错觉纸模图纸 立柱2

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几何体模型复杂折纸手工步骤教程这个四面体模型，形态比较复杂，实际上是不同大小的八面体的组合体。

即这些八面体是构成四面体模型的基本组件。

每个八面体需要4个元件。

主要材料：彩纸所需工具：剪刀制作步骤：第1步：本教程是由四种颜色的纸来完成的。

各种颜色的八面体所需数量如下：蓝色：1个八面体＝4个元件绿色： 4个八面体 = 16个元件黄色： 4 × 4 个八面体= 64个元件粉色： 4 × 4 × 4 个八面体= 256个元件（4 + 16 + 64 + 256）个八面体 = 340个元件构成这款四面体模型的八面体组件结合得十分牢靠，以致于可以将模型顶部粉色的八面体取下，其它部分也不会散架。

中间构成：八面体由四个正三角形构成一个八面体高为8.5英寸的三角形折出的八面体边长不足3英寸1、首先我们要找到等边三角形高即中线的七等分点，接下来我们需要先做个模板；如下图，将模板等边三角形的两个底角对折，折痕即为等边三角形的一条高或中线；2、为了简化这个过程，这里可以借助尺和笔来计算，并画出七等分点。

然后将底边向上，折到七分点处；第2步：3、将另外的等边三角形与模板三角形叠放在一起：三角形的底边紧贴在模板三角形的7等分线上，如下图所示左侧为模板等边三角形。

然后将右侧三角形顶点沿着左侧模板三角形的底边沿下折，折痕即为七等分线。

第3步：元件A的折法1、用模板折出三条中线的七等线，共三次，这三条折痕分别与对应的边平等。

然后依照折风车的方式，按逆时针方向顺着图中的1、2、3的次序，沿着折痕将三角形的三条边向里折，每次向里一条边。

第4步：2、折好后就是这个样子，翻面；第5步：3、翻到背面，会看一个大三角形，这个三角形也是等边三角形，将上面和左侧的两个顶点重合，这样可以得到左侧那条边的中点；第6步：4、在背面这个大三角形中，将右侧的那个顶点折到上一步提到的那个中点上，将纸抚平，会得到一条平行于左侧边的线，其实这是三角形的一条中位线；第7步：5、接下来，将上面和左侧的两个顶点分别按照步骤4的折法，折出大三角形的另外两条中位线，然后翻到背面；第8步：6、将右侧的边向左折，使这边与步骤4或5得到的中位线折痕重合；第9步：7、右下角沿图中的两条山折线折出折痕；第10步：8、将另外两个角也按步骤6和7折出折痕；到些为止，元件A 完成了。

生活中的趣味数学今天我主要来讲一讲生活中的有关数学的几个趣味问题：缪勒—-莱耶错觉看看上面的带箭头的两条直线,猜猜看哪条更长? 是上面那条吗? 错了!其实它们一样长。

