IC16: Atractor - Visualization Of Mathematics Using 3D Televisions And Realistic Virtual Exhibits

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IC16: Atractor - Visualization Of Mathematics Using 3D Televisions And Realistic Virtual Exhibits
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In recent years, Atractor Association has been engaged both in producing mathematical stereo 3D contents and in creating realistic virtual versions of mathematical physical exhibits. In this presentation we highlight some of Atractor‘s contributions in these fields: 1) Atractor‘s contents for 3D televisions-movies, images, applets (some of them accessible from Atractor‘s site) and 2) examples of interactive realistic virtual exhibits, which can also be used in 3D televisions.
Mathematics Attractor Mathematics Presentation of a group Logic Associative property Numerical analysis Attractor
Real number Materialization (paranormal)
Cumulative distribution function Mathematics Cartesian coordinate system Grothendieck topology Attractor
Group action Sheaf (mathematics) Materialization (paranormal) Mathematician
Building Free group Multiplication sign Model theory Content (media) Conservation of energy Student's t-test Attractor Grothendieck topology Product (business) Mathematics Symmetry (physics) Gastropod shell Energy level Imaginary number Imaginary number
Logical constant Complex (psychology) Mathematics Group action Content (media) 1 (number)
Point (geometry) Computer programming Causality Surface Right angle Mereology
Group action Körper <Algebra>
Presentation of a group Multiplication sign Normal (geometry) Nominal number Condition number
Addition Category of being Distance
Cycle (graph theory) Renewal theory Theory Grothendieck topology
Natural number Multiplication sign Model theory Gastropod shell Parametrische Erregung Mereology
Prime ideal Symmetry group Symmetry (physics) State of matter Different (Kate Ryan album) Multiplication sign Projective plane Mereology Numerical analysis Freezing
Dynamical system Mathematics Symmetry (physics) Multiplication sign Oval Universe (mathematics) Projective plane Physicalism Attractor
Cue sports Point (geometry) Category of being Focus (optics) Building Envelope (mathematics) Reflection (mathematics) Lipschitz-Stetigkeit Parabola Maß <Mathematik>
Building Oval Moving average
Area Functional (mathematics) Mathematics Surface Surface of revolution Distance Mereology Cartesian coordinate system
Group action Oval Multiplication sign Game theory Numerical analysis
Arithmetic mean Content (media) Game theory Numerical analysis
Mathematics Imaginary number
thank you all in an hour and a half year and the well I work in that sector associations which is the number of nodes Portuguese associations devoted to the promotion of mathematics and I'm just going to start with a very small presentation of attractor so in the beginning our main goal was to build a science center that devoted to mathematics we that's goal we built a logic ibution it had more than 660
exegetes them and it was quite successful it was visited bought by more than 2 million of people it was low for the 10 years in the biggest science center in
Portugal which is of younger consonantal are Pavilion of knowledge these are some of the exhibits that we had there this is a real size and room the left person is not small but told his the tallest of of all the the man as you can see in this next picture kind so this is a bit of our exhibits and this is another 1 the for several reasons that the science center that we wanted to build in Portugal didn't materialize and so attracted to the stocks started focusing on the production of
the view to all mathematical continents and 1 of them is attractors biggest achievements its own site it contains more than 2 thousands of web pages devoted to mathematics all of the web pages or not all but most of the web pages are
illustrated by pictures and by interactive applications like cdf or applets or Flash movies until now attractive sites have a drawback it was written in Portuguese so
of course that that that the persons that would reach would be a small group comparatively to that to the world but the good news is that too we recently were able to get there there's some Portuguese mathematicians while translating our website into
English so we hope to provide all our all our work the materials also in well I'll just want to make 2 very small remarks the 1st 1 is this section of the website is already translated 1 of them is Jack lot which is in my
opinion a very good software for practicing and for the exploring symmetry you can make a symmetry in images at Sumatran black patterns roles Iet's and but then you
can also classify them and the and in can make if you want competitions the betweenness student sorrow pop persons in general of and become download for free from what's our website the this is another the freeware that can download from our website sites if you are interested in the teachings food children or if you have children yourself this is a nice the software that you can download for teaching the mathematics at an elementary level you have the ball for Windows and Mac but also for Koblitz of this is that uh web page of our society about genetical models of shells and this is our YouTube channel we have more than 15 math lapse in our YouTube channel 3 of them is submitted to the imaginary at the festival and the love you can use its and the and you as our your feedback well related to our YouTube channel is 1 of the main topics of my talk which is the construction of the production of mathematical stew real 3 D contents attractor has spent some efforts and time for some years in building
the contents mathematical constants for 3 D televisions complex and the 3 D televisions that I'm talking about are the common ones so maybe some of you have
