1 00:00:00,000 --> 00:00:06,720 Hello, good morning. In this video we are going through a couple of important geometrical 2 00:00:06,720 --> 00:00:14,280 constructions by the use of set squares, as you can see here. The use of set squares necessarily 3 00:00:14,280 --> 00:00:21,920 and mandatorily implies that one is going to always slide on the other. So we are going 4 00:00:21,920 --> 00:00:28,280 to have one that is going to serve as a rail and the other is going to be the train, so 5 00:00:28,280 --> 00:00:36,400 to say. And it can be, of course, be used in this direction, in this other, and also 6 00:00:36,400 --> 00:00:42,920 it can be slipped, as you can see, flipped, I mean, this way. So in the first exercise 7 00:00:42,920 --> 00:00:53,760 we are going to draw a parallel line. Parallel lines. That's going to be our first exercise. 8 00:00:53,760 --> 00:00:59,640 Parallel lines. In that sense, what we are going to do is we are going to draw a random 9 00:00:59,640 --> 00:01:06,400 line like this, OK, and we are going to call it R, for instance, and we are going to draw 10 00:01:06,400 --> 00:01:14,600 a couple of parallel lines to it. As you can see, we are going to line up the line with 11 00:01:14,600 --> 00:01:21,560 one of the set squares and the other is going to stay totally still. So we are going to 12 00:01:21,560 --> 00:01:32,080 be able to draw parallel lines, OK, by moving, by sliding one of the lines. So every time 13 00:01:32,080 --> 00:01:37,480 the set square that we are using, which is in movement, this one, which is the one that 14 00:01:37,480 --> 00:01:47,200 slides, moves, we will have to go back and line it up again, OK. So this is going to 15 00:01:47,200 --> 00:01:59,120 be our first couple of parallel lines. So far so good? Nice. Now we are going to do 16 00:01:59,120 --> 00:02:12,520 some perpendicular lines. And particularly speaking, what we are going to do is we are 17 00:02:12,520 --> 00:02:17,440 going to draw again a random line like this, which is going to be S, and we are going to 18 00:02:17,440 --> 00:02:26,680 draw a point, which is going to be point A. And we are going to draw a perpendicular line 19 00:02:26,680 --> 00:02:34,320 to S that goes through the point A. So far so good. So what we are going to do next then 20 00:02:34,320 --> 00:02:41,080 is we are going to, first of all, place, in this case, the 60 degree one, OK, perfectly 21 00:02:41,080 --> 00:02:48,920 lined up. Then we are going to take the 45, OK, and in this sense what we are going to 22 00:02:48,920 --> 00:02:56,720 do next is we are going to slide slightly the 60 degree one, which is going to be afterwards 23 00:02:56,720 --> 00:03:05,320 the new rail, OK. And according to that, then we are going to take the 45 degree set square 24 00:03:05,360 --> 00:03:13,480 and we are going to be able to draw a perfect 90 degree line, as you can see. And we are 25 00:03:13,480 --> 00:03:23,440 going to mark that one, OK. So if I want to draw more perpendicular lines to S, for instance, 26 00:03:23,440 --> 00:03:32,280 that go through B or through C, it's going to be as easy as, as you can see, just using 27 00:03:32,280 --> 00:03:43,000 the same rail and drawing a couple of perpendicular lines like that or even like this, OK. It's 28 00:03:43,000 --> 00:03:50,120 going to be exactly the same thing. Good. That's going to be our number 2. Let's go 29 00:03:50,120 --> 00:03:58,960 ahead and now let's go, for instance, to number 3, in which we are going to do a couple of 30 00:03:58,960 --> 00:04:15,520 45, 30 and 60 degree parallels, OK. So again, what we do is we draw a random line like this. 31 00:04:15,520 --> 00:04:23,000 We are going to call it M in this case, OK. And then again, we are going to, first of 32 00:04:23,000 --> 00:04:32,680 all, we are going to make ourselves a slightly separated rail, as you can see, and this 33 00:04:32,680 --> 00:04:42,280 is going to allow us to draw 45 degrees parallels. For instance, this one here, 45, we are going 34 00:04:42,280 --> 00:04:52,360 to draw a couple of them, 45, 45, OK. And we are going to mark it, 45 degrees. So far 35 00:04:52,360 --> 00:05:01,440 so good. And now, for the 30 and the 60 degree one, we will need to use this one here, OK. 36 00:05:01,440 --> 00:05:07,720 So we are going to switch the rail, which is going to be the 45 degree one. And we do 37 00:05:07,720 --> 00:05:12,400 exactly the same thing we've done before. We first of all line it up, as you can see 38 00:05:12,400 --> 00:05:21,160 here, and then we are going to separate it a little bit and then we are going to be able 39 00:05:21,200 --> 00:05:29,400 to draw, for instance here, 30 degree, a couple of them. I think I moved it. If I moved it 40 00:05:29,400 --> 00:05:40,400 a little bit, I have to go back and make sure it's lined up again. So, 30 