JP2 CHANGING SHAPE WITHOUT CHANGING AREA
This eighth grade mathematics lesson focuses on two-dimensional geometry - in particular, the areas of triangles between parallel lines. The lesson is 50 minutes in duration. There are 35 students in the class.
| Time | Caption |
|---|---|
| 00:00:01 | Stand. |
| 00:00:02 | He says he's not filming yet. Around here (inaudible). |
| 00:00:13 | Stand straight. |
| 00:00:14 | Stand straight. |
| 00:00:17 | Bow. |
| 00:00:18 | Onegaishimasu. |
| 00:00:19 | Onegaishimasu. |
| 00:00:20 | Okay. |
| 00:00:27 | Um, do you remember what we did last period? |
| 00:00:29 | We did mathematics. |
| 00:00:31 | Sakurai, what kind of things did we do? |
| 00:00:33 | Huh? |
| 00:00:34 | We did mathematics. |
| 00:00:35 | I don't know. |
| 00:00:38 | Huh? Hm. The last period? |
| 00:00:41 | Um. This topic, okay? |
| 00:00:45 | Is it that? |
| 00:00:46 | Yes. |
| 00:00:47 | Obtain the area of triangles which are in the places in the parallel lines. |
| 00:00:51 | That's right, huh? Um, we studied the idea that parallel, parallel lines, |
| 00:00:57 | the triangles between them, uhm, |
| 00:01:02 | with the same base or height are all the same... like this. |
| 00:01:08 | For example, here. |
| 00:01:09 | This. |
| 00:01:17 | This�since the height will all be the same, |
| 00:01:21 | we studied that the area will also be the same. |
| 00:01:27 | Uhm, we will use this this as the foundation |
| 00:01:29 | for what we will be going to study today. |
| 00:01:31 | Then, prepare just your notebooks. We won't need your textbooks. |
| 00:01:34 | Close your textbooks. |
| 00:01:36 | Just take out your notebooks. Uhm. The date. Oh. |
| 00:01:38 | It's er- erased. The date is November. |
| 00:01:42 | What day is it? |
| 00:01:45 | The twenty-ninth. |
| 00:01:46 | It's the twenty-ninth, right? |
| 00:01:48 | It's the twenty-ninth. |
| 00:01:50 | Uhm. |
| 00:02:12 | Uhm. Right now over here, okay? There is Bando's land. |
| 00:02:21 | It's okay, huh? Okay. There is Bando's land. |
| 00:02:24 | Okay? Over here is Chiba's land, okay? |
| 00:02:26 | [ Laughter ] |
| 00:02:27 | The teachers. It's the teachers. |
| 00:02:31 | Is it okay? Let's say that there is a land like this. |
| 00:02:36 | And. Is it okay? Chiba. |
| 00:02:38 | Yes. |
| 00:02:39 | And these two people's, uhm, border line is bent like this |
| 00:02:42 | but we want to make it straight, okay? |
| 00:02:45 | Bando. |
| 00:02:46 | Yes. |
| 00:02:47 | Is it okay with it around here? |
| 00:02:50 | Yes. |
| 00:02:51 | It's okay? |
| 00:02:52 | [ Laughter ] |
| 00:02:53 | Then, we'll end today's class, okay? |
| 00:02:54 | [ Laughter ] |
| 00:02:55 | Chiba, is it okay with it around here? |
| 00:02:57 | Ahhh. |
| 00:02:58 | No? |
| 00:02:59 | No. |
| 00:03:00 | Around where would you like it? |
| 00:03:02 | It would be better if mine was wider. |
| 00:03:03 | A lot more to the bottom? |
| 00:03:04 | Huh? A little more over here? |
| 00:03:05 | More. |
| 00:03:06 | Around where would you like? |
| 00:03:07 | Continue over more. More. More. |
| 00:03:08 | More over here? |
| 00:03:09 | More. More. More that way. |
| 00:03:10 | [ Laughter ] |
| 00:03:11 | Oh. [ Laughter ] |
| 00:03:12 | Bando. Is it okay with it around here? |
| 00:03:13 | No. |
| 00:03:14 | It's not okay, right? |
| 00:03:15 | [ Laughter ] |
| 00:03:16 | Then, around where would it be good? |
| 00:03:18 | Huh? |
| 00:03:19 | Date. Around where do you think would it be good? Approximately. |
