[MUSIC] Hello everyone, and welcome to this first focus group for field exercise one, which will be to look at point symmetry. We're really grateful, for your time today and also being willing to share your homework, with everybody else who's taking this course. The purpose of the field exercise and also the focus group, is to help you construct your home work in the best possible way. It's a little bit daunting I know, for some of you to go and take a photograph of yourself, plus the object. And so, if you're feeling a little shy, don't feel like you've gotta put your face in the photograph. Just wear perhaps a t-shirt or a jacket, which really identifies that this is your photograph and that you haven't taken it from the internet. Once you get the photograph, then you go through the process of identifying the point of symmetry. Now in today's exercise, we'll work through each of the group's students one by one. So we've really broken the homework, up into three sections. Of course at home, you'll be doing this yourself. Here, we'll let each student present their homework, and then the other group, will mark their homework. So this will be practice for you in both collecting and presenting your images, and also, in the way we should mark. So before we go to the students, let's remind ourselves, what this exercise is about. You have to take three photographs. One photograph, should be an image, which contains a reflection line only. The second, should have rotation only. And the third, should be a combination of reflection and rotation. So it's important not to get these mixed up. In addition, you can only use those operations, in other words, reflection and rotation, which are crystallographic or formally described. So that means, you should only use, two-fold, three-fold, four-fold or six-fold rotation. Even though you might be able to find higher or lower order rotations taking place, for example, five-fold or perhaps, eight-fold rotation. So, these are the constraints, under which you're conducting this exercise. So to begin, let's go and look at what Hui Min came up with, and she was looking for a photograph, which showed only rotation. >> Okay. So for my assignment, I was given a rotation logo. So, for this logo, I actually found it in JEM Shopping Mall. It was placed on the banner, which was outside this NTUC Supermarket. So this logo actually has one of the two fold rotation, in the middle of the S. So no matter how you turn like 180 degrees, it will still be the same. So, this logo is actually a very simple representation of the Singapore Pools Association in Singapore. >> Good, thank you very much, that's a terrific example of a diagratation. And we'll look at Wanzhen and her example of reflection. >> Okay for me, I'm doing the part on reflection on me. So basically, I actually found a magnet at home, it's actually a Paul Frank magnet that I happened to, chance upon when I went into the kitchen. And what I saw is that actually one vertical mural line, through the center between the eyes and the nose of Paul Frank monkey. And the function of this, is actually eye-catching, and it's an easy logo to recognize from afar. >> Thank you very much Wanzhen, a terrific example from your kitchen. And now we come to the difficult one, where we have reflection and rotation combined. So, Wilson is going to show his example of that. >> Okay, I was given the task of finding a rotation and reflection object and the thing that I found is it's located in my house and the thing is the, egg holder. So, initially, I've thought of finding a different like a rotation and reflection. I can find box fan. [INAUDIBLE] But I've chosen the egg case because it has, it shows through unique mirror lines, and is has a four fold rotation and the function of the, this egg holder is to protect and hold the eggs. >> Okay, that's another great example from the kitchen, where we have rotation and reflection combined. Now that we've listened to group A, we will see what group B have put together. And for that, we'll begin by listening to what Martin has done and he's looking at rotation only. >> I took recycle logo as my object of observation. And this logo, was taken from a recycle bin at NTU. The recycle bins is, are located in many places, in one university. And, they all look similar. But to be more specific it was from one school's main dorm. It has three-fold rotation points where it can be rotated 120 degrees and it still look the same. The logo itself, it was made to be, very memorable and noticeable. The logo itself, it was made very noticeable and memorable. The three arrows bended to one another. It resembles a cycle and so the people who sees it can understand immediately that it is a recycle bin and then it was the color, they was made very contrast. So, people who can see it from further distances can immediately notice it is a recycle bin. >> Okay Martin, that's a terrific example, of a threefold rotation axis. Now, we'll go to Zi Ying who will tell us about a reflection only example. >> I was test to find an, an object reflection of me, and I managed to find a toothbrush in the bathroom. It has one vertical mirror line, but the bristles are slightly out of shape, which is due to usage. The function of the symmetry in the toothbrush, is to enable easy grip for the brushing of teeth. >> Thank you very much Zi Ying, that's a terrific example from the bathroom, of a reflection only object. Now we want to go to the tough one again, reflection plus rotation combined, and for that we're going to hear from Yi Xun, who would give his example. The example that I have for rotation and reflection, comes from canteen bin, NTU. The example is a round plate. The plate is used to hold food. The rotation axis, they are infinite [INAUDIBLE]. And they are also, infinite reflection lines. >> Thank you very much, Yi Xun. That's a great example, of a symmetric object from the canteen. And what we can see, is that symmetric objects are around us everywhere. We find them in our everyday life. We see them, even though we don't notice them. So the point of this exercise is actually to focus on symmetry and pick out those objects which have particular symmetric properties. And I think you guys did a really good job at that. Now we come to the point, where we have to mark your homework. And we have a marking rubric, which you will be using, for this exercise. Now let's look, at how we'll use the marking rubric. For every object that you took a photograph of, you'll be marked in two respects. In the first part, you will be looking at have you correctly identified the symmetry symbol, and have you put it in the right position, with respect to the object. For reflection only, and rotation only, this will get you three marks, if you do it correctly. For the last one, where we have reflection and rotation combined, we've doubled up the marks. So if you get both of the symmetry operators correct, there's a total of six marks. And then, for each of the photographs that you take, and each of the objects, you need to talk about, why symmetry is important. And how symmetry is used to aid the functionality of that object. So now, let's go and listen to what group A have to say about group B's work, and vice versa. So let's begin, by having Hui