COMPARISON :South Korean Flag slightly differs from Russian Yin-Yang Symbol

Scientific Approach to the Yin-Yang Geometry by Sergey Yu. Shishkov (RUSSIA, 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**************************** ********************************** ****************************PictureFOR MEDITATION ON ADJNA CHACKRA ********************************** *************************** *********************************** ****************** ********** Научный Подход к Yin-Yang Геометрии (Sergey Yu. Shishkov ,РОССИЯ, Здесь дается (ниже) наиболее обобщенное определение астроидно-подобной гипоциклоиды как траектории точки P вращающейся с угловой скоростью "omega1" =1 по окружности с радиусом "radius1" =a, центр которой также вращается вокруг начала координат по окружности с радиусом "radius2" =1-a, и угловой скоростью ""omega2" = -3, так, чтобы "radius1" + "radius2" =1, и "omega2" / ""omega1" = -3. Тогда для координат X [t], Y [t] этой точки P мы имеем: 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) a* (1-a) =ПОЛНЫЙ КВАДРАТ! = >, если Z [t] =4*cos (t) *sin (t) * (a* (1-a)) ^ (1/2), то X [t] ^2+Y [t] ^2+Z [t] ^2=1; (то есть, Для каждого момента времени t {X [t], Y [t], Z [t]} С различными значениями параметра a мы получаем целый класс astroid-подобных гипоциклоид с ЧЕТЫРЬМЯ ЧАСТЯМИ. Ниже дается Maple5.4 Текст программы для составления графика этих траекторий.; > 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]); Просмотр также в МАПЛ 5: > factor(simplify(expand(1-((b)*cos(t)+(1-b)*cos(3*t))^2-((b)*sin (T) - (1-b) *sin (3*t)) ^2))); > Оптимальное Значение для параметра a = (1/2) * (3-3 ^ (1/2)) =0.6339, как будет показано в другом месте ; -). Этому значению соответствует наиболее "КРАСИВЫЙ" 3D-hypo-astroid. Такая конфигурация может служить также как Инь-Яньская МАГНИТНАЯ ЛОВУШКА для адиабатического охлаждения Бозе-конденсата в современных Лазерах на пучке атомов и для горячей плазмы в системах термоядерной реакции. Однако, это выходит за рамки данного сайта. Позвольте нам называть это единственное значение параметра как " ИНЬ-ЯНЬСКОЕ ПЛАТИНОВОЕ СЕЧЕНИЕ ", аналогично известному " ЗОЛОТОМУ СЕЧЕНИЮ З.С. " (то есть., З.С.=1/2*5 ^ (1/2) -1/2=0.6180339887), предложенному Леонардо да Винчи! > [> 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]); Rambler CLICK HERE! THE ONLY ONE LINK TOOLD OLDOLD WWW.NEWMAIL.RU NEWMAIL!







MY GUESTBOOK. Please, ANSWER THERE have you ever seen ball-lightning(Y/N), UFO and/or aliens and also ABOUT YOUR WEB-SITE if you have any!

