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IC16 invited talk: Fast Prototyping of Interactive Mathematical Content  Jürgen Richter Gebert
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Erkannte Entitäten
Sprachtranskript
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because of all around in a year and
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and the and
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so and I'm very happy that on the as if the 10 additional minutes then but it it because I have no idea how to of fit everything in that time that I had and so that it will everything would be a little bit squeezed of could we switch to my computer if possible yes that's the wrong were of OK is a lot of white space I what happened at the end of the I like that as this was beginning to get a little tired of sitting by her sister on the bank of having nothing to do wanted twice she had peeped into the book there was reading but it had no pictures of conversations and what is the use of books or Ellis without pictures in conversations so yes and what is the use of a big of a book and this would of pictures and conversations and I think that's why we are here because we are providing the pictures of conversation everything that x to the text in science and so we are all somehow analysts who getting bought by only reading and trying to do something to create something and I today I want to give a talk on fast prototyping of interactive mathematical content and to about how well a 1st have to explain what I mean with that talk so let's have a look at the different words let's start with interactive flow so interactive for me is everything that really gets people involved so you have kind of X a bit and so the that's bit is not only something to look at but also
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to do something and to experience to learn to become active in when content in
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I 2 days will mainly talk about virtual content so all things that run on computers think that drawn on apps uh but many of the things I'm telling you to do they will not literally but on the kind of media also applied to physical at so I will really talk a lot about this prototyping phase here and so will I I I think it's a good idea to over half a clear knowledge of what shapes and exit great when you start to plan it and I think may also be relevant for some parts of the workshops OK the the other thing fast as fast as possible but so that things have some natural boundaries
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of the so if you want to make something really complicated complicated it needs its time its time of but at least we should it gets rid of everything that is superfluous in this building process that thing sees we in programming always call it the boilerplate code code so you're doing a program and there are some parts of the code that you have to do every time you start a new project and if you do them every time so you don't have to do them at all if you automatize that role of
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process and I'm talking a lot about not talking about boilerplate code prototyping of well by prototyping I really mean the 1st stages of the design that in the sense very often shape your project and of those z's Proof of Concept implementations which well somehow of forms facts in a way and I must admit that doing something In a final form very often it's time and making something final and accessible of
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really more more or less so always well you can put any time you want in that process but in the 1st part of the project it's very often
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pays of off to be fast so I'm mainly talking about kind of public scenario where you talking about exhibitions about x about school books so you should think of contexts like for instance this here where you have this season the German Museum is in my own methods to but this is a school class of so where people really get into interaction so unclear this sets that I am involved for some time already in imaginary and so I will have to tell you something about personal history but before that so what I'm talking about is sent in a sense the designed history on the design philosophy on the 1 hand and on the other hand I'm talking about authoring tools and Exley what I want to talk about is authoring tools which incorporate already some design philosophy so whether to list built in a way such that you by definition are fast in the 1st stage OK not not for the history because this year somehow from need is a little bit special of its Paris most pressing part of the talk of so I started my 1st project involved the public exhibitions 30 years ago and almost so well it was spring some whole 1968 I was a student at Darmstadt and and out that there was this famous symmetry exhibition and at that time we broke run something on the Atari Atari is a prehistoric computer kind of a happen of and that this was really very innovative what we did there but then I had to study for a long time doing a PhD in at a certain point I is a so in my PhD I uh develops methods for automatic proving in geometry and for that ruler I wanted to have a kind of input interface where you just can't draw your trimetric CDROMs and there's started another project which is called Cinderella also Cinderella is a kind of dynamic geometry program at least it started as that now it's a kind of very general tool for mathematics visualization and to see well this project no it's about well 24 years old already and there are some other things and let me just the white the other party of for tools and the lower part for content and so then I in 2001 but I got this