| 00:03:21 | (inaudible) |
| 00:03:22 | That line... well. |
| 00:03:25 | Well, try doing it. |
| 00:03:26 | Huh? |
| 00:03:27 | Approximately. Estimate. |
| 00:03:28 | Uhm. |
| 00:03:29 | Yes. |
| 00:03:31 | Uhm. Take it between th- this line and this line. |
| 00:03:32 | Yes. |
| 00:03:34 | We got an estimate that says it may be okay if it's in the middle. |
| 00:03:38 | I see. How about other people? |
| 00:03:40 | Okay? Then, well in your notebook, okay? |
| 00:03:43 | Draw a figure like this and- |
| 00:03:45 | Please try thinking about it a little, |
| 00:03:48 | methods of changing this shape without changing the area. |
| 00:03:53 | Okay? |
| 00:03:56 | Okay, then everybody... let's try thinking about it. |
| 00:03:59 | The work time is... would you think about it for three minutes? |
| 00:04:03 | First of all, please think about it individually for three minutes. Okay begin. |
| 00:05:37 | Are you done? |
| 00:05:44 | (inaudible) You made it straight here? Is it the same? Definitely? Is it the same? |
| 00:05:49 | It's appro- approximate. |
| 00:05:50 | If it's approximate. Wouldn't they fight over it if it was approximate? |
| 00:05:52 | Huh? Around. It's the parallel line of this and this. |
| 00:05:55 | The middle of it? |
| 00:05:56 | Yes. |
| 00:05:57 | I think it's good if you draw it exactly in the middle. I see. |
| 00:06:05 | That's sharp. |
| 00:06:08 | What was the thing we studied last time? |
| 00:06:12 | If it's like this, for all we know they will fight. |
| 00:06:14 | A method that uses the same method as last time. |
| 00:06:17 | I can't solve it. |
| 00:06:19 | First of all, draw a figure and- |
| 00:06:20 | Draw the figure and- |
| 00:06:22 | The idea from last time. |
| 00:06:24 | Is there a method that uses the area of the triangles? |
| 00:06:34 | That's sharp. |
| 00:06:36 | You were able to make this a triangle, right? Okay? |
| 00:06:39 | Then if you do what... |
| 00:06:43 | Okay? Would you get triangles with the same area. |
| 00:06:46 | Would you make this the base? |
| 00:06:48 | The question is that somewhere there are parallel lines, okay? |
| 00:06:51 | Hm. We did it like this and in the last class we did it like this... |
| 00:06:54 | we get a triangle. |
| 00:07:04 | Okay. Then since the three minutes are up, so... uhm... |
| 00:07:09 | People who have come up with an idea for now go to |
| 00:07:12 | Teacher Ebina and do it with him, |
| 00:07:15 | and people who want to discuss it with his or her friends, |
| 00:07:17 | discuss it with your friends. |
| 00:07:18 | And for now I have placed some hint cards up here |
| 00:07:22 | so people who want to refer to this can refer to it. |
| 00:07:24 | Now then, uhm, in three minutes... |
| 00:07:26 | Uhm, well, think about it and please try doing it |
| 00:07:29 | with your friend or by yourself. Okay, begin. |
| 00:07:38 | You can't bring it with you. |
| 00:07:49 | You missed class the other day, huh? |
| 00:07:51 | Hm, well. It's good if you make a triangle somewhere. |
| 00:07:53 | Can't you make a triangle somewhere? |
| 00:07:57 | Huh? It's wrong. |
| 00:07:58 | I don't understand. |
| 00:08:04 | Somewhere a triangle- |
| 00:08:06 | if you draw one line somewhere you get a triangle. |
| 00:08:15 | Make a triangle somewhere. |
| 00:08:16 | Huh? |
| 00:08:17 | Draw a line somewhere and make a triangle. |
| 00:08:18 | Oh. |
| 00:08:20 | Wait. Wait. |
| 00:08:21 | Oh. I got it. |
| 00:08:23 | Take a parallel line (inaudible). |
