黄金比例市公开课一等奖百校联赛优质课金奖名师赛课获奖课件.ppt

单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,本资料仅供参考，不能作为科学依据。谢谢。本资料仅供参考，不能作为科学依据。本资料仅供参考，不能作为科学依据。谢谢。本资料仅供参考，不能作为科学依据。,Golden Ratio,Divine Proportion,Golden Section,PHI,1/81,为何许多国家国旗图案都喜欢用五角星？,中华人民共和国 新西兰,朝鲜 新加坡,2/81,美妙五角星,毕达哥斯学派,徽章,黄金分割，是古希腊毕达哥斯学派从数学原理中发觉出来一个漂亮形式。,普通来说，按黄金百分比组成事物都表现出友好和均衡。,3/81,Timeline of,Golden Section,公元前,6,世纪古希腊毕达哥拉斯学派已研究过正五边形和正十边形作图，所以可推断他们已知道与此相关黄金分割问题。,Phidias(490430 BC)made the Parthenon statues that seem to embody the golden ratio.,Plato(427347 BC),in his Timaeus,describes five possible regular solids(the Platonic solids,the tetrahedron,cube,octahedron,dodecahedron and icosahedron),some of which are related to the golden ratio.,4/81,公元前,4,世纪，古希腊数学家欧多克索斯第一个系统地研究这个问题，他建立了百分比理论。,Euclid(c.325c.265 BC),in his,Elements,gave the first recorded definition of the golden ratio,which he called,as translated into English,extreme and mean ratio.,中国古代称黄金分割为,“,弦分割,”,。,5/81,Fibonacci(11701250)mentioned the numerical series now named after him in his,Liber Abaci,;the Fibonacci sequence is closely related to the golden ratio.,Luca Pacioli(14451517)defines the golden ratio as the divine proportion in his,Divina Proportione,.,Johannes Kepler(15711630)describes the golden ratio as a precious jewel:Geometry has two great treasures:one is the Theorem of Pythagoras,and the other the division of a line into extreme and mean ratio;the first we may compare to a measure of gold,the second we may name a precious jewel.These two treasures are combined in the Kepler triangle.,6/81,Charles Bonnet(17201793)points out that in the spiral phyllotaxis of plants going clockwise and counter-clockwise were frequently two successive Fibonacci series.,Martin Ohm(17921872)is believed to be the first to use the term,goldener Schnitt,(golden section)to describe this ratio,in 1835.,Edouard Lucas(18421891)gives the numerical sequence now known as the Fibonacci sequence its present name.,Mark Barr(20th century)suggests the Greek letter phi(),the initial letter of Greek sculptor Phidiass name,as a symbol for the golden ratio.,Roger Penrose(b.1931)discovered a symmetrical pattern that uses the golden ratio in the field of aperiodic tilings,which led to new discoveries about quasicrystals.,7/81,1953,年，美国数学家,J.,基弗,首先提出优选法,optimization method,中黄金分割法,优选法,是以数学原理为指导，用最可能少试验次数，尽快找到生产和科学试验中最优方案一个科学试验方法。,1970-80,年代，,中国数学家华罗庚,在中国推广，取得很大成绩。,8/81,Golden triangle,pentagon and pentagram,9/81,58,813,1321,2134,5/8,0.625,8/130.615,13/210.619,21/340.618,以下矩形中,哪些比较匀称,?,10/81,11/81,12/81,国旗、明信片、报纸、邮票、,书本、桌面、电视屏幕、窗户、房间,等等，都常被设计成靠近于黄金矩形。,报幕员站在舞台宽度,0.618,处。,13/81,Golden Rectangle,14/81,Golden angle,15/81,Leaf arrangements,1/2,elm,linden,lime,grasses,1/3,beech,hazel,grasses,blackberry,2/5,oak,cherry,apple,holly,plum,common groundsel,3/8,poplar,rose,pear,willow,5/13,pussy willow,almond,许多植物叶片、枝杈或瓣都按黄金分割角度伸展,互不重合，,有利于光合作用，通风和采光能到达最好效果,，这是生物进化结果。,16/81,Leonardo Fibonacci,斐波那契,(,约,1175-,约,1240),是丢番图,(Diophantos),与费尔马,(Pierre de Fermat),之间欧洲最出色数论学家，出生在意大利比萨。在著作,算盘书,（,Liber Abaci,）中，引进了印度阿拉伯数码（包含,0,）及其演算法则。数论方面他在丢番图方程和同余方程方面有主要贡献。,17/81,Fibonacci,s Series,算盘书,“,兔子问题,”,：假设一对兔子每个月能生一对小兔（一雄一雌），而每对小兔在它出生后第三个月，又能开始生小兔，假如没有死亡，由一对刚出生小兔开始，一年后一共会有多少对兔子？,18/81,将问题普通化后答案就形成著名斐波那契数列,斐波那契数列：,1,1,2,3,5,8,13,21,34,55,89,144,233,从第三项开始每一项都是数列中前两项之和。第,n,个月时 兔子数就是斐波那契数列第,n,项。,19/81,Fibonacci numbers and the Golden Number,20/81,Fibonacci Numbers,the Golden Section and Trees,著名,“,鲁德维格定律,”,是,F,数列在植物学中应用。数学家泽林斯基在一次国际数学会上指出，树年分枝数目就是,F,数列，即枝数增加遵照,F,数列规律,21/81,英国,T,W,汤姆森爵士指出假如一棵树一直保持幼时长高和长粗百分比，那它终将会因自己,“,细高个子,”,而翻倒；所以它选择了长高和长粗最正确百分比：,0.618,禾本植物,(,如小麦、水稻,),茎节，可看到其相邻两节之比为,11.618,或,12.472(,依品种不一样而异,),血管粗细比：,11.618,。