Mathematical Formula Of Yinyang

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Mathematical Formula Of Yinyang

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http://www.geocities.com/yinyang_symbol/
http://www.tao.nm.ru
http://www.geocities.com/shishkov2002
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The unknown Formula by S.Shishkov of TAI-JI-TU (Yin-Yang Symbol)Note, that such an invention of Yin-Yang Symbol is similar to the invention of wheel, bicycle, fire, baseball,etc. and nobody know WHO was the first inventor of the wheel or of the bicycle or of fire!

cos(t)+(1-a)---cos(3---t);" class="copylinks" target="_blank">Y[t =(a)---sin(t)-(1-a)---sin(3---t); 1-X ---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 ;(i.e., For every time t {X[t ,Y 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( t=0..2---Pi ); plot( 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! > (3---t),t=0..2---Pi ); plot( t=0..2---Pi ); plot( t=0..2---Pi ); See pictures on my web-page http://www.tao.nm.ru/imagepage8.htm

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