My old Letter to Ro Mu Huen

My YinYang Symbol is only EXPRESSED in terms of SIN and COS which are the typical Yin and Yang for me from math point of view and surely were known to ancient chinese people long ago, though the exact formula for 3D(baseball!) yinyang symbol is a little bit SLIGHTLY MORE COMPLICATED, see the LETTER below for the exact EQUATION. Now I have developed the CONFORM THEORY ON UNIT SPHERE of this Symbol within the framework of Analytical Complex Functions F[z] Theory and conform transformations of complex variables z.( See for example Zhukovskiy’s conformal transform F[z]=(1/2)(z+1/z), etc.) The next letter was sent to South Korea embassy : Dear South Korean ambassador! I am sending You my refined mathematical model of Yin-Yang Symbol TAI-JI-TU used in South Korean Flag Taegeukgi. Perhaps this new refined Yin-Yang Symbol will seem to be more beautiful on the proud South Korean National Flag Taegeukgi and more suitable to fulfil because it may be accurately drawn with any computer. Below is the brief description of my refined mathematical model of Yin-Yang Symbol TAI-JI-TU used in South Korean Flag Taegeukgi. —————————————————————— Scientific Approach to the Yin-Yang Geometry by Sergey Yu. Shishkov (RUSSIA, Shishkovser@rambler.ru) Here is given (below) the most generalized definition of the astroid-like hypocycloid as the trajecory of a point P of a rotating with angular velocity “omega1″=1 circle of radius “radius1″=a, with centre of which also being rotating around the origin by the circle of radius “radius2″=1-a , and angular velocity “omega2″=-3, so that”radius1” +”radius2″=1, and “omega2″/”omega1” =-3. Then for coordinates X[t], Y[t] of this point P we have: X[t]=(a)*cos(t)+(1-a)*cos(3*t); Y[t]=(a)*sin(t)-(1-a)*sin(3*t); 1-X[t]^2-Y[t]^2=factor(simplify(expand(1-((a)*cos(t)+(1-a)*cos(3 *t))^2-((a)*sin(t)-(1-a)*sin(3*t))^2)))=16*a*cos(t)^2*(cos(t)-1) *(cos(t)+1)*(-1+a)=16*a*cos(t)^2*(cos(t)^2-1)*(-1+a)=16*a*cos(t) ^2*(sin(t)^2)*(1-a)=FULL SQUARE!=> If Z[t]=4*cos(t)*sin(t)*(a*(1-a))^(1/2), then X[t]^2+Y[t]^2+z[t]^2=1 ;(i.e., For every time t {X[t],Y[t],Z[t]} is on the unit SPHERE!!!). With different values of the parameter a we obtain the whole class of astroid-like hypocycloids with FOUR PARTS. Below is given the Maple 5.4 Text programm for plotting of these trajectories.; > a=0.6339;plot([(a)*cos(t)+(1-a)*cos(3*t),(a)*sin(t)-(1-a)*sin(3*t) ,t=0..2*Pi]); plot([(a)*cos(t)+(1-a)*cos(3*t),4*cos(t)*sin(t)*(a*(1-a))^(1/2), t=0..2*Pi]); plot([(a)*sin(t)-(1-a)*sin(3*t),4*cos(t)*sin(t)*(a*(1-a))^(1/2), t=0..2*Pi]); Look also in Maple 5: > factor(simplify(expand(1-((b)*cos(t)+(1-b)*cos(3*t))^2-((b)*sin( t)-(1-b)*sin(3*t))^2))); > The Optimal Value for the parametr a is a=(1/2)*(3-3^(1/2))=0.6339, as will be shown elsewher;-). It corresponds to the most “BEAUTIFUL” 3D-hypo-astroid. Such a configuration may serve also as the Yin-Yang MAGNETIC TRAP for adiabatic freezing of Bose condensate in modern Atomic Beam Lasers and for hot plazma in thermonuclear fusion systems. However, this is beyond the scope of this site. Let us call this unique value of the parameter a as “THE YIN-YANG PLATINUM SECTION”, analogous to the famous “GOLDEN SECTION GS” (i.e.,GS=1/2*5^(1/2)-1/2=0.6180339887), suggested by Leonardo da Vinci! > [>a:=0.6339;plot([(a)*cos(t)+(1-a)*cos(3*t),(a)*sin(t)-(1-a)*sin (3*t),t=0..2*Pi]); plot([(a)*cos(t)+(1-a)*cos(3*t),4*cos(t)*sin(t)*(a*(1-a))^(1/2), t=0..2*Pi]); plot([(a)*sin(t)-(1-a)*sin(3*t),4*cos(t)*sin(t)*(a*(1-a))^(1/2), t=0..2*Pi]); See pictures on my web-page http://www.tao.nm.ru/imagepage8.htm ————————————————————– Attached to this letter is the picture “SKorea.gif”
http://www.tao.nm.ru/SKorea.gif) of new refined South Korean Flag Taegeukgi that I’d like to suggest. . I’d like to ask You to forward this letter with an attachment to Mr. President of South Korea and/or to the South Korean government in order to acquaint Mr. President (unfortunately, I do not know his E-mail ) and the South Korean government with this new mathematical model of Yin-Yang Symbol TAI-JI-TU refined by me and with the consequential new refined South Korean Flag Taegeukgi. If needed, I’ll be glad to present more detailed descriptions of my refined mathematical model of Yin-Yang Symbol TAI-JI-TU used in South Korean Flag Taegeukgi. Sincerely, Sergey Yu. Shishkov,E-mail:Shishkovser@rambler.ru, a theorist in Plazma Physics, Moscow, Russian Federation, 11 of February 2006

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