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IC16: The Self-Sustaining Domes By Leonardo (Extended Talk)

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thank you to all the people in the area and the world and the theft of my own about our we are going to build a very big outside just the use but before that we'll give you 2 different presentations that 1 about real experiences that the dome building bomb by on the and I will start with a small introduction about the history of this complete project them for me it all started with that these objects as well it does look like a goal and I agree that it's a spherical cross-section built of just paper but this was my 1st object that led me to read don't concessions and this object has a lot to do with this section of a cue so I start examining how would you could make a nice decisions of cubes in interval parts but at that moment I what's more concentrated on the lines on the face of cues the parts itself so when you take those lines and you extend to faces and you get an object and when you round off all you get this spherical concessions that you've seen and well I built models in wood and well this was the 1st step for me to come to the don't concessions uh because when you make that medical
representation of this object and so you only use order lines and corrections of a graph and then you see that the connecting lines have all the
same quality they all connected so these lines connected to for or alliances and in a special way because all the end points of of lines the endpoints of this line are connected to 1 of points of or reliance the so this is the basic definition of this kind of construction and I call this positive negative negative positive so all the elements have this property and
that can be connected in this way and I built my 1st sculpture uh in this way uh this on a school the but also here can see these elements is connected to the 4 others and endpoints always meet points on our objects the I found it's so interesting
that I studied and the possibilities of of the system and further and I came to the conclusion that if you have the change positive and negative 2 over and under like the destroying but in fact
this is a description of but uh the construction of a salt dome residency and then when you extend the drawing
with more elements as well you'll get
a bigger don't and finally this was my 1st only well you can see it's created well about 25 years ago and so this is very old picture the but for me this was the started to don't building so starting from year's steps when
and they're studying the system of positive negative negative positive it led to a lot of different patterns that could use to
build don't and all kind of those
could be created this is the same elements the same very simple wooden elements on this side made to institutions directed Boston negative negative Boston sources variety
of different patterns in regular but also more irregular you see tentacles in the middle and well and the possibilities go and and well
that was the moment that there have told well in this system is so nice and so simple that I could imagine I was the first one to use this to do to make these it just 1919 uh so at that time and rest protocol reverse broke all the
structures I went the sorry alone and also internet wasn't available for me to to search for for our uh examples so I have to go to libraries and I found the final part of this
page uh only cycle see joints that are well almost the same time and this page and is a base of from a notebook of Leonardo da Vinci
so if very all source and well I have to
admit that will be when you compare his drawings to mind well there are almost the same as he was the 1st and also this 1 well this is my drawing but yeah I have to admit that he was the front of the system them well I explored the possibilities of of these kinds of elements with the Commission's since I told you and but uh I was able to make a lot of different patterns you see 6 patterns he different patterns the false same properties but in total lack of more than 100 different patterns the the well and I have from into
like and entiation this so exploits some more possibilities of these patterns and uh I think this is a ghost close to tuition
the so when I discovered that there the 4 idea of of possibilities of the simple stakes for the simple elements this simple
positive negative positive elements the I went on searching for 4 of
our other things and 1 of the things he says you can distort but that pattern without leaving the system because again every element is connected in the right way so you can ignite distortions and uh
welfare document the human annotation of sensor distortion when you start of the peptide this and let's say you take a few elements in the middle the and just rotating little bit thing and offers a distortion but the system is followed the
perfectly and in real time the distortion
patterns like this well when you can make a distortion I don't want you can do it all over the tree contains from 1 pattern to another this way the more the tessellations uh I did discover but uh I will leave minus 1 so from 1 pattern you can create a new 1 that well and I talked about but talked about edges and so in its form for me it was very simple to take step to trials that so these lines that there is a line of of an element of a norm but there's also a line in between the tiles in this case but the pattern is I 2nd the same the but when you then take a step to Paris and you see on possibilities and 1 of them is this 1 but I can change the tiles of In our consent