chair in Munich and today I opened a smaller mass exhibition of the AEC's Scott can't so except crops of it's really more less literally describing the exhibition because it is a room was 9 times 9 meters and if you read this by EECS here as a roman number so it's 9 times 9 and so goes to the out we had the 1st appearance of imaginary so there is this is a place where people really into and well at some point Macherey imaginary came over into it and not to be town which is an internet portal I liberated for instance was Dodger and at some point I started as a project you will hear about 4 and I started to write apps which are somehow related to that point of view you see some loose connections about symmetry drawing and just recently we started a new project which is now really a crucial part of what we're doing a which is kind of follow up flora Cinderella of hot I will explain what's going on there that's called JSJ S stands for JavaScript's because well Cinderella was written in Java or is written in Java and most of you will know job indirect simply diet and at some point so went think about alternatives so talking about fast prototyping I want to focus on will a tiny part of this time scales approximately here of so that's the time between 26 November of 20 15 and 17 Kappa of 20 and and this is already laughing ahead of because it the if you ever came to gather with some players you have to be prepared for fast prototype there is no other way of because things like that happens he gives you a called uh November 20 says all well there might be this cool exhibition in Heidelberg and we will do something really in normative there I don't know whether this will really actually happened over but it and it's very likely it's very likely and 0 so what you contribute to just weight of a Cleveland and you just wait on generous 6 so you get an email from him OK let's go for it I got the money and then you ask OK I had 1 somehow spring or summer so no no it's February and so actually this is under US this young me so it's really could project between 2 so big discounters supermarkets in in a shopping mall and below that actually of this last 17 that's 4 AM in the morning go reverse still sitting there and already at 3 PM in the afternoon people very actively using that and this is an extra but that really run 724 so this is really designed for very stable use so all well long period of and continuous so what I want to do today and I hope I haven't used up too much of my time in the world of I want to give you 5 softer the most of 5 the most of different projects that are more or less inter connected to and have their interrelations and from each of these most I want to draw out some lessons to be learned so I already told you that I work a lot with this Cinderella so that's our own tool and the 1st of all I have to introduce you to Cinderella so the 1st mobile about will be about Cinderella and the lessons to be learned is well 1st of all I want to introduce the tools and the 2nd lesson is what I just said to avoid boilerplate code so far yeah so what is Cinderella about so Cinderella is so broken for doing dynamic geometry and this here is some screenshots over Cinderella just the sum of region metric parts but in the meantime Cinderella act rule with 2
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years so there was a time where people ask for more and more functionality and at some point 3 really decided to seriously in lots approach the scope of the program the Cinderella as a joint project of the analyst copy company who is a professor at so university of what some and so so the current architecture of Cinderella looks approximately as follows well there it's like a kind of flow so it will be very very old part of the cortex of there you have the geometry part but on top of that you have the scripting language Mrs. which is very high level and versatile and you also have a physics simulation engine and putting these 3 things together with very thin interfaces between each other of you can do very interesting things and so so the main philosophy behind Cinderella is it should sh not to be a specialized tool it should be as generic as possible within its scope so you cannot cook coffee with the flow and you cannot directly so well create we chose from it at a kid actually there was some time what we had to version which was not seen relevant but we could create use but that broke processes at some time was no longer of followed up but it should test no artifacts so if you don't program and this broken should model mathematics then no well this program has some inner logic and logic in behind Cinderella we try to have it as close to mathematics as possible and actually this is really complicated tho the that part really serious mathematics is involved it should be modular you already saw that in the global design and I would say it should even be atom so there should be very very small units that work together in a good way of it as a collection of legal pricks in and it should be easy to use of but at the same time it could not be oversimplified so think of Einstein who sets of things should be as simple as possible but not simpler uh so if you want to cover a certain range of flow problems you must essentially also have the so let me start with today more and so this will be a challenge with this microphone here uh but will make that somehow so perhaps at some point I have to so which to some of the mode of talking about OK this Cinderella and I don't want to talk a lot about the geometry part I want the right away that we talk about things where different parts come together but I still want to show you at least a tiny example of what you'd do could do just with geometry so what you see here is a circle with the center and here's another circle was a certain center and