,22/81,Pine cones,许多植物叶片、花瓣、果粒数与,F,数列相吻合松果上鳞片分布都与,F,数列相关,23/81,Petals on flowers,3 petals,:lily,iris,5 petals,:buttercup,wild rose,larkspur,columbine(aquilegia),8 petals,:delphiniums,13 petals,:ragwort,corn marigold,cineraria,some daisies,21 petals,:aster,black-eyed susan,chicory,34 petals,:plantain,pyrethrum,55,89 petals,:michaelmas daisies,the asteraceae family.,24/81,Petals on flowers,菲氏数过月季花，为,21,瓣。,达尔文数过波斯菊恰好,144,瓣，其中,55,瓣和,89,。,米切尔马斯花，,157,瓣，真中,13,瓣与另外,144,瓣相比，尤其长且弯曲向内，他认为,157,为,F,数列中,13,和,144,合成。,向日葵外缘花瓣分为,55,和,89,瓣两种不一样形态。瓣在形态上有显著差异：一个长丝卷曲向内，一个平展舒放向外。,25/81,Fibonacci Rectangles,26/81,Fibonacci Spirals,A logarithmic spiral,equiangular spiral or growth spiral is a special kind of spiral curve which often appears in nature.The logarithmic spiral was first described by Descartes and later extensively investigated by Jakob Bernoulli,who called it,Spira mirabilis,the marvelous spiral.,上帝之眼,27/81,Cutaway of a nautilus shell showing the chambers arranged in an approximately logarithmic spiral,海洋鹦鹉螺、蜗牛，一些动物角质体上，有甲壳软体动物身上，都有黄金螺线,28/81,A low pressure area over Iceland shows an approximately logarithmic spiral pattern,The arms of spiral galaxies often have the shape of a logarithmic spiral,here the Whirlpool Galaxy,Romanesco broccoli,showing fractal forms,蕨类植物琴状梢头，其螺线为黄金螺线,29/81,Fibonacci Phyllotaxis,30/81,Flowers,Vegetables and Fruit,31/81,Seed heads,向日葵不但葵盘上有一左一右黄金螺线，而且每朵小花或果花上也有两条黄金螺线；更奇异是，每套螺线总数都符合,F,数列：如有,21,条左旋，则必有,13,条石旋，其总数必为,34,条,32/81,Fibonacci Spirals,33/81,34/81,Man and,Golden Section,菲波那契大量调查后，人体肚脐以下长度与身高之比比值,0.618,，被视为,“,标准美人,”,。芭蕾舞蹈员身形合黄金百分比，在人体绘画和雕塑等应用，如古希腊神话中太阳神阿波罗形象，女神维纳斯塑像。,肚脐以上部分黄金分割点在咽喉，肚脐以下部分黄金点在膝关节，上肢部分黄金点在肘关节,人体肚脐还是胎儿营养供给，同时也是医疗效果黄金点。,35/81,36/81,普通人腰与脚底距离占身高,0.58,，而下肢较长人显得身材颀长，更有美感。,踮起脚尖能够增加腰与脚底距离，使得这一距离与身高比值更靠近,0.618,。给人以更为优美艺术形象,.,37/81,人体最感舒适温度约,23(,气温,),精神愉快时，人脑电波频率下限,(8,赫兹,),与上限,(12.9,赫兹,),之比，恰为黄金数。,38/81,Fibonacci Fingers?,2 hands each of which has.,5 fingers,each of which has.,3 parts separated by.,2 knuckles,39/81,Golden Section in Production and Science Research,1953,年美国基弗在首先提出来，,1970,年以后在中国进行了推广。为了到达优质、高产、低耗等目标，逐步发展起来优选法中,0.618,法,(,黄金分割法,),，在生产实践和科学试验中有广泛应用。,40/81,Golden Section in Architect and Art,世界上许多美好建筑物都是按黄金分割百分比建造古希腊雅典女神庙；法国埃菲尔铁塔。,意大利著名画家达,芬奇在他作品中经常选择,0.6181,百分比关系。,从声学角度来看，管弦乐器在黄金分割点上奏出声音最悦耳，许多著名音乐作品，其中高潮出现地方大多和黄金分割点靠近。,41/81,42/81,The ancient Egyptians were the first to use mathematics in art.It seems almost certain that they ascribed magical properties to the golden section(golden ratio,divine proportion,phi)and used in the design of their great pyramids.,43/81,If we take a cross section of the,Great Pyramid,we get a right triangle,the so-called Egyptian Triangle.The ratio of the slant height of the pyramid(hypotenuse of the triangle)to the distance from ground center(half the base dimension)is 1.61804.which differs from phi by only one unit in the fifth decimal place.If we let the base dimension be 2 units,then the sides of the right triangle are in the proportion 1:sqrt(phi):phi and the pyramid has a height of sqrt(phi).,44/81,The Medieval builders of churches and cathedrals approached the design of their buildings in much the same way as the Greeks.A good geometric structure was their aim.Inside and out,their buildings were intricate constructions based on the golden section.,45/81,46/81,Pythagoras(560-480 BC),the Greek geometer,was especially interested in the golden section,and proved that it was the basis for the proportions of the human figure.He showed that the human body is built with each part in a definite golden proportion to all the other parts.,47/81,Pythagoras discoveries of the proportions of the human figure had a tremendous effect on Greek art.Every part of their major buildings,down to the smallest detail of decoration,was constructed upon this proportion.,48/81,The Parthenon was perhaps the best example of a mathematical approach to art.,49/81,Once its ruined triangular pediment is restored,.,50/81,the ancient temple