already dead those uh 3 D televisions at home it's not be work like the cinemas with the passive glasses but unfortunately it is not possible to show you here because it was not possible to have the appear at 3 D television so I hope you believe me when I say that the effect is completely different from the when you see here because you'll see into the archive the this is an example of this
is not to build by attracted was built by imaginary 0 using social program of an image that's completely different if you see in the 3 D
television for it but when you look at it to heaven and then the idea about the surface so here this at this point is in the front and you can see that this part is being so you have an idea of the surface but only looking at 3 D television you have the sense of depth and so you can see how this surface is in spite of I and this is a very striking when it to see for if the the the image in a 3 2 of the 3 D television and if you have access for a 3 D television you can do those in the from our website right cause it's there the now I'm going to show a movie that it's in our YouTube channel not
opening I have to which of a now
effect so you can see this field in our my selection but
an unseen my screen the and see the in
which yeah that's the I'm sorry appendices clinical isn't I
think this effect and see the norm of the words in the you all have no real use so 1 of the ways that it works so this morning it was tested this morning on the whole what's happening on collective conditions of vision which in the time and I would like to show
you some of the world's and even that sometimes In the matter of presentation from the end of the island to the of the presentation of each of the and and show can you hear us was in of my nominal that this is a presentation of problems when I opened the movies some of it is useful and that's not what happens to the planet that close these are minimized what if you think you have to use and how can I solve the problem that solutions because no answers the problem is that and there is you
have to put it into things and all of its resources and the not I'm sorry for this trouble you this a lot of room this the of course on the start of medical resulted in 1 screen knowledge of the and 1 of as you know I mean memory of we is same of the and from the head of the properties in to the no just In addition to the case some kind of see
the but in the summertime this this all right now we can see no such and sorry for this travel distance didn't happened this morning the kind all starts now the moving this the
OK so what we have here I don't know if ever seen as a politically the scope of the killed it's formed by 3 nearest applied and of the the this is cut so that it forms a cubic that said DCU a kind to the 3 nearest renewals are here here's 1 here's the 2nd thing is that the now what is happening is that we are going to add a 4th OK and you are going to see what we would see inside of the Kaleidoscope and this is uh the uh situations where a virtual reality is very good because what would happen if you close the kaleidoscope you won't see anything because it's closed right so you can see the light by using virtual reality and this is what we are going to do some of them vertices work out so that the produced theorists and 1 produces available pyramids and kind now again I hope you believe me it's totally different when it's in a 3 D televisions much more realistic and the most striking of course claim this 1 it can seen our YouTube channel and some of our ends at 3 380 can't it's a consignor cycles the their so now it's closing the 4th nearer so imagine there's a camera sites and now imagine you can travel in size by this is going to what's going to happen it's going to starts to apply like you could travel inside this OK so this is 1 of the films that you have both for you to open but also for
the 3 D televisions I'm going to show you another 1 hopefully
Her playful and press showing so I want to be able to show this but this is
about what semantic models of shells on and help when we check this part shall that exist in nature and how we can change from 1 shall to the other just changing parametres in this uniform apply but I don't have time Chol them also
other possible next time which I hope it opens no and no and no and and
closed states this as a pet so this is this images exist in a
number of immigrant and spine and this is 1 of the 7 types of the symmetry patterns that you we have now we are building a stamp for this pattern every 1 of these 17 the symmetry groups is a such a ciated with the stamp on Prime and this is the good stand for stamping this pattern which is a mug is meant so imagine that this Bebis spent has ink in it and now it starts going to the role and it's going to stamp out this and member pattern of time now again to help you believe me it's completely different to see this in a 3 D television so you have to imagine that it has ink in it well of knowledge that his all his stamp it's on stamping a freeze on it has to pass to the other kind of like and what this is about the interesting part in the but it is also interesting to see in a 3 D television dispersing and then they took continuous so on ended stamp all the pattern kind the well and we have stands for all the 17 part the patterns for the 7 for and for the 2 Platt different types of rows it's the OK so another project that I would like to mention here
while this is related to a DVD that 1 should 2009 called symmetry the dynamical white the last animation by where the oldest stamps are the presented now