form the pattern from well that's starting to write learning but
this but story you can now because when you look at all the lines that in between those trials as well you can see a say this is a simple line but you can also see this line is the edge of this tile and also the because of this title In the case of the style and the edge of this tile so in fact this line consists of 4 different lines will like this and because of the system the these lines always equal length and also these or also all the planes so in fact you for a parallelogram that makes it possible to have some movement to
systems like this just because you used positive negative negative positive elements the better the that well there's a lot of possibilities and this is a In our pattern of of the debt to create the good that can be used for a dome but also the transformed in trials
and it still works just because of the simple elements thank you can even go
over there where have got a point with the heck's going here I can move the box and the bit away from the center Cycorp space for new it's more ones to make a more ex-con fractal stem when you
change that translates into tiles will again the this transformation still works so this is a lot of dynamic systems the with simple piles all based on a dependence with the plus minus minus plus structure the so
you also 1 so this is you can see this line this there aligned that with that you can use for a dome but the the trials I can make this transformation and you can see it since wants into an hour great that also has the same quality of for dimensions the 4 . tha so this is a one fields of of exploration for me and that and other fields basal this pattern was well when you uh superimposed in order but a grant from the 1st grade you can use the blue trade how to make a point here those triangles can be seen as faces of such a policy on but now descriptors decoration of the final polygon so when I fall together with
the 2 parties on I have to get completely around this what are know so achievements of concession majors goes simple this one's ones plastics and when you make it in real and this is the result and this is fear you can build it uh in this case 24 people elements and you don't need to do more open it just holds itself together and then it has nothing to do with tension but only if position there's no parts that can fall every box that that is prevented to fall that by that these 2 orders so the total social stay the the essential research when I found this way of of working after Leonardo creates a made because we like this this 90 elements in total will more than a 1 meter in diameter and to shoulder uh this is just a loose construction are made this fall animation somehow when I was just
1 and and at the same so that's about as was to build the season 2 seconds at a and the spherical also give postal due to their use the space that inside the sphere that such things here and so this element he was the space inside the sphere so it is not the the surface of the sphere that you use but the complete inside so this is a real to the construction of the sphere can be seen as just a service so in fact you've got 2 degrees of freedom but now you really need to dissidents and also a well you're recognizing and now so with for connecting points here all over the sphere but and well you create a double-layer effect under well this is also a nice the an application of of the system uh by just the placing for elements real fish you make this 1 but also for efficient for correcting points and that's enough to to to make concessions to the the and you can think of a word in the minimal concession out with this system and all that that's just 1 detector young uh only 2 elements there but
also here plus minus minus plus so to women's it just fits and this is false 1 the acidosis
experiments and all I want you to create a real big also we replaced the small wooden stakes wire be used uh these things are about 4 long uh I was invited to add the next station for exhibition in the whole world and so we built the real big don't nice thing about about this kind of don't she says we can build it with and you just a few people and you don't need to know how much force and just because you start in the middle and you add states at the edge of conservation always so you you only have to lift spot and then they had no mistake or only being and In total the concessional rise itself and finally you get this 1 that we build tools those that at a 4 tradition so 2 lectures are and when you look from the inside and you can see the other 1 here the but he's a reverse goes them at all I came in contact with uh uh a group called nexus from QQ millions the nexus is
a group that studies imagination arch-texture and um their base in
Italy and uh candles invited me to do a project together with some people nexus to study the the base softly on defense and and more and that's because
all those pages so that if you don't diagrams and so lines but there's also a lot of text and that that text wasn't