| 00:08:27 | If we (inaudible), then the area of the triangle. |
| 00:08:31 | I don't know. |
| 00:08:37 | They're not parallel lines. |
| 00:08:49 | Now. |
| 00:08:50 | Oh. I got it. |
| 00:08:51 | Draw it. |
| 00:08:52 | Teacher. That's not right. A B- |
| 00:08:53 | Hum? |
| 00:08:54 | It's different from mine. |
| 00:08:55 | Hm. You see it is. You see Fujita's is. |
| 00:08:57 | If these are parallel then you can say something like this. |
| 00:09:00 | Oh. That's right. |
| 00:09:01 | Do you understand? Since it's like this if you l- |
| 00:09:03 | compare the area over here and over here, |
| 00:09:06 | well it seems the one over here is smaller, right? |
| 00:09:08 | Oh. It's the same, huh? If they are parallel then, okay? |
| 00:09:10 | Well, I also have a feeling they will be the same. Yes. |
| 00:09:12 | Oh. That's right, huh? I got it. I got it. |
| 00:09:13 | Yes. |
| 00:09:15 | But the way of thinking was good. It was quite a sharp thought, okay? |
| 00:09:17 | The assumption was good. |
| 00:09:18 | Can I borrow the (inaudible). |
| 00:09:19 | Oh. I got it. I got it. I got it somewhat. |
| 00:09:20 | Teacher, teacher, teacher. |
| 00:09:21 | Yes. |
| 00:09:22 | This okay? Went to here and here, okay? |
| 00:09:23 | I got it somewhat. |
| 00:09:25 | (inaudible) |
| 00:09:26 | [ Laughter ] |
| 00:09:28 | (inaudible) |
| 00:09:29 | If it's approximate, of course it will become a fight, right? |
| 00:09:30 | Oh. Did you get it? |
| 00:09:31 | How do you do (inaudible)? |
| 00:09:32 | Oh. Take this. You make a triangle somewhere. |
| 00:09:35 | Well, here, draw one like this. This. |
| 00:09:38 | You make a triangle like this. And, then you make this like that TV. |
| 00:09:42 | To make the triangle you move your neck like this. Okay? |
| 00:09:43 | Yes. |
| 00:09:44 | If you do that you get a triangle, right? |
| 00:09:45 | Yes. |
| 00:09:46 | And here, here all you have to do is draw a parallel line somewhere. |
| 00:09:50 | Then where would you draw a parallel line? |
| 00:09:51 | A parallel is you understand? It's sideways like this. |
| 00:09:52 | Oh. Like this? |
| 00:09:53 | Over there isn't (inaudible). |
| 00:09:55 | You don't get a triangle. |
| 00:09:57 | You draw it here, huh? Hm, well where is it the same area with this triangle? |
| 00:09:58 | Yes. |
| 00:10:00 | Which is it? |
| 00:10:01 | Hm. |
| 00:10:02 | It's three (inaudible). |
| 00:10:03 | Yes. And then. Yes. The area that is the same with this triangle becomes like this and it also becomes like this, okay? |
| 00:10:04 | (inaudible) |
| 00:10:09 | Oh. This then this is straight up like this. Here also. |
| 00:10:11 | That's right, huh? Well. |
| 00:10:12 | Oh. From here to here? |
| 00:10:14 | That's right. That's right. That's- that's right. It's good if you do it like that. |
| 00:10:16 | Oh. |
| 00:10:17 | There aren't any complaints for that, right? If you do that. |
| 00:10:18 | Oh. Well, let me try (inaudible). Teacher. |
| 00:10:20 | [ Laughter ] |
| 00:10:21 | It's here and here right? |
| 00:10:22 | Yes. And is it just here and here? |
| 00:10:25 | The more opposite side too. |
| 00:10:27 | (inaudible) right? That's right, huh? Okay. |
| 00:10:28 | What? |
| 00:10:30 | [ Laughter ] What are you doing putti- marks? |
| 00:10:31 | Don't erase it. |
| 00:10:32 | Is it (inaudible)? |
| 00:10:33 | [ Laughter ] |
| 00:10:34 | [ Laughter ] It's okay now. Did you get it? You don't get it? |
| 00:10:40 | Did you get it? |