这就是有名的缪勒-—莱耶错觉,也叫箭形错觉。

它是指两条长度相等的直线,如果一条直线的两端加上向外的两条斜线，另一条直线的两端加上向内的两条斜线，则前者会显得比后者长得多。

现在明白了吗？大金字塔之谜墨西哥、希腊、苏丹等国都有金字塔,但名声最为显赫的是埃及的金字塔。

埃及是世界上历史最悠久的文明古国之一。

金字塔是古埃及文明的代表作，是埃及国家的象征，是埃及人民的骄傲。

金字塔，阿拉伯文意为"方锥体”，它是一种方底，尖顶的石砌建筑物，是古代埃及埋葬国王、王后或王室其他成员的陵墓。

它既不是金子做的，也不是我们通常所见的宝塔形.是由于它规模宏大，从四面看都呈等腰三角形，很像汉语中的”金”字，故中文形象地把它译为”金字塔”。

埃及迄今发现的金字塔共约八十座，其中最大的是以高耸巍峨而被誉为古代世界七大奇迹之首的胡夫大金字塔。

在1889年巴黎埃菲尔铁塔落成前的四千多年的漫长岁月中，胡夫大金字塔一直是世界上最高的建筑物。

据一位名叫彼得的英国考古学者估计，胡夫大金字塔大约由230万块石块砌成,外层石块约115000块，平均每块重2.5吨，像一辆小汽车那样大,而大的甚至超过15吨。

假如把这些石块凿成平均一立方英尺的小块，把它们沿赤道排成一行，其长度相当于赤道周长的三分之二.1789年拿破仑入侵埃及时，于当年7月21日在金字塔地区与土耳其和埃及军队发生了一次激战，战后他观察了胡夫金字塔。