translated to all that time so as well we thought it would be good to to be read the text and to see what the value himself says about those diagrams so we studied that detects but also today in across at our all the page of of you know and the odds and she was um telling about the sizes of being said he had in mind we don't know if he really build those don't but he said it might be handy for foreign army to make this kind of construction uh when they are in a forest and they just can't take beams and and they can put schemes over the conservation and they have a can't they can't sleep and it and uh so it it could be helpful and so we talked about the size of 2 beams and also said but there's something about and that the height that you get when you uh use a certain thickness of the beams and so uh 1 of the things he did this he viewing message if the article was right and will do became very close to to his measurements so uh well maybe you really build this and also the test distance of causation and you could evolve over it and muscles In this also you license and that also at that time I started doing
their shops and if children than well till the time I built don't have just districts but when you build own statistics as well below glider wafer usually and and so I decided to change the design a little bit and that made this type of elements and these are used with this construction and you can see it now you can the extent you construction in the face a big way the it the children are
experimenting with the patterns this is what happens I gave them but you see when the experiment themselves define new patterns but they follow the rules exactly so each element is connected in in the right way so noble and that's what I like this those virtual said that children come with their own ideas and own patterns and they were together for the nicely and the build corners solutions so I had to make a lot of those elements that they + quite easy to make them so
the so this suggests that traditional station and and you can see at a certain moment to position the consonants keep down there distasteful died away and that's a problem that we also have missed big don't but will say something about that later and these are elements in the year that we used to color code so major area were yellow and you can see it but the and areas recalled during so they have to put the correct green to yellow all this solid that 1 simple rule and they can build a concession so I went on the the designing better elements to make the better constructions and will discuss denial signed for me and I made this from pi 0 2 the the length of this about 40 50 40 to 50 centimeters and then I could make them with my milling machine and so I produce a lot of them and then I started to if those elements that they don't like the way data correct very easily uh so can be built domes in half hour a big domes and well and also the patterns are very clearly to to be seen and this was my 1st an experiment to those new elements and so also here you you can follow 1 after the and that's I showed before but also tried to find new patterns it because you built it so quick you can experiment in a for the so the list accounts that have to go and you can make all kinds of of patterns and you can use the system often the and in this case that did this you lose their thoughts bottom bottom cells like and he started an article so he started optical and nodded it had to find out how to go on and as well as they came to the conclusion that he tentacles and actuals and as long as you can go over to only and the practical's but this is what they found themselves and it's also nice to to take the complete don't together and tilted and so you have room you you can go on and the concessions very stable and well brought a few elements what so you just label is on top of the taller and so that they can't move so this person all the so this is not a reversible editing and can't uh in Belgium but simple costs and I was invited by the accountable compared to the words of a fish students of art structure and they experimented with the system the he she did in different kinds of elements and will uh this this was the most popular the the pattern that bitch Texaco's but also here exposed in actual in the middle so that is already a combination of 2 different patterns and then In this vicious if they had current loop uh well we talked about the possibility of a not only having parts of the sphere as for your dorm but also try to make the hyperbolic services so double services them well after the discussion and well I've tried to find the to to solve this uh with the same simple elements as well as we use here the and so this is the
the the element that can had killed them and will have to some experiments I came off if no and maybe you don't see the difference
but uh if you put it next you see
that there dishonest negative and 1 has positive curvature so now you
can use the negative curvature elements at the moment as the concession becomes steeper and then you solve the problem and you can built in on the way you you can order serious so you can also build on it you can make the consolation bigger and you got very wavy surface now so positive and negative curvature in the same structure well it's found if you have a lot of elements and well this was a project if you didn't portal and again if connections to the together with some from Portugal the thank you started to to build on uh well the the surface but also that does matter you can just start building in the dorm and the cross-sectional fall what you are doing you already she here the positive and negative curvature uh it's it's very nice and when you build it in a group and there's no 1 will taste these uh and the moment someone decides well we need you connective curves to here and then well the the completed shape after building is quite natural