| 00:10:42 | Teacher. Would you point to me later, okay? Teacher. |
| 00:10:45 | You talk too much, you stupid. |
| 00:10:46 | If you were to make a triangle somewhere if you |
| 00:10:47 | draw a line where would you get a triangle? |
| 00:10:49 | Where? |
| 00:10:50 | There. |
| 00:10:51 | There. |
| 00:10:52 | Here, right? You get one triangle, right? |
| 00:10:53 | Then where is the same area as this triangle? |
| 00:10:57 | Oh. If you were to draw a line parallel to th- |
| 00:10:59 | this triangle where would you draw it? |
| 00:11:00 | (inaudible) |
| 00:11:02 | You would draw it here, right? |
| 00:11:04 | Right? Then where would you get a triangle that is |
| 00:11:06 | the same area as this triangle? |
| 00:11:09 | Those two. |
| 00:11:10 | Hm? |
| 00:11:11 | Ha. The two. |
| 00:11:12 | You can also make one like this, you can also make one like this. |
| 00:11:13 | You can make a lot, right? You can make multiple numbers of it, right? |
| 00:11:15 | Th- That's what you mean. |
| 00:11:16 | Oh. I have no clue what he is saying. |
| 00:11:18 | Then to make this nicely into one line somewhere where should we move this? |
| 00:11:26 | Ah. |
| 00:11:27 | I got it. |
| 00:11:28 | Ah. |
| 00:11:29 | What should we do? |
| 00:11:30 | Like this- like this. |
| 00:11:31 | Like this. |
| 00:11:32 | Okay. That's right. Okay? |
| 00:11:34 | Huh? |
| 00:11:35 | (inaudible) |
| 00:11:38 | That's right. That's right. That's, that's right. |
| 00:11:39 | Goto isn't good. |
| 00:11:42 | Hey. I got it. |
| 00:11:55 | In the end. |
| 00:12:02 | Is it just this one line? |
| 00:12:04 | Hm. That's right, huh? You also need the side over there, right? |
| 00:12:06 | Ah. |
| 00:12:07 | That's right, huh? |
| 00:12:08 | Teacher, Teacher, Teacher. |
| 00:12:09 | Yes. What is it? |
| 00:12:10 | (inaudible) |
| 00:12:11 | I don't really understand it but. |
| 00:12:12 | Yes. Now then, okay? You got a triangle here, right? |
| 00:12:14 | And they're parallel, right? |
| 00:12:17 | All you have to do is look at it like this, like last period. |
| 00:12:19 | Then since here it is parallel so... where is the |
| 00:12:21 | area that is the same as this triangle? |
| 00:12:23 | Like this. |
| 00:12:24 | This and this and this. |
| 00:12:25 | Yes. You can get one like this. You can get one like this. |
| 00:12:28 | You can get a lot of (inaudible), huh? |
| 00:12:31 | Then for this to neatly become straight where does the triangle form? |
| 00:12:33 | Neatly? |
| 00:12:36 | This becomes a straight line- we want to make it straight. |
| 00:12:38 | Oh. |
| 00:12:39 | From here to here? |
| 00:12:40 | Yes. Or... |
| 00:12:41 | From here to here? |
| 00:12:42 | That's right. That's right. That's right. That's- that's right. |
| 00:12:43 | Teacher? |
| 00:12:44 | Yes. |
| 00:12:45 | Uhm, this and this are- |
| 00:12:46 | Hm. |
| 00:12:47 | parallel, so- |
| 00:12:48 | Hm. |
| 00:12:49 | even if we move this- |
| 00:12:50 | Hm. Hm. Hm. |
| 00:12:51 | they are parallel bu- Since the area is the same so- |
| 00:12:54 | Hm. |
| 00:12:55 | aren't here- the obliq- oblique lines here and- |
| 00:12:57 | Hm. |
| 00:12:58 | this white part- |
| 00:12:59 | Hm. |
| 00:13:00 | the same? |
| 00:13:01 | You're sharp. |
| 00:13:02 | Hm. |
| 00:13:03 | Okay. |
| 00:13:04 | Uhm. Hamada. |
| 00:13:07 | Here. Teacher. Here. |
| 00:13:09 | Hm? |
| 00:13:10 | (inaudible)? |
| 00:13:11 | How did you do it? |
| 00:13:12 | Try explaining it. |
| 00:13:13 | Since this and this are parallel so- |