fits almost precisely into a golden rectangle.,51/81,Further classic subdivisions of the rectangle align perfectly with major architectural features of the structure.,52/81,53/81,Mathematicians had the contribution of the Greeks in mind when they christened the ratio phi in tribute to the great Phidias,who used the proportion frequently in his sculpture.,54/81,55/81,56/81,But whilst in architecture there was this very great interest in geometry,artists seemed to have lost all interest in the golden section and in mathematics as a whole.In the 16th Century,Luca Pacioli(1445-1514),geometer and friend of the great Renaissance painters,rediscovered the golden secret.His publication devoted to the number phi,Divina Proportione,was illustrated by no less an artist than.,57/81,He had earlier,like Pythagoras,made a close study of the human figure and had shown how all its different parts were related by the golden section.,58/81,59/81,60/81,Leonardos unfinished canvas,Saint Jerome,shows the great scholar with a lion lying at his feet.,A golden rectangle fits so neatly around the central figure that it is often said the artist deliberately painted the figure to conform to those proportions.Knowing Leonardos love of geometrical recreations as he described them,this is quite likely.,61/81,Leonardo da Vinci,(1451-1519).Leonardo had for a long time displayed an ardent interest in the mathematics of art and nature.,62/81,Notice how the classic subdivision of the rectangle lines up with St.Jeromes extended arm.,63/81,The golden rectangles in Da Vincis,Mona Lisa,abound.Visit the web page Mona Lisa Applet to add golden rectangles interactively to his famous masterpiece.,64/81,65/81,Michelangelos,Holy Family,.,is notable for its positioning of the principal figures in alignment with a pentagram or golden star.,66/81,Hacking back to classical themes and techniques for their inspiration,artists of the Renaissance like Michelangelo(1475-1564)and Raphael(1483-1530)once more began to construct their compositions on the golden ratio.The proportions of Michelangelos,David,conform to the golden ratio from the location of the navel with respect to the height to the placement of the joints in the fingers.,67/81,Raphaels,Crucifixion,.,is another well-known example.The principal figures outline a golden triangle.,68/81,which can be used to locate one of its underlying pentagrams.,69/81,This,self-portrait,by Rembrandt(1606-1669).,is an example of triangular composition-holding together an intricate subject within three straight lines.The different lengths of the sides add a little variety.,A perpendicular line from the apex of the triangle to the base would cut the base in golden section.,70/81,The English romantic artistic Joseph Mallord William Turner(1775-1851)is admired for his use of color and light.,Of particular interest are the geometric similarities in his various canvases,with their obvious golden subdivisions.,71/81,72/81,73/81,74/81,The more recent search for a grammar of art inevitably led to the use of the golden section in abstract art.,La Parade,painted in the characteristic multi-dotted style of the French neo-impressionist Seurat(1859-1891),contains numerous examples of golden proportions.,75/81,According to one art expert,Seurat attacked every canvas by the golden section.,His,Bathers,.has obvious golden subdivisions.,Three golden figures have been added here.Can you find more?,76/81,77/81,The Sacrament of the Last Supper,by Salvador Dali(1904-1989)is painted inside a golden rectangle.Golden proportions were used for positioning the figures.Part of an enormous dodecahedron floats above the table.The polyhedron consists of 12 regular pentagons and has fundamental golden connections.,78/81,79/81,米勒名画拾穗者亦是依黄金百分比而绘成。,80/81,小鹿母子摆放位置最适中？,81/81,