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MATHEMATICS of TAOISM. The First in the World special Mathematical site on TAO-http://www.geocities.com./shishkov2002/yinyang.htm MATHEMATICS of TAOISM. RUSSIAN VERSION! The First in the World special Mathematical site on TAO-http://www.tao.nm.ru. My URL:www.tao.nm.ru CLICK HERE! THE ONLY ONE LINK TO OLD NEWMAIL! ALL THE 1012 FORUMS were AVAILABLE!!! THE HYPER-LINK TO RUSSIAN VARIANT IN NEWMAILRETURN TO RUSSIAN VERSION OF THIS SITE !

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 THE MOST RELIABLE SOLUTION OF The YIN-Yang GEOMETRY PROBLEM-IS THE ANSWER:For the coordinates X[t], Y[t] of a given point 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=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., lies on the unit SPHERE!!!). For some reason, which will be published elsewhere(Sic!),The Optimal Value for the parametr a is a=0.6339, as will be shown elsewhere. Let us call it "THE YIN-YANG PLATINUM SECTION" And we shall always put a=(1/2)(3-3^(1/2))=0.6339 ;Below is given this ParametricPlot3D of such a 3D-ASTROID
 Index 1 of 1

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Maple 5.4 Text Adobe-4 PDF "Scientific Approach to the Yin-Yang Geometry by Sergey Yu. Shishkov"

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