: -The measured CIRCOMFERENCES are multiples of 3.1446, in meters, by a very little approximation, in opposition with 3.1416! And now, I have in construction a simple instrument,which I did name <QUADRIGA 4sqrt(phi)>*!!!

*Practically, the <QUADRIGA> is finished and TESTED on the ground (see you later!), but it's necessary to solve some technical details .