Min, comment on Martin's example of rotation. >> Okay, so I'm going to grade Martin's logo which is the rotation only and you have chosen the, recycling bin logo. So for this logo right, you have chosen a very good symmetry because you have shown the three fold rotation. So for that I gave you the full marks, three marks. And then, for the next three marks you're supposed to explain the symmetry features, which you did very well in the previous section. So I gave you three marks for that as well. right, I will be grading for the reflection only, the part. So for your selection of the toothbrush, is a correct positioning of symmetry symbol, as I can see from the mirror light that you put onto the image. So, three marks for that. And for the explanation wise, you actually stated that there is actually one vertical mirror line, and it is equipped for brushing of teeth. So, another three marks. >> Okay, so I actually think that's a great mark, you get full marks for that, no question. But the other thing of course to point out is that, we're always approximating symmetry. And as you spoke about when you were discussing the toothbrush. Maybe the hairs on the toothbrush are not symmetrical, that they've been damaged. But that doesn't matter. This is still a good representation, because it's clear that the intent of the object was to have mirror symmetry. So, when you're grading other students' photographs, you always have to take into account, what did the designer of the object intend? Did he intend to have it, as a perfectly symmetrical object or not? The wa, the way in which wear and tear on the object might have destroyed the symmetry, we should always ignore them. >> Okay, I'll be grading on Yi Xun's rotation and reflection. And before I, before I begin, I realize that it is very difficult to find something that is a rotational and reflection base. I find that Yi Xun, you, you found something which is quite unique, which is circular, which also displays rotation and reflection. I have to commend you on that. Okay. But now going back to the grading, for correct selection and the positioning for reflection and rotation, I, I feel that you got both of them correct and now you get, six marks for that. For the description, explanation symmetry features unfortunately, unfortunately, it's only one unique mirror line and the, you have an infinite rotational symmetry. However, what was requested from Prof was a maximum of six fold maximum of the symmetry, rotation symmetry. So, unfortunately, I have to give you only two points for that segment. So in total you'll be having eight marks. Sorry about that. >> All right. So now what we've seen, is that putting together reflection and rotation, is a little more tricky, and you have to look a bit harder, to find examples. The comment about the plate that Wilson made, is completely correct. It's not quite in line with what we wanted with the homework. So, I'm sorry about that Yi Xun. Good effort, but not quite what we wanted. It's important when this homework is done, to only use those reflection and rotation axes which are used in crystallography, because in the end of this course, these will be the only orders of these that we use. So well done everyone very good marking and also good effort by group B and for group B, you scored 20 out of 24 marks. Now, let's move on and let group B, assess what group A did. >> I've been working, on Hui Min's works to represent rotational only. You took a Singapore Pools Logo it is good representations to the rotational only. I'll, I'll be giving treatments for the correct selection and positioning, because you put the correct two fold rotation points, on the middle of the logo. And I'll be giving three marks for the description and explanation too, because you did a good job in explanation, explaining where the logo can be rotated 180 degrees and still be the same shape. But, I'm giving additional comments on the logo. If you see the upper part of the logo it's have a shorter length, if you compare it to the bottom length. And if you want to consider these parts, it mi, it might mean that they're not symmetry. >> Firstly I would like to commend on Wanzhen for finding such a good example, at home. And I think that most of the blends actually have some form of symmetry, because it is eye catching and can catch someone's attention. So I will be able to give her three marks because she has the symmetry operators on the diagram placed correctly. And she also explained the symmetry features correctly and I have to give her three marks for that, so she can get six marks for this, this part. Yeah. >> Okay. For Wilson's egg cup example. Yes, it is correct. There is a fourfold rotation, and two unique mirror lines along the center. Therefore, his selection is correct, and he deserves six marks. Okay? For the description explanation as well, six marks. However, we need to also note small little details in the overall picture. The middle of it is very symmetrical, but by design, the egg cup at the corners, they are as, asymmetrical, but this is besides the point. So, yeah, it's okay. It's quite good. So he will 12 marks overall and yep. >> Go up. >> Okay, thank you very much Yi Xun. This is a very interesting example that Wilson has, because I can see if this was part of the peer to peer marking, the mark spread might be quite large depending how tough students chose to be, on this particular example. Actually Yi Xun is right when he says strictly, this does not satisfy the criteria for four fold rotation, as it's presented. Equally, Wilson is correct, if he changed his presentation just a little bit. And the way to do it, is to crop the photo a bit harder. Yi Xun said it obeys the symmetry in the middle of the photograph, which is actually correct. So the way to present this is not to take a whole new photograph, but simply, present it in a slightly different way. And we can do it, by cropping down the photo as follows. Simply take the central part and if we crop it in this way, and then expand it again, now I think, we're correct. We have clear mirrors of two types running through, and we do have the four fold rotation. But once we open out to the wider egg carton, then the plastic pressing has been a bit different, I guess to let the carton click together properly. So I, I would support the four marks for this, the, the, with no, no marks taken off. But probably to avoid confusion, it could be presented a little bit better, by cropping harder, then there can be no ambiguity, about the symmetry. I just want to remind everyone and especially those who are doing this course for academic units, that we simply can't tolerate plagiarism. So, if you take other people's work perhaps from this course or from the previous versions of the course and use their photographs, then that will automatically result in a zero mark. Similarly, you shouldn't take photographs from the internet, we really want them to be photos that you've taken yourself. And if you feel a little bit shy and you don't want to show your face, that's okay, but wear some clothing or have some way of showing that they are really your photographs and that will be perfectly fine. So let's draw this focus group to a close. Thank you again, to the students who helped us out.