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Dimensions | Chapter 6

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Automatisierte Medienanalyse

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mine eyes long line of
top and then chastened transition
nations transforming a lot well if you don't mind we're going to transform 1 portrayed caps a let's begin as something simple the transformations Edgar's is added to each point on the photo corresponds to a complex numbers this divided by 2 we get another point intimidated by the transformation into new picture less surprised by shrank a half the size since each is being divided by 2 this transformation is called a harmless back John they let's go to the multiplication by Carl him easy we know that multiplied by eyes just a quarter turn also noted the modulus does not change the beyond image increased 90 degrees by indeed this is quite a sophisticated way of saying that we just rotated the picture at sea back well but a bit more complicated not vacation by 1 plus sign a look at a complex number 1 plus sign it corresponds to the point with a 1 and warden it on its argument is 45 degrees at its modulus the square root 2 Bush using Pythagoras Iran hints a modification by 1 plus on announced Pfister multiplying but the square meters to and they adding 45 degrees to the argument it's simple 1 has to combine a homer 50 and a rotation this is called a similarity as a rule Croat up Is that a more interest we're going to transform the points state into their squad the state multiplied by saying that a let's begin by placing the photo a suitable place flush against the cold taxis that is man I assume little bit since the squaring process will change the size of things and I need space to show you took change now we can transform a photo progressively notice that the argument is square is twice the argument is so that the right angle of the left of the doubled on the transformation after now it is turned into a 180 degree angle let me place the photos somewhere else she lets to look again at the same transformations it square elects to gain the same argument toppling a incidents the combined extinct pull the transformation its argument is about 45 degrees and after the transformation points at 90 degrees she did you could also observe the marginalized way tho a the big not go-between new transformation sending the point Z 2 minus 1 bring man don't forget with complex numbers on had multiplied but also not not play 0 schools does doesn't this image remind you of the Sistine Chapel bring back large complex numbers With a large margin becomes more money and takes maybe and comments here's a similar transformation look at the formula the value of k changes slowly some parts are expanding others a contracting if 1 looks close to shake presented even dialects on not Air better where a circle remains circular even in so it might cross my hand grew my face became smaller still recognized me yeah at an and 1 more transformation more involved well this 1 is not really a weight-loss program me but now wants more that evangelical because I shapes small plots did not change for if you look at that but on my show he keeps a secular Shiite on these transformations are calm formal Fulham Norfolk rather complicated laughing in Greek words saying that 1 presenters shapes indeed with complex numbers what could do quite a lot 1 could even take the exponential if you know what this means but even if you don't have to
look at the treatment or have to suffer from the exponential have I had disappeared not if you look through a microscope nearly origin you
could see my beard now that you know but complex numbers I use seems transformation I would
explain somebody objects or been studying closely she here you see a number of points some opted inside these days a it's all Council measures that's a former transformations it squares ponds and let's look at the resort you could see that point stains on the disk and the yellow points on the contrary escaped from the disk and even escape from screen laughter my mom 1 says that the big disk Is the fielding Jr. said of the transformation square points outside the issue said escaped to infinity with on repeats the transformation death we
have but we can play the same game with transformation like for instance that perform Zed Swed we see is a complex number we can't use at will for each complex number perceived therefore have Julius shake changes would see change you could see a few examples here the plan all of us removal will
soon Havel said we have on for the full we live in a room that that house William here is someone like caught the rocks they about more column please Of course I'm a
who half how it a a R really is polluted river is meant to have at I don't In order to
understand how these shapes change I will show you several things in parallel on the left-hand side the red sign you could see a point that Stockton this is the point on the right-hand side you see the corresponding Jr. said this is performing as he slowly changing but sometimes for some values and the Junious said seems to disappear but cannot see anything anymore on the screen what now for instance the truth is that Jr. said 3 walked into an infinite number of pieces so small that you didn't see anything on the screen they were mental approach who popularized practical steps suggested the study of this thorny red that describes the values of the which 1 concede that Julius clearly on the screen in other words that issue which they GSA did not into multiple beast Of course is red said his call the man Price said I spent quite a lot of sun studying it To I suggest that we look closely very closely at dismantle products said ends you lean side said you can appreciate how beautiful it let's go here it is that but
once I will not explain everything imagine the mantle bread said as bright colors surrounded by tropical seas and that you could see that often but really your looking at Troon microscope picked details if the mantle process With size a soccer field well we will be looking at details the size a single act a feel water million mm if if ahead if they have a right now they say him ahead if if they had a bad if if if if if a have room a head of maybe you want Dre while I he'd Tracy Ms. vegetables because it is beautiful and because understanding subjects gay much pleasure the main is reason enough to spend time on this question also because these transformations simple what can find these essence of chaos such a fundamental concept in modern science but simple things generating rich structure but To study complicated phenomena through their simplest incarnation this is off the role of the mathematician but a
a a my 1st review your we owe although my if say because they are on a year a E will have to do them after all
Randverteilung
Punkt
Prozess <Physik>
Komplexe Darstellung
Gruppenoperation
Formale Potenzreihe
Transformation <Mathematik>
Drehung
Kombinatorische Gruppentheorie
Inzidenzalgebra
Raum-Zeit
Computeranimation
Ausdruck <Logik>
Multiplikation
Meter
Wurzel <Mathematik>
Kontraktion <Mathematik>
Optimierung
Parametersystem
Kreisfläche
Mathematik
Winkel
Ähnlichkeitsgeometrie
Schlussregel
Kugelkappe
Minimalgrad
Quadratzahl
Komplex <Algebra>
Rechter Winkel
Mereologie
Dimensionsanalyse
Aggregatzustand
Exponent
Komplexe Darstellung
Transformation <Mathematik>
Computeranimation
Objekt <Kategorie>
Punkt
Quadratzahl
Mathematik
Spieltheorie
Komplexe Darstellung
Körper <Physik>
Zahlenbereich
Transformation <Mathematik>
Einflussgröße
Computeranimation
Unendlichkeit
Ordnung <Mathematik>
Computeranimation
Beobachtungsstudie
Fundamentalsatz der Algebra
Prozess <Physik>
Punkt
Wasserdampftafel
Zahlenbereich
Transformation <Mathematik>
Biprodukt
Computeranimation
Unendlichkeit
Algebraische Struktur
Multiplikation
Vorzeichen <Mathematik>
Mathematikerin
Unordnung
Ablöseblase
Körper <Physik>
Kantenfärbung
Dimensionsanalyse
Grothendieck-Topologie
Computeranimation