a fixed radius that take the search 1 was so points that is related to the boundary here and then let's just at a few line segments so this is a quite simple construction of so the good thing hyperbole at the moment so they did you recognize what I just constructed II make segments of length this are dependent on the radio I of circle so if I don't change the radio I the length is small and change and if I start to move that but it behaves like a little mechanism here and so so this is not physics this is just mechanism both just geometry and for instance you could ask well if I take this middle point here what is the trace of the middle point and to see well this is the trace and this trace can have in effect very interesting shapes so if I move Aransas things you see have everything can happen here so not everything about its scope of so let's make this a little bit bigger so you you see this has really interesting stage and if you don't believe that this is the right thing you could say well these animate that for me and to see that this is really the right curve the reason I'm showing that example at the very very beginning is if you want to do that to right you really have to dive into mathematics and i if what Cinderella in the background stars it's it makes complex the tourists so it in that in that everything in the complex entered ambient space it resolve singularities by making complex detours and I could give so 1 term lecture about what what you see happening in that picture I will give that L but it would be fun but I want to do something very different and jump to the other end and so show you what you can do if you can if you combine through seeks scripting and a little bit of geometries of geometry will be almost in was a bull in this example so let's 1st drop walks so this here is the box and in that box let's put some oops I have a little problem I don't have problems just of a considerations so these are masses so if you have a mass it may moles so if I press this button see nothing happens because there are no forces involved but you could for instance pick 1 of those points and say OK go ahead and the world is 1 point will have a life so so far not very interesting but you could say well let's take all these masters and let's charge them so select all these things and say well each of them should have a charge and let's assume that charges really cost forces and if you then press a button or something like that so the parts repel each other and you see a little smaller particles now I want to show you the how way very very simple and basic ideas you can go from there to a little swarm simulation aware where this particle become models for fish essentially that of follow up in a swarm so you see so far we did almost nothing no boilerplate tool of create that so let's open the
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script editor and now I have the problem that I will type was 1 hand but and make it that should be doable so like that but I I think that stitch is also physics simulation and good OK the the so let's do something with that and so the scripting language single as something like mathematical are not only doing number G so take mathematical stroll is and that it was a lot of you know the symbolic part and just do the number crunching part of it and then you are closed source that the language so there is for instance the statement that is called on massive seeds murmur but that's exactly the so this is called on masses which simply gives you a list of all involved masses here and that's called variable masses the all masses and 1st of all let's find out how many of them are there that the in years the length of these layers and as the 1st thing that they calculate the average precision of our model is so what would be be the error position so you sum up over all masses and that's college moss and and use some off the X and Y position and you have reached by the Working by and and you strong this thing is called made Prof made it so I added a little script novel and if I start that is the main point here and the green point is directly coupled to the animation going west side is the kind of interest in mathematics that discrete point moves significantly slower than all the other points of individual so let's continue and say well if this is the wall so what is the basic idea of on this would we will I see some vision I want to be where they are so let's just correct so how do I get there and Pereira my losses you direction of the others and so on so I would say well performances here this way ieee goes through all masses and are for each of these are correct the velocities are connected with lots of the was thought to be of and I want to say whether it is my old velocity fast I want to get a little bit the components of well when I want to go I want to go to meetings so I mean the difference the work of where I and to make it and I want to get this to my house and if I do that you see that while the online costings heat up the way so we have 2 of these tenants when that fast so let's restrict the velocity by saying well let's take em they think that we lost the and say is the old velocity of velocity divided by the absolute value of the velocity so now we have no a loss at the hands that make in a little bit so that yeah and so obviously playing with the parameters is an interesting thing and you could perhaps put that on a slider and we have close to getting its here I don't know but we recognize it would just reading an accident within 5 minutes on the floor of so these are not fish these are mosquitoes more or less here and mosquitoes don't sense speed of their neighbors so let's sensors as well so let's say we don't only have so many point we also have to make velocity and we get the correct answers the indirection well let's when