据说他对塔的规模之大佩服得五体投地。

他估算,如果把胡夫金字塔和与它相距不远胡夫的儿子哈夫拉和孙子孟卡乌拉的金字塔的石块加在一起，可以砌一条三米高、一米厚的石墙沿着国界把整个法国围成一圈。

在四千多年前生产工具很落后的中古时代,埃及人是怎样采集、搬运数量如此之多，每块又如此之重的巨石垒成如此宏伟的大金字塔，仍是十分难解的谜。

Asse m bly inst ruct ions forT i tan icAbout R MS T i tan i cTi tanic i s p robably the bes t-known sh ip in modern hi s tory. S ince s ink ingin 1912 her s to ry has been re to ld many t imes in books and f i lm, and hasente red popula r cul tu re a s a t a le o f human pr ide and t r agedy.The Royal Mai l S teamer T i tan ic was the second o f th ree mass ive oceanl ine rs in tended by the White S ta r L ine to domina te the lucra t ive t ransa t lan t icpassenger t r ade. T i tan ic was s l ight ly heav ie r than her s i s te r-ship Olympic,making he r the la rges t sh ip in the wor ld a t 883f ee t long and over 46,000tons. The sh ips were a t the lead ing edge of engineer ing t echnology a t the t ime fea tur ing rec ip roca t ing and tu rbine s t eam engines develop ing 50,000 horsepower,a modern e lec t r i ca l sys tem power ing cargo c ra nes and passenger e l eva tors,and an ar rangement o f wate r t igh t compar tments and emergency doors tha t caused them to be dec la red“v i r tua l ly uns inkable”. Passenger ameni t i es were no l es s advanced. F i r s t-c la ss passengers enjoyed accom modat ions and mea ls equa l to the f ines t ho te l s,and a gymnasium,swim ming poo l and squash cour t fo r r ec rea t ion. Second c las s,though le ss lav ish, was the equiva len t o f f i r s t c l ass on many o ther l ine rs. By compar ison th i rd c l ass, o r s t ee rage, was ra ther spar t an but comfor tab le by the s tandards o f the day.After sea t r ia l s T i tan ic l e f t Southampton fo r he r f i r s t com merc ia l voyage on 10 Apri l 1912,s topping a t Cherbourg and Queens town be fore head ing across the At lant i c to New York. Shor t ly before midn igh t on 14 Apr i l an iceberg was seen in T i tanic’s pa th and before the sh ip could turn as ide the s ta rboard s ide g razed the ice, opening s ix o f the fo rward compartments be low the water l ine. When i t became apparen t tha t th e pumps could no t keep up wi th the incoming wa ter and tha t the sh ip would founder, Capta in Edward Smith o rdered the evacuat ion o f passengers by l i f eboat.Due to outda ted mar i t ime r egula t ions T i tan ic had l i feboa t capac i ty fo r fa r f ewer than the number o f people aboard.In sp i te o f th i s the f i r s t l i f eboat s were lowered only ha l f-ful l,the passengers be ing re luctan t to l eave the apparen t secur i ty o f the l iner. While f i r s t- and second-c l ass had easy access to the boat deck those in s t eerage,roused f rom thei r cabins deep in the sh ip,f aced de lays and obs t ruct ions. Most r eached t he deck too la te to f ind a p l ace in the boat s.By 2:00 a.m.the bows o f the ship were submerged and the c rowded s t e rn began to r i se above the wa ter. Twenty minutes l a te r the l ight s f ina l ly fa i l ed and the hul l,s t r essed beyond i t s l imi ts by the unsuppor ted weigh t p ro t ruding f rom the sea, b roke in two. The fo rward par t sank im media te ly whi le the s te rn hung ve r t i ca l ly fo r a shor t t ime before fo l lowing. The sea was f i l l ed with s t rugg l ing men, women and ch i l dren but in the f r eez ing wate r mos t would soon d ie o f exposure. Of the 2200 passenger s and c rew on ly 700 survived the n igh t.The loss o f th i s l a rges t and most modern ocean l ine r caused shock wor ldwide. Formal inqu i r ies were he ld in both Br i ta in and the USA, and sa fe ty regula t ions fo r passenger sh ips were im media te ly s t r eng thened.Improvements inc luded inc reased l i f eboat capac i ty, 24-hour r adio wat ches on sh ips,and the es t abl i shment o f an in te rnat ional i ce pa t ro l to warn of the presence o f i ce in the sea lanes.Ti tanic’s s i s t e r sh ip Olympic en joyed a long,success ful ca reer be fore f ina l ly be ing sc rapped in 1935. The th i rd sh ip in the c l ass, Br i tanni c, never ente red passenger se rv ice bu t was t aken in to use a s a hospi t a l sh ip dur ing the F i r s t Wor ld War,and sank in 1916 a f te r s t r ik ing a mine in the Aegean Sea.Long af t e r s inking T i tan ic again made newspaper head l ines in 1985 when a team led by Dr. Rober t Ba l la rd d i scovered the wreck. S i nce then severa l exped i t ions have v is i t ed the s i t e,in some cases recover ing a r t i f ac t s. Cur ren t ly T i tan ic r es t s a t a dep th o f 12,500fee t and i s s lowly decay ing. Some exper t s e s t imate the r emaining s t ruc tu re o f the once-grea t l ine r wi l l have co l lapsed by the middle o f the 21s t century.The ModelThis model i s a 1:1200sca le wa ter l ine r ep l ica o f T i tan ic, and i s approx imate ly 9inches long.M odel par t s a re con ta ined in the document t i tanic_parts.pdf. The op t iona l d i splay base i s in document t i tan ic_base.pdf. P r in t ou t t he par t s document on 8.5"x11" o r A4 s i ze whi t e paper card s tock su i tab le to your p r in te r. 67lb.cover s tock(approx. 