| 00:13:14 | Hm. |
| 00:13:17 | if you connect them like this- |
| 00:13:18 | Yes. |
| 00:13:20 | they become equal. |
| 00:13:21 | Oh, okay. |
| 00:13:22 | I'm going to the teacher's one. |
| 00:13:23 | Wait a second. |
| 00:13:24 | Teacher. |
| 00:13:25 | Why? |
| 00:13:26 | Ikeda. Ikeda. |
| 00:13:27 | Teacher. |
| 00:13:28 | Wait- wait a second, okay? |
| 00:13:29 | Excuse me. Wai- |
| 00:13:31 | Mos- have you finished most of it? |
| 00:13:33 | How about the height? |
| 00:13:36 | Uhm. Jimbo. |
| 00:13:37 | Yes. |
| 00:13:38 | Would you do the one you were showing just now up at the front? |
| 00:13:39 | The one just now? |
| 00:13:40 | Yes. |
| 00:13:41 | Am I supposed to explain it? |
| 00:13:42 | Yes. An explanation. |
| 00:13:43 | Huh? |
| 00:13:44 | Please go ahead. |
| 00:13:45 | What is it? |
| 00:13:46 | Huh? You got to be kidding me. |
| 00:13:47 | If you draw the parallel lines and why it becomes like this why- |
| 00:13:48 | Well you see. |
| 00:13:49 | Yes. |
| 00:13:50 | This is okay? |
| 00:13:51 | You look at it like this and then you think about it. |
| 00:13:52 | You look at it like this. |
| 00:13:53 | For now please explain it one more time. |
| 00:13:54 | If you do that, this will become the same, like last time. |
| 00:13:55 | Oh. That's right, huh? |
| 00:13:56 | Do you get it? |
| 00:13:57 | Yes. |
| 00:13:58 | If you look at it this way... you have to change the way you're thinking. |
| 00:13:59 | And if you look at it like this, and if it's a triangle with parallel lines drawn then... |
| 00:14:01 | Yes. |
| 00:14:02 | Which one is the same area as this triangle? |
| 00:14:04 | With which one? Tri- |
| 00:14:05 | The area that's the same as this triangle? |
| 00:14:08 | You won't get any numbers, right? |
| 00:14:09 | Yes. |
| 00:14:10 | And, for example, in what kind- what situations does this become a straight line? |
| 00:14:12 | A straight line? |
| 00:14:13 | Yes. We want to make it a straight line. |
| 00:14:14 | We want to make the border line a straight line. |
| 00:14:15 | A straight line? |
| 00:14:16 | Should I do it like this? |
| 00:14:17 | Hm. Hm? |
| 00:14:18 | [ Laughter ] |
| 00:14:19 | I don't understand what you are saying. |
| 00:14:20 | The triangle is the one that moves, okay? |
| 00:14:21 | The triangle? |
| 00:14:22 | So a triangle like this becomes a triangle like this? |
| 00:14:23 | Then when it goes to here does it become a straight line? |
| 00:14:24 | Oh. |
| 00:14:27 | What do you mean by a straight line? Oh. |
| 00:14:28 | It's at the end of the (inaudible), right? |
| 00:14:29 | I got it. |
| 00:14:30 | So. |
| 00:14:31 | I got it. I got it. Already. Already. I got it. |
| 00:14:32 | It's okay with this. |
| 00:14:33 | Is it correct with that- with that? |
| 00:14:34 | But you can't (inaudible). |
| 00:14:35 | With this. This- this original side. |
| 00:14:36 | The triangle and the area over here are the same. |
| 00:14:37 | Do you understand what I am saying? |
| 00:14:39 | This triangle. |
| 00:14:40 | Then doesn't it become the same as this figure? |
| 00:14:41 | Yes. Over here is the same from the beginning, okay? |
| 00:14:42 | It's not involved, right? |
| 00:14:43 | It's the same? |
| 00:14:44 | Because here. Right now only here is involved, right? |
| 00:14:45 | Oh. This is a straight line- oh. That's right. That's right. |
| 00:14:46 | Make it into a straight line. Did you get it? |
| 00:14:47 | So. |
| 00:14:48 | Jimbo hurry up. |
| 00:14:49 | Anything. |