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THE PREGNANT WOMAN GIOCONDA. SEE ALSO BBC NEWSScientists Figure Out Why Mona Lisa Smiles By TOBY STERLING AMSTERDAM, Netherlands (AP) - The mysterious half-smile that has intrigued viewers of the Mona Lisa for centuries isn't really that difficult to interpret, Dutch researchers said Thursday. She was smiling because she was happy - 83 percent happy, to be exact, according to scientists from the University of Amsterdam. In what they viewed as a fun demonstration of technology rather than a serious experiment, the researchers scanned a reproduction of Leonardo da Vinci's masterpiece and subjected it to cutting-edge ``emotion recognition'' software, developed in collaboration with the University of Illinois. The result showed the painting's famous subject was 83 percent happy, 9 percent disgusted, 6 percent fearful and 2 percent angry. She was less than 1 percent neutral, and not at all surprised. Leonardo began work on the painting in 1503, and it now hangs in the Louvre in Paris. The work, also known as ``La Gioconda,'' is believed to have portrayed the wife of Francesco del Giocondo. The title is a play on her husband's name, and also means ``the jolly lady'' in Italian. Harro Stokman, a professor at the University of Amsterdam involved in the experiment, said the researchers knew the results would be unscientific - the software isn't designed to register subtle emotions. So it couldn't detect the hint of sexual suggestion or disdain many have read into Mona Lisa's eyes. In addition, the technology is designed for use with modern digital films and images, and subjects first need to be scanned in a neutral emotionless state to accurately detect their current emotion. Lead researcher Nicu Sebe took the challenge as seriously as he could, using the faces of 10 women of Mediterranean ancestry to create a composite image of a neutral expression. He then compared that to the face in the painting, scoring it on the basis of six emotions: happiness, surprise, anger, disgust, fear and sadness. ``Basically, it's like casting a spider web over the face to break it down into tiny segments,'' Stokman said. ``Then you look for minute differences in the flare of the nostril or depth of the wrinkles around the eyes.'' Stokman said with a reading of 83 percent, it's clear happiness was the woman's main emotion. Biometrics experts not involved with the experiment said the results were interesting even if they aren't the last word on the Mona Lisa. ``Facial recognition technology is advancing rapidly, but emotional recognition is really still in its infancy,'' said Larry Hornak, director of the Center for Identification Technology Research at West Virginia University. ``It sounds like they did try to use a data set, even if it was small, and that's typical of work in an area like this that's relatively new. It's an interesting result,'' he said. Stokman said he knew the University of Amsterdam effort won't prove or disprove controversial theories about the painting. One is that it was actually a self-portrait of Leonardo himself as a woman. ``But who knows, in 30, 40, 50 years, maybe they'll be able to tell what was on her mind,'' Stokman said. Hornak agreed the idea was entertaining. ``It's always fun to apply technology to areas of public interest, and sometimes you can come up with results that are very illuminating,'' he said. Jim Wayman, a biometrics researcher at San Jose State University agreed. ``It's hocus pocus, not serious science,'' Wayman said. ``But it's good for a laugh, and it doesn't hurt anybody. MY SIMPLE EXPLANATION: SHE IS HAPPY BECAUSE SHE IS PREGNANT!!! Such interpretation is quite natural to painting of the Epoch of Revival, as the theme " MADONNA WITH the BABY" can include also the pre-natal status of this baby. (Look, as she " SUPPORTS by her HANDLES her own PREGNANT TUMMY " so writes Lev Nickolaevich TOLSTOY in " War and Peace " about the wife of Andrew Bolkonsky, sent on war with the French in 1812. The position of hands of GIOCONDA is characteristic for the earliest stage of pregnancy, and the smile expresses a sneer at ignorance environmental about to this her own personal secret - " IT IS TOO EARLY! ". To same version one adheres also known English professor of medicine.) By the way, Did you Know, that LEONARDO da VINCHI was not simply homosexual, but also hated the women, and the process of reproduction of life inspired him disgust? (Source: The book " the SECRET OWNERS of TIME " (Jacques Bergier, " LES MAITRES SECRETS DU TEMPS "), Moscow, Crowns - press, 2000, Series " the Mysterious World ", page 79) In a picture " MONA LISA ", hence, he has represented that most of all... hated?! The same in Russian: БЕРЕМЕННАЯ ДЖОКОНДА. Такое толкование вполне естественно для живописи Эпохи Возрождения, так как тема мадонны с младенцем может простираться вплоть до внутриутробного состояния этого младенца. (Посмотрите, как она "ПОДДЕРЖИВАЕТ РУЧКАМИ СВОЙ БЕРЕМЕННЫЙ ЖИВОТИК" -так говорил Лев Николаевич Толстой в "ВВойне и Мире" о жене Андрея Болконского, отправляющегося на войну с французами в 1812 году. Положение рук Джоконды характерно для ранней стадии беременности, а улыбка выражает насмешку над неведением окружающих об этой её личной тайне - "ЕЩЁ СЛИШКОМ РАНО!". Этой же версии придерживается также один известный аглийский профессор медицины.) Знаете ли Вы, что Леонардо да Винчи был не просто гомосексуалистом, но к тому же ненавидел женщин, а сам процесс воспроизведения жизни внушал ему отвращение? (Источник: книга "ТАЙНЫЕ ХОЗЯЕВА ВРЕМЕНИ" Жака Бержье(Jacques Bergier, "LES MAITRES SECRETS DU TEMPS"),Москва,Крон-Пресс, 2000, Серия "Таинственный Мир",стр.79) На картине " Мона Лиза", следовательно, он изобразил то, что больше всего ...ненавидел ?!

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