## Dimensions | Chapter 6

Video in TIB AV-Portal: Dimensions | Chapter 6

 Title Dimensions | Chapter 6 Title of Series Dimensions Part Number 6 Number of Parts 9 Author Contributors License CC Attribution - NonCommercial - NoDerivatives 3.0 Unported:You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor. Identifiers 10.5446/14688 (DOI) Publisher Release Date 2008 Language English Producer École Normale Supérieure de Lyon (ENS-Lyon)

 Subject Area Mathematics

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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
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