consumers but fewer patients but it just flows from the old and this is and the the end of the analysis of on so called false false fuel to building uh he's seen that I used to different patterns so the hexagons and the squares over here and you can combine several patterns that in a very good way uh reality losing system and this is the inside of concession so national here the we did a few more apt vs and if those elements this again and again to lift students far structure and so we experiment this several patterns and social shapes of of the dome so this is not a pattern and you can see the top few of fast domes so so acquired natural way of of building don't the well this is Mrs. very suitable up to use the children and so the last 2 approaches are with children's uh accrual build this themselves and myself of doing this of small children said they build something that's bigger than themselves so they can stand in that and to spot file picture and now I will give it over to the West more experiences and thank
Phil
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the book the ieee balloon the bulk of all my work out these that these exceed uh many decimal we have step
that exceed the neonatal each the the the United Woody the classical at the Science Museum we find do that a lot of these concepts who are not the dimension we found on the Internet there are all of
these features and the the the triangles the problem with the 3 most would but er would even want to be they copy and we er 0 no uh went to make uh we have developed a my all events here the all we store the the the concept the the we
thought these quantities the reciprocal thing union of the rocket to prove war he said well no but in the architect pool all war people use the the the the set in the sign for each piece the of the bones that you not alone used the same the size of the the we make these
these these of for the the the the of the estimate of the friends of materials last week of World War and the food and profiles the variance of patterns we what we use these uh 11 the that you have seen that you'll the the work this in the and you'll website in the House candidate of the tenants but that was OK these things on the other the the simple but don't with some kind all symmetry the these Eastern in active the week angle all using the the no but what have on uh that on the crucial point is the the lower back on the notches not the online reason in model in the same way this is change the they they got the and labeled and change the good to we the designed for a uh make the of our weak bond with when the uh in 11 inside on the sees the the prices on I and all the question use their them
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but the the friends in in the the size of but we have eyes obviously Europe uh you events you and Europe water I no we decide to the water where the Florida make because uh these the sign would would put in in alright the website the the sense of the yet the or website will also we offer a pool of everybody especially schools these of the sign for made these the activity OK but we recognize the a you will but now we the no all better you on uh might be signed my of hobbies the tool uh I mean Africanized better these uh these war the the the the the
set when the that long properties uh the uh them that you know music out and he's the 1 that piece uh that piece can Baikal or sweep away I the it is possible to people and in of a lot like a eats the for marker like that of a
house with them from collapse with the uh the constant Sudanese fast everybody 1 than we can be the every loop cylinder under the patterns the the the moment dialog annotation forest pacifique Pascal as factor In the financial case we want we use
all NH mn wizard rules police size years old but the the the long the global these 1 3rd the the owning a series of the building within plants inside the long the sub but I can the spectacle lot of ending a we cast always right rule south are quite it's a
moment we people's tool reflection and questions right
at the State Fair that almost i an objection point finally some people all for all areas all Adafruit price hold we use a simple patterns and without so fast in ink elements or
lactose stopped at ease with the with the that we see uh Schacht through social need what we these aspects no In
conclusion Leonov along the 78th wrestles Tobosan mass said body at it unmalted boat on by I believe I have of that
working together with every move we move multiple the the immediacy and also the set the reading and will have find uh I knew that was you know possibilities uh we invite you all a built 1 moral uh diamonds and in this space that the team of the confidence trusted thank you very much the we thank thank thank you very much for your promising presentation and the hope you'll find enough hopeless and other questions yeah you can walk hair the you have hello and thank you so it at some point in the oven and immersive presentation there were children's who started with an octagon and event to be found they have to develop the bottom in a certain way from that do they know what a what the mathematical reason so the pattern to do further on is last the 1st question my 2nd question is what I do people examined which so of patterns are more robust than others are stronger than others and why and what reason is of these examined by the people the dome or is that discussed afterward after the activity on and just to 1st question Monday they solves the problem when it started sort of on a day-to-day make you really don't talk to in middle and they do not know um do matter medical background but and that it may also be the 1st solution then so maybe there's no solution itself but they become now interested in those kind of problems and I think that that's the important thing you have to have some of this book is about the 1 that is yeah well under this did they start setting up the article that that's a 1st step and then uh you you've got a few points on the states as well so for earlier uh don't pattern it is important that