degree ones. OK. 41 00:05:40,400 --> 00:05:47,360 So here I'm going to mark it, 30 degrees. And what about the 60 degree ones? I'm going 42 00:05:47,360 --> 00:06:00,240 to draw them like this here. Again. And, for instance, again. So, here we have 60 degree 43 00:06:00,240 --> 00:06:14,520 ones. So we have a couple of 45, 60 and 30. In this exercise, we are going to draw a parallel 44 00:06:14,520 --> 00:06:28,680 gradient for parallels. Gradient. OK. So we are going to start with the first parallel 45 00:06:28,680 --> 00:06:35,520 gradient, showing you what I mean. So, I'm going to draw first, as you can see, one single 46 00:06:35,520 --> 00:06:44,440 line. And parallel to it, I'm going to draw several parallels, so that the 47 00:06:44,560 --> 00:06:57,560 distance in between these parallel lines is becoming gradually bigger. It's important 48 00:06:57,560 --> 00:07:07,640 to leave enough space in between the ruler and the drawing that we are drawing, and we 49 00:07:07,640 --> 00:07:13,960 shall all the time be able to see what we are drawing. You see what I mean? Good. And 50 00:07:13,960 --> 00:07:26,840 now, we are going to draw a wave. Una ola. And in order to do so, we are going to first, 51 00:07:26,840 --> 00:07:32,120 as you can see, with pencil, very slightly, we are going to draw a double curve, like 52 00:07:32,120 --> 00:07:42,720 this. And we are going to try to draw this same curve, only a couple of centimeters away. 53 00:07:42,720 --> 00:07:54,440 So that this distance needs to, or should be, basically the same everywhere. For instance, 54 00:07:54,440 --> 00:08:05,560 like here, and like that. Let's go a little bit bigger. OK. So, we try to get those distances 55 00:08:05,560 --> 00:08:14,680 as necessary. OK. And as equal as necessary. It's true that we are going to get those lines, 56 00:08:14,920 --> 00:08:25,800 as you can see, not perfectly equal, I mean not totally sharp. That's going to be enough. OK. 57 00:08:25,800 --> 00:08:33,240 And then, as I told you before, we will need to see what we are drawing all the time. What does 58 00:08:33,240 --> 00:08:39,560 it mean? If I start drawing here, this line, and I continue on drawing in this direction, 59 00:08:39,560 --> 00:08:46,200 I'm going to hide, as you can see, with a ruler what I'm drawing. So that is not a good idea. 60 00:08:46,200 --> 00:08:54,440 Therefore, I change the position, so I'm able to see all the time the distance in between the 61 00:08:54,440 --> 00:09:00,520 lines that I'm trying to draw. So here, for instance, these lines are going to be rather 62 00:09:00,520 --> 00:09:11,160 separated. Here we go. I can even leave a lot of separation in between. And then, the moment I 63 00:09:11,160 --> 00:09:22,200 start getting closer to the crest, la cresta, to the crest of the wave, here, I start getting 64 00:09:23,160 --> 00:09:37,480 those lines gradually tighter. OK. Tighter and tighter and tighter. You see? It's exactly the 65 00:09:37,480 --> 00:09:44,760 same principle as we used on the monster, that is, that texture. And now, here, in the inside 66 00:09:44,760 --> 00:09:53,400 of the wave, the parallel lines are going to be even tighter, because there is a shadow, 67 00:09:55,160 --> 00:10:02,600 as you can see. It's the bell ringing here. It doesn't matter. I am going to continue on 68 00:10:02,600 --> 00:10:11,960 drawing. It's perfectly clear that I am in the school right now, in the building. I'm not at home. 69 00:10:12,760 --> 00:10:19,720 And here, I'm committing a mistake. What mistake? Because I'm hiding the drawing, 70 00:10:19,720 --> 00:10:29,640 and that's something we don't want. OK. So, again, make sure you put the 71 00:10:30,360 --> 00:10:38,280 the ruler so that you do not hide, at any moment, what you are drawing. OK. So, again, 72 00:10:38,280 --> 00:10:42,360 let's blend it up, because we continue on drawing some parallel lines, like this. 73 00:10:43,560 --> 00:10:51,720 And here we go. We start getting up. As you can see here, the pattern of parallel lines 74 00:10:52,280 --> 00:11:04,520 is quite different to the inside. And we go up. And here we go. 75 00:11:06,520 --> 00:11:17,720 And gradually, we come closer to the crest of that wave. And here, 76 00:11:18,360 --> 00:11:25,720 now, almost abruptly, the lines are becoming very, very tight, 77 00:11:31,160 --> 00:11:38,760 which allows us to have this feeling, you know, of three-dimensional curvature. 78 00:11:39,240 --> 00:11:44,040 Now, I'm going to erase 79 00:11:46,840 --> 00:11:54,440 the pencil. I don't need that anymore. And if I've drawn those parallel lines 80 00:11:55,560 --> 00:12:05,960 correctly enough, I should be able to see the wave, even though I don't have drawn any outline 81 00:12:05,960 --> 00:12:11,240 at all, as you can see. So, see you in the next video. Thank you so much.