1 00:00:11,170 --> 00:00:15,140 This is the pangolin of Eric Joisel. It is an origami, 2 00:00:15,140 --> 00:00:18,850 it is folded by only one esagonal sheet of paper, without any cut. 3 00:00:18,850 --> 00:00:21,410 Origami's rules are easy: 4 00:00:21,410 --> 00:00:25,760 (Applause) 5 00:00:30,140 --> 00:00:35,610 you take a sheet of paper and fold it, you don't use any scissors or glue. 6 00:00:36,800 --> 00:00:40,890 Origami is an art - and it takes a bit of courage to say it - 7 00:00:40,890 --> 00:00:44,039 because almost all think that origami is simply... 8 00:00:44,039 --> 00:00:46,839 a child's play. 9 00:00:46,839 --> 00:00:49,000 I will try to change your mind. 10 00:00:49,000 --> 00:00:51,359 Today origami is this: 11 00:00:52,479 --> 00:00:57,629 every model has its author, this is a horse made by Roman Diaz... 12 00:00:57,629 --> 00:01:02,250 who is a veterinary capable to capture the essence of animals. 13 00:01:02,250 --> 00:01:06,470 Instead Robert Lang is one of the origami's theorists. 14 00:01:06,470 --> 00:01:10,010 Among other things, he formulated a theory... 15 00:01:10,010 --> 00:01:14,040 about how to design complex origami, of which I will just tell you something. 16 00:01:15,200 --> 00:01:18,659 This is a model of mine, a three-dimensional pram. 17 00:01:20,669 --> 00:01:26,630 Satoshi Kamiya is known for creating very complex models like this wasp, 18 00:01:26,630 --> 00:01:32,380 while Giang Dinh made simplicity his magic bullet: 19 00:01:32,380 --> 00:01:34,120 he works with wet cardboard, 20 00:01:34,120 --> 00:01:37,789 he sprinkles it and he can obtain these plastic figures. 21 00:01:39,169 --> 00:01:45,270 Eric Joisel is an other author, the pangolin's author too, 22 00:01:45,270 --> 00:01:48,690 and he is a master in creating also human figures 23 00:01:48,690 --> 00:01:52,350 and using the volume of the paper 24 00:01:52,350 --> 00:01:56,950 to create effects like, for example, Harlequin's legs. 25 00:01:58,040 --> 00:02:02,310 How have we reached this point? 26 00:02:02,630 --> 00:02:07,429 Let's start from the simpliest thing: the square base. 27 00:02:07,969 --> 00:02:13,830 It is a paper square. First you fold the medians, then the diagonals, 28 00:02:13,830 --> 00:02:19,709 close it and you obtain this figure: it is a square base and it has 4 flaps. 29 00:02:19,709 --> 00:02:23,720 No surprises, it comes from a square: 4 sides, 4 angles, 4 flaps. 30 00:02:23,720 --> 00:02:26,000 Folding a model by John Montroll, 31 00:02:26,000 --> 00:02:29,959 at a certain point, you get your hands on this stuff, 32 00:02:29,959 --> 00:02:33,819 which seems a square base, but has 5 flaps instead of 4. 33 00:02:33,819 --> 00:02:36,290 So you ask yourself, 34 00:02:36,290 --> 00:02:39,870 "But how, I started from a square: where does the fifth flap come from?" 35 00:02:39,870 --> 00:02:42,510 The trick to understand this, 36 00:02:42,510 --> 00:02:46,290 to understand how it works, is to reopen the sheet. 37 00:02:46,290 --> 00:02:50,800 So you reopen the sheet and you will see that the author... 38 00:02:50,800 --> 00:02:54,209 didn't do nothing but drawing a pentagon inside the square... 39 00:02:54,209 --> 00:02:56,330 and hiding all the exceeding paper. 40 00:02:56,330 --> 00:02:59,269 So the message here is, 41 00:02:59,269 --> 00:03:04,119 "If you want to understand how it works, reopen the model." 42 00:03:06,899 --> 00:03:13,950 This is one of the scorpions made by Robert Lang... 43 00:03:13,950 --> 00:03:14,989 it has a lot of tips. 44 00:03:14,989 --> 00:03:19,900 To understand how this runs, it has to know how an umbrella works. 45 00:03:19,900 --> 00:03:23,950 So imagine: a closed umbrella is the folded end, 46 00:03:23,950 --> 00:03:27,860 an open umbrella is the paper which is needed to obtain that end. 47 00:03:29,290 --> 00:03:33,019 A bigger umbrella will give a longer end. 48 00:03:34,219 --> 00:03:37,989 This is the same model, the same scorpion but reopened. 