8.5thousand ths o f an inch o r 0,2 m m th ick)i s r ecom mended.A word of cau t ion:th i s model i s not su i t able fo r assembly by young chi ld ren, due to the use of sharp too ls and the complexi ty o f some assembly s teps. Prev ious exper i ence wi th ca rd model ing i s s t rongly recom mended.I f you have any com ments o r sugges t ions regard ing th i s k i t,you can contac t me by emai l a t model s@curre l l.ne t.Too lsBefore beg inning, you wi l l need the fo l lowing too ls and mater ia l s:a) b) c) d) e) f)whi te g luea glue appl i ca tor such as a smal l pa in tbrush o r toothp ick, and wate r o r g lue so lvent on hand to r inse theb rush a sharp kni fe fo r cut t inga f la t cu t t ing su r facea rule r o r s t r a igh t edgea scor ing too l o rb lun t kn i fe forc reas ing the fo ld l inesa f la t p iece of wood or foam core fo r a bu i ld ing suppor t o r d i sp lay base(op t iona l)spray adhes ive fo r a t tach ing the d i sp lay su r face to the baseg)h)t i t an i c_i n s t r.pd f v1.0© Apr i l2007by Ra lph Cur r e l l h t tp://ww w.cur r e l l.ne t Page1o f6Hintsa) b) c) d) e)Selec t a we l l -l i t , comfor tab le work a rea tha t wi l l r emain und is tu rbed when you a re not the re . Keep your hands and too ls c lean when work ing , to avo id ge t t ing g lue on vi s ib le par t s o f the model . I t ’s ea s ie r to s tay organ ized i f you only cu t out those par t s you need for each s tep . M ake sure your kni fe i s sharp . When cu t t ing s t r a igh t l ines , u se a s t r a igh t -edge . Study the d iagrams ca refu l ly , and a lways te s t -f i t the pa r t s before apply ing g lue .Asse m blyPortAft (Stern)Forward(Bow)StarboardIn these ins t ruc t ions , the t e rms fo rward (bow) and a f t (s t e rn) r e fer to the f ron t and rear ends of the ship . Por t and s t a rboard r e fe r to the le f t and r ight s ides . Scor ing o f pa r t s i s ind ica ted by th in b lack l ines ou ts ide the pa r t ’s ou t l ine , and by dashed or shaded l ines on the par t ’s su r face . For smal l pa r t s such as the deckhouses and c ranes i t i s r ecom mended tha t ou ts ide corners (‘mounta in ’ fo lds ) a re scored b y gen t ly scr ib ing t he score l ine wi th a kn i fe re sul t ing in a sharp corner when fo lded . Score par t s be fore cu t t ing them out . In the d iagrams , subassembl ies a re ident i f i ed by a number wi th in a c i rc le (e .g . ), cor responding to the s tep in which i t was assembled . Step 1: Lamina te the la t e ra l fo rmers to heavy ca rd s tock , such tha t the combined th i ckness i s abou t 1m m or 0.04 inches . Cut ou t the formers af te r lamina t ing . Assemble the l eng thwise fo rmer (s tep 2) t aking ca re to on ly g lue the cent ra l (b lue shaded) a rea and a l lowing the f l a ps a t the bot tom to fo ld ou tward . Cu t the upper p rof i l e a f t e r g lu ing and fold as shown in the d iagrams . Assemble the in t e rna l s t ruc ture by g l uing the la t e ra l fo rmers in to s lo t s in the leng thwise fo rmer (s tep 3). Some p ieces must be o r ien ted such tha t the p r in ted s ide f aces a f t ; these a re l abe l led as such . At tach the we l l deck s t i f feners (s tep 4) in to the appropr ia t e s lo t s . At th i s s tage the model should be a t t ached to e i ther a temporary work base (s tep 5) o r to the opt ional d i sp lay base (s tep 6). Th is p revent s the f rame f rom warping dur ing subsequen t s teps . I f us ing a t emporary base , app ly on ly a smal l amount o f g lue so the sh ip may be la t e r d etached eas i ly . At tach the fo recas t l e and poop decks to the f r ame (s tep 7). The fo rward t ip o f the fo recas t l e wi l l p ro t rude s l ight ly beyond the f ron t o f the f rame.The shap ing and a t tach ing o f the hu l l su r faces a re some what cha l leng ing . Dry-f i t t ing and ca refu l a t t ent ion to the d rawings wi l l he lp . At t ach the connec t ing s t r ips to the main and s t e rn sec t ions o f the s t a rboard hul l sur face (s tep 8). To avo id gaps , bend the par t s as c lose ly as poss ib le to match the contour o f the f rame before g lu ing the s te rn sec t ion to the main sec t ion . Repea t for