like the others this political this was the so and was this correction see then they move coherently into 1 direction and let's make it just a little bit more of optically interesting and say well each of them should leave a trace and personal too long yeah and the creation of them out it the middle and perhaps we don't want to have labels on it and the grid quite realistic swarm simulation just by doing almost nothing so we essentially head of the line and online who were I'm just you can teach that people you can really explain how other people are or how to do these things up and so on so we actually do that out 1 important thing so you could also say please export that tool and HTML page and then we got an HTML page with the 2nd this 1 you know of no this is running on HTML page and you can put it on the web somewhere and so so let me come back to the talk of and it's so this was essentially part also over workshop that 3 dates about complex behavior from simpler rules of where we talked about 2 things namely crystal formation on the 1 hand and swarm folic formation on the other hand and we taught teachers how to do that and these were the teachers sitting in our workshop and I really was amazed they got the front as though they got into a level where they could do these things completely on their own within I would say for 3 hours from scratch none of them experience in programming and these features then went to their classes
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and of so I had contact was 1 of them is is that we had to spend in our class who we wanted to find out what is better a little role that's cuts the cross are ahead of sheep and so they simulated on the 1 hand a robust and on the other hand the head of sheep and
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found out that the head of sheep was much more effective that if it's doesn't forget part of the cross so if it gets disconnected from 1 part of the cross it won't get there uh back again except for accident but you could also I should show them to you with a 2nd to show you 1 thing you could also do these things more realistic so I have 2 or more Web this is some horror showcase side
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and on that showcase side in this little bit slow here so you will have for instance this here so this year is not really the
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playground of we really can't say I want them not to care about position and not to care about direction I want to let them to care only about position or only about direction I want them for instance to see only 1 neighbor which is interesting which has to do something with small apartments see just 2 so that's take away the direction so you see little molecules are forming here that you can only you can really learn a lot from just the simple things it's also interesting to find each other in the serpent chases them uh that's so of the well known party game among teenagers so this EP you can go further OK I have to speed up a little other was ever go over time of so what we're trying to do with the Cinderella project we want to try to give very nature of high level of operations of that award to everything that so should have been done always over and over again and so far so here's little list of the scope of what we're doing so i don't go into everything that I just want to mention 1 part here so currently we are working on an interface that allows our scripting language to run directly on the GPU which gives a highlevel exorcists who will paralyze graphics power which is fascinating OK the more tool I talked about the German Museum and the lesson to be learned is now something about interface design and the main lesson is if you create an bit try to focus on 1 phenomena don't put everything into 1 thing and so on so this is about a museum in Munich and they have so little part in the museum where they show mathematics and together with unveils and another group of persons we created this well in the active part where will you use the server using J. reality and uses Cinderella and I want to stop a little bit about the Cinderella part so what we did there is we provided great so well single phenomenon that that we wanted to show and so each of them really focuses on 1 effect but you have a rod of rather big range of different effects that you can see here so the typical Design Cycle of such a single part in that great looks as follows you have a prototyping phase that should be rather short where you fix I want to show
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that and the basic functionalities that and then you start to polish
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and so I think there's no way uh of fomenting that face but uh this party is really the crucial 1 of so I would say as basic guidelines sink as simple as possible and think about what you really want to shoal focus on 1 effect and try to minimize the user interface and this things can
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really also literally be taken to physical experts not only to
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programming things and here are a few screenshots from our things from the bottom is the only so you see for instance something about moving mirrors and about kaleidoscopes and evolves are can be consolidates author Pinsky that through the draft or order of broken was which you could draw ornaments and I just want to so I didn't know what I would do that or not and I will do it but
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so here is part of the crates just that you get the impression so here you have for