49 00:03:39,709 --> 00:03:43,950 It has been folded and then reopened, 50 00:03:43,950 --> 00:03:46,900 marking the position of its different ends. 51 00:03:46,900 --> 00:03:49,049 Every point is a circle, an umbrella: 52 00:03:49,049 --> 00:03:52,180 that big umbrella, the blue one, is for the tail, 53 00:03:52,180 --> 00:03:56,530 the red ones are the paws, the green ones are the claws. 54 00:03:57,460 --> 00:03:59,239 Now we go back to our presentation. 55 00:04:03,409 --> 00:04:05,420 This is the figure you have just seen, 56 00:04:05,420 --> 00:04:07,489 and this map of the folds... 57 00:04:07,489 --> 00:04:10,260 is called technically ‘crease pattern’. 58 00:04:10,260 --> 00:04:16,130 This is the Lang original version, where you can see all the work folds. 59 00:04:16,130 --> 00:04:20,320 Therefore the problem of projecting a complex origami turns into... 60 00:04:20,320 --> 00:04:26,050 the mathematic problem of having the circles on the plane opportunely. 61 00:04:26,050 --> 00:04:31,570 It's not only circles, you can see that there are also some figures, 62 00:04:31,570 --> 00:04:35,380 they are lightly out of sorts but they would show some streams... 63 00:04:35,380 --> 00:04:38,850 which divide the points and can give a topology to the model. 64 00:04:40,870 --> 00:04:45,870 Let's take a step back in time: there is as such geometry of origami, 65 00:04:45,870 --> 00:04:47,630 made of axioms and theorems. 66 00:04:49,090 --> 00:04:53,160 It is a more powerful geometry than the ’ruler and compass‘ one, 67 00:04:53,160 --> 00:04:56,650 meaning that all the workable constructions with ruler and compass... 68 00:04:56,650 --> 00:04:58,350 are also workable with origami, 69 00:04:58,350 --> 00:05:03,320 but origami can do other ones, such dividing an angle into three equal parts. 70 00:05:04,560 --> 00:05:06,720 A small example of origami geometry: 71 00:05:06,720 --> 00:05:10,370 we start from this square, we make these folds... 72 00:05:10,370 --> 00:05:12,500 and what we obtain is this figure here. 73 00:05:12,500 --> 00:05:14,330 They are only three folds, 74 00:05:14,330 --> 00:05:20,070 but you can glimpse a big triangle, which I state it is equilateral. 75 00:05:20,070 --> 00:05:23,600 It is equilateral because its sides... 76 00:05:23,600 --> 00:05:26,800 are three of the square's sides, so all they are equals, ok? 77 00:05:26,800 --> 00:05:30,690 And if it is an equilateral triangle these are exactly 60 degrees, 78 00:05:30,690 --> 00:05:35,800 therefore I can find very easily 60 degrees from a square. 79 00:05:35,800 --> 00:05:41,200 An other example concerns... 80 00:05:41,200 --> 00:05:44,200 the division of a sheet in equal parts. 81 00:05:44,200 --> 00:05:47,210 As you can see, the points on the diagonal are six... 82 00:05:47,210 --> 00:05:50,160 and so they divide that segment into five equal parts. 83 00:05:50,790 --> 00:05:53,440 On the other diagonal the division is in thirds, 84 00:05:53,440 --> 00:05:57,070 therefore, through very few folds, which are that ones highlighted here, 85 00:05:57,070 --> 00:06:00,190 I can obtain a division in fifths and thirds. 86 00:06:00,190 --> 00:06:03,900 Why do I need this for, maybe we will discover it later. 87 00:06:03,900 --> 00:06:07,780 In origami, one of the best moves is the twist. 88 00:06:07,780 --> 00:06:12,780 The twist is built on a central polygon 89 00:06:12,780 --> 00:06:15,780 going around and some parallel folds... 90 00:06:15,780 --> 00:06:18,340 which spread out two by two from the polygon. 91 00:06:18,340 --> 00:06:20,650 It is so called because when you make this fold, 92 00:06:20,650 --> 00:06:23,220 the central polygon actually makes a rotation. 