the por t hul l pa r t s and g lue por t and s t arboard toge ther a t the rudder on ly (s tep 9). S l ide the hul l p ieces a round the f rame f rom the s t e rn , such tha t the rudder i s pos i t ioned undernea th t he s te rn overhang (s tep 10). The rear edge of the hu l l p l a t ing shou ld a l ign wi th the cen t re o f the r earmost la t e ra l fo rmer . Beginn ing a t the s t ern and working fo rward , g lue the hul l sur face to the f r ame. The wel l deck cu tout s on the top o f the hu l l should match the fo re and a f t bulkheads o f the well decks . F inal ly , jo in the por t and s t a rboard su r faces where they meet a t the bow. Form the coun te r p la t ing in to shape (s tep 11) and a t t ach over the s t e rn f ramework . I f you a re us ing a temporary work base , the sh ip may be de tached now. Fold and a t tach the decks and bulkheads jus t beh ind the fo rward we l l deck (s tep 12) and in f ront o f the a f t wel l deck (s tep 13). The a f t promenade deck B48 has a somewhat complex shape and requi res p rec i se scor ing and ca re ful fo ld ing . At tach the boat deck (s tep 14) so tha t the top of the longi tud ina l fo rmers p rot rude th rough the ho les in the deck . Steps 15 through 20 show the as sembly o f the va r ious deckhouses to the boat deck , beg inn ing a f t and work ing fo rward . Severa l o f these requi re care fu l fo ld ing , so c lose a t ten t ion to the d rawings i s recom mended. Blue loca t ing marks a re pr in ted on the boa t deck indica t ing the pos i t ion o f the deckhouses .Bend the wheelhouse bu lwark B14 to shape (s tep 21) and a t t ach to the f ront o f the boa t deck , add ing the wing roofs B13. Bu i ld and a t tach the off ice rs quar te r s and whee lhouse to the boa t deck (s tep 22) such tha t the f ron t o f the wheelhouse abu ts the f ron t f ace of the bu lwark added in the p rev ious s t ep . I t may be necessa ry to t r im s l igh t ly the rea r edge o f pa r t B51 to ach ieve a snug f i t aga inst the deckhouse a f t . At t ach the promenade deck s ides (s tep 23), wi th the r a i sed bulwarks p rot rud ing above the boa t deck and the f ron t edge nes t ed beneath the br id ge wing overhangs a s shown in the d iagram. A typ ica l e l ec t r ic c rane as sembly i s shown in s tep 24. At t ach the c ranes and cargo ha tches as shown in the d iagram (s tep 25). Fold and a t t ach the dock ing b r idge to the s t e rn (s tep 26). The forward ca rgo ha tch , b reakwater and anchor c rane a re added in s tep 27. Step 28 shows a typica l funne l a ssembly . Note tha t the funnel s a re no t iden t ica l in s ize . A l e t t e r i s p r in ted on the connec t ing s t r ip , cor responding with the le t te r a t the funnel ’s loca t ion on the deckhouse roof . Also , the funne l cap for the a f t funne l i s d i f fe r en t f rom the o ther th ree f unnel s . Attach the funne ls (s tep 29) wi th the seam fac ing the s t e rn , so tha t the funne ls s lope af t s l ight ly . Build and a t t ach the compass p l a t form (s tep 30). For g rea ter r ea l i sm you may rep lace the bo t tom suppor t B42 with four l egs made f rom wire . A t emplate fo r shap ing the two mast s i s shown on the par t s shee t . Too thp icks whi t t l ed o r sanded to s i ze , o r s t re t ched p l as t i c sprue , a re recom mended fo r these par t s . Bu i ld and a t t ach the c row ’s nes t and inse r t the mast s in to the ho les in the deck (s tep 31). The base of th e mas ts shou ld res t in no tches cu t in to the in t e rna l fo rmer . I f des i r ed , shrouds (suppor t ing cab les fo r the mast s ) can be made f rom f ine wi re o r ny l on l ine . Attach the upper ends o f the shrouds to the mast and the lower ends to the ou ter edge o f the we l l deck . Const ruct the l i f eboa ts as shown (s tep 32). There a re th ree s izes o f l i feboa t , a t tached to the upper decks as indica ted in the d iagram.t i t an i c_i n s t r .pd f v1.0 © Apr i l 2007 by Ra lph Cur r e l l h t tp ://ww w.cur r e l l .ne t Page 2 o f 61La minate la tera l formers toheavycardstock2LengthwiseformerA20Glueonly inarea ind icatedbyblueshading(o ther areaswi l l fo ldou tward).C ut formerlayout f ro mpartssheet 'A '. C o m binedth icknessshouldbe approx imate ly1m m or0.04inches.C utupperpro f i leands lotsa f terglu ing.ABCNOPDEFGHIJKLMAft ForwardBo w a ndsternf lapsfo ldouthor izontal l y . C entref laps fo ld outwardasshown.3Latera l formers4W el ldeck st i f feners5O pt ional temporarybase(So me partso mit ted forc lar i ty .) 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视错觉会产生强烈的视觉效果，容易引起受众的注意力，而这正是平面设计的一个前提因素。