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instance some spirals and and more secure gotten so there of or to another 1 of the this 1 here you have platonic solids and you can see how the so octahedron fit into week you'll how does and I could see transferred into an octahedron it's amazing if you the whites of the segments in the golden ratio in the octahedron you get like from and you can play with that and I think you get the idea and so having this in the shape form an action I have to admit shaping took
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some time here the the fish are still running of shaping took some time here was a complicated process but the prototype phase for each of these things was Ross simple and so right after the opening of the columns of of this exhibition I did something which is almost nothing but which was perhaps 1 of the most important things I did over the last 10 years of I took screenshots of what we had there and put them on my I think we are now 2011 iPads just appeared on the market and so I set together with so an editor from my own online company of providing interactive for content national attached to him and he immediately went into that images and wanted to do something and nothing happened because of this was just a screenshot and respond to have that on the and the
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betting at that time was of we didn't have any environment that would make it possible to put these things on the iPad so you said I will hire programmers would do that and I said this impossible then all of a a many to lower lot of mathematics to let pride
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and so at the end we decided not to do anything but another challenge some knowledge started I wanted to do at least 1 of those things really go and this is where some of the project started this up ornament drawing at i ornament which is somehow related to this very very 1st activity in 1986 and so well talking about I ornament lesson to be learned you really want to make it simple you really want to make it fun and this is terribly hot so actually in in that situation at the prototyping phase what's actually tiny compared to all the rest but the this tiny part here was only due to my experience knowledge to the working environment is it so I had to learn all jails from scratch at that time so I I learned a lot in that phase and it took I think over 7 months or so to finish the project to print something and I want to show you at least little of that of how things look if they are polished so here we are on
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my iPad at this here is I ornament and its current version you can well it just ask you please draw here and locavore put down my finger and I draw here will it immediately draw symmetric pattern I can switch colors I consumed in with a very very high school factor so I can make really small annotations here something like that of there is even something like a cloak pattern with which by can only act collar which give such a nice going effect here of so that it's easy to create symmetric patterns with that you can switch between the difference crystallographic to can say please show me what you've done what I've done in a different group for instance in the simplest of all people to be pretty boring below so this is not the key correct this so here's a the better so you can even go below to a situation where you say please show me what I've done on the sphere and to interpret that in a different way so really there's also mass education pardon that so that really when the lot of the signed into that at and so on FIL in OK we get so
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I speed up a little the news comes a little in terms of I spoke about the job crisis and the job crisis essentially is well below the origin of what we call Cindy BJS look to the to s is the JavaScript version of what Cinderella can do and the lessons to be learned is summed up sometimes you surprise yourself this happened in that case tell you why of so what's happened here is so we had Cinderella cause the authoring tool and now we have this in the JISC based on JavaScript that the content of your between that that was his job at prices were at some point we really recognize we have to redo everything stay alive and the point wise this surprised ourselves because now now we are about the 2014 and I told you that we didn't have a way to
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put our examples on the iPad actually with this view or you can just run JavaScript on the iPad you could test what we had In the bottom seen before we could just have it on the iPad and say well here we have 1 part of the credit for instance some kind of double pendulum and this now runs perfectly here on my iPad and we had to do nothing for it because simply the environments fitted together and we were so proud about so I will make that was in the fight against 3 minutes of
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so becomes the next the mall which about it's about suggests and music and the only reason I want to show it to you it's there's no less and it's just found the so so right for that group shall I started to release so wife
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of reanimate the sound interface of Cinderella and I just want to show you just 1 game more to see what is possible in principle so here you know the the the the of the of the
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and and and and and and and and and and and and the and and and and the and and a lot of this is a step in the right and and and and and and and and and the really realism and put them in a and the demands of the of the