93 00:06:23,220 --> 00:06:24,750 What is twist used for? 94 00:06:24,750 --> 00:06:28,050 The twist it is for creating some roses like this. 95 00:06:28,050 --> 00:06:32,640 This one is built on a pentagonal twist, 96 00:06:32,640 --> 00:06:35,640 it is by Naomiki Sato. 97 00:06:35,640 --> 00:06:39,650 Or it is for creating tessellations, like these here. 98 00:06:39,650 --> 00:06:41,910 Especially look that in the middle, 99 00:06:41,910 --> 00:06:44,530 which soon you will see in a new light. 100 00:06:45,580 --> 00:06:48,240 Tessellations can also be very complex, 101 00:06:48,240 --> 00:06:51,240 like this made by Alessandro Beber: 102 00:06:51,240 --> 00:06:55,990 this has some twists with 12, 3, 4 and 6 sides. 103 00:06:57,990 --> 00:07:01,090 Twists are also used in technology: 104 00:07:01,090 --> 00:07:03,610 here the question is that of a solar panel... 105 00:07:03,610 --> 00:07:05,930 which has to be locked up in a rocket... 106 00:07:05,930 --> 00:07:10,490 or a shuttle, to be thrown and, when it is in space, 107 00:07:10,490 --> 00:07:14,540 it has to be opened with minimum effort and damage. 108 00:07:14,540 --> 00:07:19,630 This is the series of moves to be done. 109 00:07:22,670 --> 00:07:23,670 It is this. 110 00:07:24,750 --> 00:07:27,560 This is how it is thrown, then, 111 00:07:27,560 --> 00:07:32,150 once it is high, it opens. 112 00:07:32,810 --> 00:07:35,810 (Applause) 113 00:07:40,080 --> 00:07:43,110 This is a twist... 114 00:07:43,110 --> 00:07:46,890 and this is a tessellation of a twist, it is the former beehive. 115 00:07:46,890 --> 00:07:50,680 So, as you can see, each hexagonal stuff... 116 00:07:50,680 --> 00:07:52,370 can be opened. 117 00:07:56,020 --> 00:08:00,190 Therefore these are related to each other. 118 00:08:00,190 --> 00:08:04,970 I go mad for motion origami, which are these I'm showing you. 119 00:08:04,970 --> 00:08:07,400 This is a fractal: 120 00:08:07,400 --> 00:08:13,440 it means that I have a row made of 12 external petals, 121 00:08:13,440 --> 00:08:15,310 a bit smaller one, 122 00:08:15,310 --> 00:08:17,870 which have the same shape but different dimension. 123 00:08:17,870 --> 00:08:21,050 And this is a single paper sheet. 124 00:08:21,500 --> 00:08:23,670 (Applause) 125 00:08:23,670 --> 00:08:29,920 The surprising thing is not only its opening, 126 00:08:31,020 --> 00:08:35,299 but its closing, because paper remembers. 127 00:08:35,299 --> 00:08:38,299 (Applause) 128 00:08:38,689 --> 00:08:41,950 I want to amaze you again with a pair of motion models: 129 00:08:42,630 --> 00:08:47,750 this is called flexicube, 130 00:08:47,750 --> 00:08:50,670 it is made from a single paper strip... 131 00:08:50,670 --> 00:08:52,480 which composes 8 little hinged cubes, 132 00:08:52,480 --> 00:08:54,719 in order to have this continuous movement. 133 00:08:54,719 --> 00:08:58,360 Instead this is its father: the double star flexicube, 134 00:08:58,360 --> 00:08:59,970 a model by Dave Brill. 135 00:08:59,970 --> 00:09:03,860 Although it is a flexicube also, it is the only model not made of... 136 00:09:03,860 --> 00:09:07,600 a single paper sheet, there are 64 fitted modules. 137 00:09:07,600 --> 00:09:10,530 It can go round also, but at a certain point I can stop, 138 00:09:12,000 --> 00:09:16,610 I can open the trunk and pull out the first star. 139 00:09:17,840 --> 00:09:23,290 But it is a double star felxicube, 140 00:09:23,290 --> 00:09:26,290 because there are two stars. 141 00:09:26,290 --> 00:09:29,290 (Applause) 142 00:09:29,820 --> 00:09:34,459 Here I let you imagine how much geometry is inside here, 143 00:09:34,459 --> 00:09:38,139 but this is half cube and this an other half cube: they are pulled together. 144 00:09:38,139 --> 00:09:43,379 But also this is half cube: this is half cube, the star, 145 00:09:43,379 --> 00:09:46,250 and if I turn it, it will become a box for stars, 146 00:09:46,250 --> 00:09:50,060 that is a box which exactly has the space to contain a star inside. 147 00:09:53,720 --> 00:09:56,720 (Applause) 148 00:09:56,740 --> 00:09:59,050 Why would anyone make origami? 