another positive I would like to mention is and the attractor is spend a lot of time and effort in this project is the construction of verb mutual versions of physical exhibits these exhibits that you see here they exist they belong to what might have even by which have spoke in the beginning but attractor is building views tall realistic version of this of course it's very nice to have a physical exhibits but mutual eggs of its but it have some advantages 1st of all at 1st of all is the fact that you can provide schools museums the universities mathematical bits that otherwise they wouldn't be able to have it and it can provide it in a cheap way and the anatomy the In effortless white guy and that when they are tyrants it's they only have to change the file also it can make experience that would be very difficult to Mike if you have a physical exhibit
this is an example we have this exited in particle important and what ended its season you know that's what you and there are these are examples of this during then of conical billiards
surprise so this is an example the public builder that we have now dadvantage it's that you can construct your own conic billiards and you can flatter than Eliot's you can change to upper at a parabola and I parallel and when I had been you construct your own units it's of but then again on sort of like you can the making spirits that would be very difficult if you will wouldn't will use if you were using as physical at X that's not what happens in this building that is that if you point to a focus the ball will enter the other focus OK this is the properties of the reflection in the and their lips OK now interesting particle make experience and let's see what happens if you take off the whole and if you point not still does that verse the focus but a point outside this statement applies might come going to do this no it see what happens if a guy so after a while you I don't see a lot of segments and after a while they began to notice that these statements are envelope be another LHC and I know if you are going to I was starting to see their lips here apply it has the exactly same focus of high but it's is another 1 and this is something that you can experience with a vigil exhibit that would be very difficult to do it in a physical once it had to be changed at least OK so Welch show another 1 that we have run also the this the exit it is available on
our website the kind so
another 1 is this when we have these eggs of it's important in University of Porto it's very striking it's in the rectory building building and what you'll see at 2 bars that are going to roll and they are passing through tools fleet to cops sleeps but they never bump into the sleeps a prime so and it's starting again the because so this is
then X admits persons being changed working properly because that there is a it's not going down we let's see if how this works in a no concise have close at hand all technical problems look at the so this is a
photo and so OK so can see it
here the it's working now I'm going to that the interesting part of the distal exited that doubt now can change everything now for instance imagine it can construct area on the particle it Obelix slate apply so you can check size you can change the tilt you can change the distance to direct relation revolution axis and then 1 that you are interested you can see how a to be and then it can change in real time thank and make all the changes here and it will about and now if you don't do not understanding why these functions and what is behind this you exit it you can generate the surface and it's much more clear because that the um bond that is rolling is generating that surface OK that apart the lights so that's why it's working
and so I don't know if I have time for answers so another 1 you stock a kind now this is another eggs they all this exhibit
exist in the magic of even a kind
and the now we have about building virtual exhibit so that any everyone can use at home or anywhere else now these are for dies and these nice are very strange because the blue 1 is better than the yellow and effect that when I say better it has the double of the probable probability of winning tool but uh yeah the warnings when kind now the orange 1 is better than the the green 1 again because it has a double of the probability just look at the the number supply the has a double the probability of 2 in the way now the green 1 is better than the pink 1 of Ki so when you say these would sigh immediately while the blue 1 is a bit better it's the it's better than the the yellow and orange 1 which is better than the green 1 which is better than the pink 1 or not what is changing this situation is the pink 1 is better than the blue 1 OK there was no transient the transitivity here on time so now we can use this exhibit and you can use of it all of and contriver yourself Of course this all can also give a very good lesson because sometimes it fails to probability a type and if not a good thing playing on a number of games that's not very big it'll probably it's probably no the can the
but so we can ask to people to play now this is mean means player 1 player tool now let the player 1 chooses from crying later when will choose the orange 1 and then well play a tool that's a lot that set to play when now you'll you'll chills is of course the 1 that has the biggest probability of winning so he'll choose the the blue 1 apply then you can choose the number of course to be it's better to have a big number 10 is not too much but it now can simulate a game guide the the the and so player 2 wins by a player 2 is always an advantage because he has always advise that in with probability it to be better than the other 1
kind a kind so and here are all contents contacts so it's so well as I tell you to channel our Facebook in our e-mail if you want to collaborators just let me know or just write an e-mail to us all kinds so this is what a lecture and sorry for the future and who thank you very much and other questions
hi and so was wondering how many people actually what can develop these a online exhibits how people developing how many people are involved in most of our team is it's for people for people working full-time going the other questions the we may be looking for
coffee to mention so thank you again and few