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almost done 1 last the mall of taking them together take I ornament take Cinderella takes a new tree as few words and to create something new as Sunblest that connect everything in 1 project we're just working on is the following of so with in our page I have this page here where tends you please drag and drop on ornaments tool that so you imagine you created the tile was our ornament and then you make a dragon drop here and then you get this here of and you can switch to something else and if you really want to build it here's how the cut out your paper and so you can take i ornament created tile export it and use it as a well who planned for creating interesting things this also the possibility to create collider cycles so let's take
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another 1 let's take some I love my fish where my fish the talking on of let's take these fish this appears where desire to the collection of fish of so you can move that here and you get something like that and if you want to build it you hear what you have to cut out and we're now giving with that of this summer brings together all different projects and we are about to start with this in next week so we already had a little workshop on next week will have really is a serious was 1st serious workshop was a workflow full and this brings together some all everything I in in the last 3 years in a strange way and I sing I have to send for you attention be fit and
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maintained that we can have some questions you have a few minutes left and is that development we have a 2nd microphone was a summer running around to it and then you can get it from the which there
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was a question and the microphone as well you can also shout that's although OK test now all of 2 of the success factor and 1st of all thank you for fantastic presentation that was released by link at my question is about this indigenous against the new version and those that do Diena's system inside this of willful um meeting data kind photosynthesis medial Open Sound control those so for the music part of that 2 parts of the for the
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music 1 is directly so actually the music part is very very young it's just 2 and a half weeks I started it uh so everything is still some floating around so this 1 component talking directly to lose those sound so energy in a way you can uh prowhite Busines sine functions and doing interesting things with that talking about really the physics of sound and the other is so just riding a MIDI sequencer essentially it doesn't of this so it it uses this JavaScript sound font of formant where you have to the pieces of M P 3 which correspond to each node and they are a schedule in the right time and actually it's it's really hot because sound is way more critical than optical and it's really a health programming but we doing we try to do as good as we thank you there were at least 2 or more questions some was there you of the the the yes it is a complete brain limitations all so if you
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look at the anatomy for say so we had the is of wait a 2nd it's so this well fish that we created and if you look at the the source code of this page it looks as following a as follows here OK forget about that he you know load our library here we literally have such scripts that I rolled so this is our library makes their browser understand our language which is a very very powerful thing because you can still edit in the HTML text but then it creates a geometry and actually I'll edit many points at some point here are the points of and I said each of them should be a minus so use each of them are masses and some of the segments were bounces and that's it so it is also part of it part as a geometry part is jason formant that describes the geometry so you have the part of it which is chasing description of the the geometry of physics and sing a script that can communicate with the not and what yes the and and yes so actually I am currently you be using those Cinderella all the engine only very seldomly I coat the idiot you know so much more sense of that I had to make mention 1 more thing 1 just 1 just 1 of so the wait a 2nd I just have to find it because I by the this and other but the chapter of yeah thank so the
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all about putting everything of grounds so the using that as a form by Ireland so the by another part of the you do that combinations the graph and this is 1 of the history of the around you know that that was the year it was is here is really at the very end it all the using of the people that is all but 1 of the log of the sum of it so a few thank you we is areas burden names in there uh yes so you come at at the the very very very 1st plan for the very very 1st version of this thing was done in 1990 in Sweden when I was Henry crepe or was it was a professor in Paris was on the boat named Cinderella prevalence and and so this name simply got stuck to the project and I love it so of it so that the reason but you could other
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states of computer interactive drawing Environnement really elegant but it was not the reason a 1 last question FIL of method I think it was thank and because much for the wonderful presentation and Saracens to be origin that not to have a major problem but to medical problem you could tell me alone did try to think about the this problem I mean as a speed about mechanism at the part is speech in talk about mechanisms you put some books and on circles haven't got isn't so and that couldn't be sort of a 1st if you go if you have the given and subtrees some of curve as possible to construct a mechanism that be close not to be the exact OK uh difficult and deep mathematical question . 1 and F a plastic about the the removal of all edges and ascension of so so 1st of all uh this answering this question some all really in was the mathematics and this is the we on purpose don't have primitives for these kind of questions because this would not be this generic approach that you should so only prowhite the most fundamental things that you really use over and over in our framework of that dutiful papers on it uh there is uh very amazing paper that so translates this project go problem into something of algebra and it really creates a literally of moving mechanism that even can move append with a tilde and everything but I make examples of that was Cinderella of of solving the problem itself is not part of center OK