149 00:09:59,050 --> 00:10:01,660 There are a lot of reasons. 150 00:10:01,660 --> 00:10:05,930 Origami instigates manual skills, fantasy and creativity, 151 00:10:05,930 --> 00:10:08,170 makes children like Maths. 152 00:10:08,170 --> 00:10:09,799 The reason why I fold origami... 153 00:10:09,799 --> 00:10:14,610 is because it is nice: it is magic, the magic of transformation really. 154 00:10:16,130 --> 00:10:20,310 The ‘Center for diffusion of origami’ is a no-profit association... 155 00:10:20,310 --> 00:10:25,529 which gathers all Italian origamists and also organise meetings. 156 00:10:25,529 --> 00:10:27,970 The meetings about origami are hotbeds of ideas... 157 00:10:27,970 --> 00:10:30,970 where everyone brings his own models, shows them, 158 00:10:30,970 --> 00:10:33,860 explains them and makes them fold by others. 159 00:10:33,860 --> 00:10:36,120 In this way there is a fusion of ideas... 160 00:10:36,120 --> 00:10:40,649 that has also brought to meetings about origami and teaching. 161 00:10:40,649 --> 00:10:42,389 Now we are organizing... 162 00:10:42,389 --> 00:10:44,499 the third meeting for next April. 163 00:10:44,499 --> 00:10:47,769 It will be a great chance, for teachers and instructors... 164 00:10:47,769 --> 00:10:49,399 who wants to use origami... 165 00:10:49,399 --> 00:10:55,100 for their job, to get in touch with different opportunities. 166 00:10:56,860 --> 00:11:01,819 I wanted to finish with Zsebe's bear, showing how it folds, 167 00:11:01,819 --> 00:11:04,609 but I don't know if I still have time... 168 00:11:05,439 --> 00:11:07,849 Yes? Do I still have time? 169 00:11:07,849 --> 00:11:09,350 Claudio Ruatti: Take a minute! 170 00:11:09,350 --> 00:11:14,089 RG: I will take a minute then, here it is! 171 00:11:14,089 --> 00:11:20,350 I have already folded something because otherwise I could not do it. 172 00:11:20,350 --> 00:11:23,619 Here one can already infer a little structure: 173 00:11:23,619 --> 00:11:28,100 this will become a bear, with head and tail. 174 00:11:28,100 --> 00:11:33,829 From the head one can obtain the ears in some way, 175 00:11:33,829 --> 00:11:38,189 then the great thing is the way you shape the head. 176 00:11:38,189 --> 00:11:42,939 Now here we need to zoom in really to this part. 177 00:11:42,939 --> 00:11:46,470 So, first you fold up, now I have exactly a rhombus. 178 00:11:49,590 --> 00:11:53,540 I fold up its face, then I squash from the inside... 179 00:11:53,540 --> 00:11:56,699 and I close the top part, which will become the bear's hump. 180 00:11:56,699 --> 00:12:00,610 It is taking the shape of a bear, you can see its face, 181 00:12:00,610 --> 00:12:05,209 but now the basic move: it is an upstream fold here, 182 00:12:05,209 --> 00:12:07,479 followed by a downstream fold placed right down, 183 00:12:13,439 --> 00:12:16,709 which make the bear's face pop up. 184 00:12:16,709 --> 00:12:19,800 Sorry, it has come off a bit like that. 185 00:12:19,800 --> 00:12:22,309 (Applause) 186 00:12:24,439 --> 00:12:28,389 This is how the model should be. 187 00:12:29,609 --> 00:12:33,569 I have finished my presentation, more or less. 188 00:12:33,569 --> 00:12:36,420 This is a model created for this occasion: 189 00:12:37,990 --> 00:12:41,499 it is a model which basically has a cut. 190 00:12:41,499 --> 00:12:44,259 What happens is that... 191 00:12:44,259 --> 00:12:48,659 one has a sheet of paper and folds it 192 00:12:48,659 --> 00:12:51,189 - as you can see, the TED logo has been drawn. 193 00:12:55,009 --> 00:12:57,930 What happens is that if one just cut it, 194 00:12:57,930 --> 00:13:04,129 which you should not do with origami, but if one makes a single cut here, 195 00:13:04,559 --> 00:13:09,639 he will separate the three letters and obtain the figure you were seeing. 196 00:13:10,199 --> 00:13:13,199 (Applause) 197 00:13:13,199 --> 00:13:14,209 Thank you.