面对日益丰富的各种信息，如何抓住受众的注意力，是设计师所面临的首要问题之～。

平面广告设计中常常利用视错觉。

视错觉的形态常常表现出某种深邃的思想或出现不可思议的形象，或引人入胜，或令人不安。

在广告设计中和用视错觉这个视觉语言可以引起人们的视觉注意、激发兴趣、增强记忆力，具有强大的震撼力．图形是人为创造的形象，是人的视知觉的反映，而矛盾空间是将图形按照严格的形式逻辑推导而出的。

这种图形结构的表达方式在平面的二维空间可以成立，然而在三维的真实空间中却因互相矛盾而难以存在。

矛盾空间的形成通常是利用视点的转换和交替，在二维的平面上表现了三维的立体形态，但在三维立体的形体中显现出模棱两可的视觉效果，造成空间的混乱，形成介于二维和三维之间的空间，矛盾空间的表现形态使图形与空间交融，图形不仅是自身的形，也是空间的背景。

这种视错觉手法经常应用在海报设计中。

如［图１－１］是日本著名平面设计大师福田繁雄先生的作品。

除了矛盾空间，福田繁雄的作品还经常使用图底错觉等其它表现形式。

１９７５年他为自己在东京京王百货店举３【图１－１］福田繁雄海报设计［图１－２］福田繁雄。

个展”海报［图１－３】福田繁雄海报设计办的。

个展”所设计的海报中［图１－２］，以及［图卜３］都是运用“正倒位图形反转”的手法，非常巧妙地利用正负形，简单而又富有趣味，是现代视错觉的新层次意义上的创新设计。

企业形象设计尤其是字体及标志设计中应用视错觉原理的例子更是举不胜举，如［图１＿４］是１９９０年意大利世界杯标志，设计中应用了闭锁图形错觉。

除了应用视错觉原理，在一些情况下要通过纠正视觉错觉来获取更好的视觉效果。

比如法国国旗红：白：兰三色的比例为３５：３３：３７，而我们却感觉三种颜色面积相等［图ｌ－Ｇ］。

这是因为白色给人以扩张的感觉，而兰色则有收缩的感觉。

奥运五环标志［图ｌ＿６】运用了周样的原理进行视觉调整。

第8章　视错觉第8章　视错觉
视错觉是指人们属于知觉判断范围的视觉经验同所观察到的对象之间存在的差异，如图8-1、图8-2所示。

图8-1　视错觉之一
图8-2　视错觉之二
了解视错觉不仅可以避免设计上的偏差和失误，还可以巧妙地运用这一视觉生理现象为造型设计服务，表现特殊的视觉效果。

一、分割视错觉
两个体积完全相同的长方体，分别进行水平和垂直方向的分割，由于水平线和垂直线的视觉诱导作用，长方体在造型感觉上发生了偏差，水平分割长方体的比例关系在视觉上显得扁一些，垂直分割长方体的比例关系在视觉上显得高耸一些，如图8-3所示。

图8-3　水平分割和垂直分割
现代设计大师贝仑斯为德国通用电器公司AEG设计的透平机车间，如图8-4所示，正是利用这一点进行垂直与水平长方体的分割调和。

在整个厂房建筑中，柱子是在高度方向延展的长方体，厂房主体是在水平方向上延展的长方体，所以为了调和这两个主要形态，柱体进行了水平方向的分割，而厂房主体进行了垂直方向的分割。

这样，不同方向上的长方体之间
083。