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Inhalt <Mathematik>
Gerichteter Graph
Wärmeübergang
Mathematisierung
Ausgleichsrechnung
Mathematisierung
Imaginäre Zahl
Inhalt <Mathematik>
Massestrom
RaumZeit
Computeranimation
02:08
Randwert
Inhalt <Mathematik>
Mereologie
Inhalt <Mathematik>
Phasenumwandlung
03:07
Inhalt <Mathematik>
Prozess <Physik>
Beweistheorie
Mereologie
Gebäude <Mathematik>
Phasenumwandlung
Bilinearform
Optimierung
04:18
Quelle <Physik>
Axonometrie
Punkt
Prozess <Physik>
Gewichtete Summe
Mathematisierung
Kondition <Mathematik>
Klasse <Mathematik>
Besprechung/Interview
tTest
Zahlenbereich
Imaginäre Zahl
KappaKoeffizient
Symmetrie
Äußere Algebra eines Moduls
Inhalt <Mathematik>
Optimierung
Einfach zusammenhängender Raum
Zentrische Streckung
Linienelement
Mathematisierung
Ruhmasse
Schlussregel
Imaginäre Zahl
Inhalt <Mathematik>
Beweistheorie
Mereologie
Phasenumwandlung
Projektive Ebene
Reelle Zahl
Beweistheorie
Geometrie
Symmetrie
11:38
Länge
Einfügungsdämpfung
Punkt
Prozess <Physik>
Momentenproblem
Massestrom
Komplex <Algebra>
Gerichteter Graph
RaumZeit
Übergang
Richtung
Wechselsprung
Einheit <Mathematik>
Dämpfung
Tropfen
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Parametersystem
Güte der Anpassung
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Randwert
Betrag <Mathematik>
Forcing
Verbandstheorie
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MechanismusDesignTheorie
Geometrie
Geschwindigkeit
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Ortsoperator
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Klasse <Mathematik>
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Mathematische Logik
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Optimierung
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Innerer Punkt
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26:00
Mereologie
Klasse <Mathematik>
Besprechung/Interview
26:52
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Subtraktion
Ortsoperator
Natürliche Zahl
Mathematisierung
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Richtung
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Numerisches Modell
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Fokalpunkt
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Mathematiker
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Projektive Ebene
29:56
Lineares Funktional
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Phasenumwandlung
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Ordnung <Mathematik>
Fokalpunkt
31:01
Gruppenoperation
Mereologie
Ausgleichsrechnung
Platonischer Körper
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31:49
Thermodynamisches System
Prozess <Physik>
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33:07
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Thermodynamisches System
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35:47
Thermodynamisches System
Prozess <Physik>
Punkt
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Vorlesung/Konferenz
Inhalt <Mathematik>
Term
37:27
Spieltheorie
Gruppe <Mathematik>
Gruppenkeim
38:09
Parkettierung
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39:45
Projektive Ebene
41:06
Sinusfunktion
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Verschlingung
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43:05
Deskriptive Statistik
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Punkt
Graph
Flächeninhalt
Last
Mereologie
Physikalismus
Ruhmasse
Projektive Ebene
Kombinator
Bilinearform
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46:48
Stammfunktion
Kreisfläche
Sortierte Logik
Mathematisierung
Mereologie
Besprechung/Interview
Projektive Ebene
Kombinatorische Gruppentheorie
MechanismusDesignTheorie
Aggregatzustand
Metadaten
Formale Metadaten
Titel  IC16 invited talk: Fast Prototyping of Interactive Mathematical Content  Jürgen Richter Gebert 
Serientitel  Imaginary Conference 2016 
Teil  2 
Anzahl der Teile  26 
Autor 
RichterGebert, Jürgen

Lizenz 
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DOI  10.5446/33845 
Herausgeber  Imaginary gGmbH 
Erscheinungsjahr  2016 
Sprache  Englisch 
Inhaltliche Metadaten
Fachgebiet  Mathematik 
Abstract  Designing interactive content for mathematics exhibitions is a challenging task. Multiple aspects ranging from educational value via mathematical correctness to performance issues and user interface design have to be taken into account. The talk will illustrate the complete path from an idea of an exhibit to a fully functional interactive implementation in various scenarios. Special emphasis will be laid on aspects of user interaction and on high level implementation possibilities. Scenarios will be taken from interactive exhibits in big museums, teacher training courses, interactive web pages and apps. Mathematical topics will include swarm simulation, 3D polyhedral geometry, connections of art and science, as well as hybrid scenarios where virtual and real world meet. The talk will contain many life demos in the framework Cinderella/CindyJS and (at least partially) demonstrate the full workflow of designing an interactive exhibit. 