every knowledge is used so let's start here that I have to at once a year and that can be in this election or distillation it so in that does Jezebel bottle you have and that
then you have to to to solve it in such a way that every notch accused verb as in my own the the in and any other questions on the 4 all the patterns that I made a I've also calculated to deduce density so and debt and the number of states per square units so to say so as you can see that if you have concepts of the states and uh you take this pattern and that all will be that big or that big but that I'm not that interesting forces that are most filter so when I better get a West Texan it's their problem to calculates they're just essential source constructions construction the talk and something to that of the so the
thing is I'm I work at the marker museum with with and became 1 of the people walking through the workshops and know precisely what you said the 2nd question do they realize that there's difference in size and density would made as was saying they precisely do because the built not 1 don't they build 3 maybe 4 because they can be used to 1 dome in 10 minutes are record is 3 minutes with 30 students and 300 sticks the that's pretty much what you need to add 10 so the work that you do the math and the up mathematical work is something that he do after the experiment not previously experiments that have and that can be done either at that immediately or it can be done at school usually it is done at school cause this activity can be it can be just translated to the planet signings but it can also be translated to why don't planner sightings work with with a occurs structure so obviously it's quite obvious that
so go up talking about 310 cells and speaks how do you organize a mass production and how expensive is then what we have now here's itself on the station that I made them all myself so thank you the of the the my casting my uh the the plugin the subproblems in tests enormous rule the results of animal matter is uh ways to leave because the would it we call the the expand these and and that we need more copies and uh you know the the school that they adding difficult is these I studied because
the César tool where would also be aware of for each mystique and and multiplying EC ESA these difficult to and what what's happening if you remove that peace in the middle the don't hold down like this this is this is very interesting question and and the so and even when 1 of the breaks it'll collapse locally but not globally and so that's a very nice property of this we we had a vector the 2 big dogs of the 2 beams of forming to land a lot of
beams all right in the middle and broke and then you think well listen social collapse but no it's just a local work a problem and you can solve it locally the the hi and what in regard to that production costs I think I have I could share our experience data and the fact base we also produced some of whom elements of lease re-nest contour that drawing in type 1 cell in our team meeting intrigues edition in Taipei we gate the ontology don't we string S and now also led that we could probably in that way we all produce 8 we stay on manufacturing they're coming to that our we could also do it in the space of contours so we can compare which might be more it on effective in other cost can't think you I'm Havilland Fontaine 1 yeah an therefore for schools and you don't have to start if 2 big ones you can also start if this false issues seen in and the pictures and that I so this is small a copy of this form and it's made by laser cutting and this may be cost 10 cents so
you can produce a lot of them and chilling can experiment and uh solve mathematical problems with these elements and will defend this of course there's too big elements but uh this is also a possibility and then I would
say because the In sensation and started the dome known building activity is invited to join the ridiculous outside and some really then I'm just float into the lunch break so were from this and we already please go for lunch and we meet make again here at half past 1 for the next session
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Metadaten

Formale Metadaten

Titel IC16: The Self-Sustaining Domes By Leonardo (Extended Talk)
Serientitel Imaginary Conference 2016
Teil 10
Anzahl der Teile 26
Autor Brasó, Enric
Roelofs, Rinus
Lizenz CC-Namensnennung 3.0 Deutschland:
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DOI 10.5446/33868
Herausgeber Imaginary gGmbH
Erscheinungsjahr 2016
Sprache Englisch

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Fachgebiet Mathematik
Abstract Hidden in a corner of the writings of Leonardo da Vinci, there are sketched two structures of self sustaining domes made from sticks without any clamping element. Rediscovered and studied by Rinus Roelofs, recently a work group from the MMACA Association has developed on this concept and designed 11 dif- ferent patterns. We are taking this activity to schools, museum workshops and street fairs. This activity is spectacular, attractive and adaptable to all ages, we can even work with groups of five year old.

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