SIC-1580   INSIGHTS

 ```Why the P Y T H A G O R A S can be calculated with the P2, P1 & Q-Scales ??? ****************************************************************************** c2 = a2 + b2 Starting with a scale of lenght 2p ... 0 1/4 1/2 3/4 1 1.25 1.5 1.75 2 |--------+--------+--------+--------+--------+--------+--------+--------| Take the SQUAREROOT of this scale ... 0 0.5 0.707 0.866 1 1.118 1.225 1.323 1.414 |--------+--------+--------+--------+--------+--------+--------+--------| |<=============== P1 ==============>|<=============== P2 ==============>| |<=============== Q ===============>| P2 = sqrt( 1 + P12 ) 1 0.866 0.707 0.5 0 Q = sqrt( 1 - P12 ) |--------+--------+--------+--------| = P1 inverted Proof: P2 = sqrt( 1 + 0.52 ) = 1.118 ====== sqrt( 1 + 0.7072 ) = 1.225 ... Q = sqrt( 1 - 0.52 ) = 0.866 sqrt( 1 - 0.7072 ) = 0.707 ... Now the scales P1, P2, & Q can be used for ADDING SQUARES ( see EX.A ) ... ======== a=0.4 0 v 0.5 0.707 0.866 1 1.118 |<====|--+--------+--------+--------+--------+--- |--------+--------+--------+-----|=>| 1 0.866 0.707 0.5 ^ 0 c2 = a2 + b2 b=0.3 0.52 = 0.42 + 0.32 The Hyperbolic Functions of the BACK SIDE, based on scales P1 & P2 ... o have an extended domain and resolution o AND use P2 for calculating CosH(X) directly o AND calculate directly HYPERBOLIC FUNCTIONS OF COMPLEX QUANTITIES Back to the SIC-1580 Main Page Papers presented at the 3rd BERLIN-BRANDENBURGER SAMMLER-TREFFEN (BBST) in Berlin impressum: ********************************************************************************* © C.HAMANN http://public.beuth-hochschule.de/~hamann 03/15/09 ```