Metadaten

Formale Metadaten

Titel Dimensions | Chapter 6
Serientitel Dimensions
Teil 6
Anzahl der Teile 9
Autor Leys, Joe (Images and Animations)
Ghys, Étienne (Scenario and Mathematics)
Alvarez, Aurélien (Image Rendering and Post-production)
Mitwirkende Bullet, Shaun (Speaker)
Delong, Matt (Speaker)
Guaschi, John (Speaker)
Grant, John Lewis (Music)
McLeod, Kevin (Music)
Ghys, Florent (Music)
Lizenz CC-Namensnennung - keine kommerzielle Nutzung - keine Bearbeitung 3.0 Unported:
Sie dürfen das Werk bzw. den Inhalt in unveränderter Form zu jedem legalen und nicht-kommerziellen Zweck nutzen, vervielfältigen, verbreiten und öffentlich zugänglich machen, sofern Sie den Namen des Autors/Rechteinhabers in der von ihm festgelegten Weise nennen.
DOI 10.5446/14688
Herausgeber Joe Leys, Étienne Ghys, Aurélien Alvarez
Erscheinungsjahr 2008
Sprache Englisch
Produzent École Normale Supérieure de Lyon (ENS-Lyon)

Inhaltliche Metadaten

Fachgebiet Mathematik

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