| 00:14:50 | Please go ahead. |
| 00:14:51 | Now I can't explain it since I'm not Japanese. |
| 00:14:52 | Don't worry. We'll cheer for you. |
| 00:14:53 | Since I'm not Japanese. |
| 00:14:54 | Do it with confidence. |
| 00:14:55 | [ Laughter ] |
| 00:14:57 | Well, it's time, huh? Fifteen minutes. |
| 00:15:03 | I'm not Japanese. |
| 00:15:04 | What are you saying? |
| 00:15:11 | Then Ikeda will you do it? |
| 00:15:12 | Huh? |
| 00:15:14 | Please go ahead. |
| 00:15:15 | I don't know (inaudible). |
| 00:15:16 | Will you do it in the two ways for us? Then, Ikeda, this side. |
| 00:15:18 | Please draw this side. |
| 00:15:19 | Yes. |
| 00:15:20 | Jimbo, this side. |
| 00:15:21 | I draw it from bottom to top? No. From bottom to top is (inaudible). |
| 00:15:22 | Bottom? |
| 00:15:24 | [ Laughter ] |
| 00:15:25 | From right to left? |
| 00:15:26 | Oh. I'm sorry left to right. |
| 00:15:27 | Le- le- ft. |
| 00:15:28 | (inaudible) |
| 00:15:29 | From left to right. |
| 00:15:30 | Yes. Yes. Yes. Yes. Yes. |
| 00:15:31 | From right to left. |
| 00:15:32 | I want the one from the left. |
| 00:15:33 | Huh? Is that from right to left? |
| 00:15:34 | From the top? |
| 00:15:35 | Hurry. Hurry. Hurry. |
| 00:15:36 | Teacher. Please have Jimbo go first. |
| 00:15:39 | Yes. |
| 00:15:40 | Is it not okay with from the top? |
| 00:15:41 | Of course, it can be said, right? |
| 00:15:42 | It is okay from the top? |
| 00:15:43 | It's the same even from the top, right? The area, okay? You're sharp. |
| 00:15:46 | It's okay even if it's particularly from the top. |
| 00:15:47 | Oh, well. |
| 00:15:48 | What? You thought very hard? |
| 00:15:49 | Okay, go ahead. |
| 00:15:50 | Huh? |
| 00:15:51 | Can you explain it? |
| 00:15:52 | I want to explain it. |
| 00:15:53 | I'm to explain it? |
| 00:15:54 | The body is (inaudible). |
| 00:15:55 | Yes. |
| 00:15:56 | I see. |
| 00:15:57 | But- |
| 00:15:58 | Yes. |
| 00:15:59 | I got it. I got it. I can't go back. |
| 00:16:00 | What is it? |
| 00:16:01 | It's one minute, right? |
| 00:16:02 | Shut up. |
| 00:16:03 | Hm. Wait a second. I'm sorry. |
| 00:16:05 | Then I'll draw it for you so, okay? Mostly the same as the original. |
| 00:16:09 | Just the base. |
| 00:16:15 | Okay. |
| 00:16:16 | (inaudible) Is either one okay? |
| 00:16:17 | Whichever is fine. |
| 00:16:18 | Do you want to use a ruler? |
| 00:16:19 | I'll use it. |
| 00:16:21 | (inaudible) but I have only two. |
| 00:16:23 | It's the same as (inaudible), right? |
| 00:16:25 | Teacher. Pick me. Pick me. |
| 00:16:26 | Hm? Assistance, okay? Next, okay? Chiba. |
| 00:16:28 | I don't understand that. |
| 00:16:29 | Next, next. |
| 00:16:30 | That? |
| 00:16:31 | Yes. In the meantime today since Chiba, you are the main character, right? |
| 00:16:33 | You're cool, okay? Huh? |
| 00:16:34 | Well. Do the ones that are wrong because- |
| 00:16:36 | Do the ones that are wrong? |
| 00:16:38 | I don't mean that. (inaudible) |
| 00:16:40 | Huh? |
| 00:16:41 | [ Laughter ] |
| 00:16:42 | No... well, okay? That is okay? The mistake is what's important. |
| 00:16:45 | Why? |
| 00:16:46 | Huh? |
| 00:16:48 | Because okay? If people can do it from the beginning |
| 00:16:50 | then they don't have to come to school. |
| 00:16:51 | (inaudible) |
| 00:16:52 | Huh? |
| 00:16:53 | Just the left (inaudible). |
| 00:16:54 | It's not okay. What? Don't worry about me. It's you who is learning. |
| 00:16:57 | Hm. |
| 00:17:01 | Do it as fast as you can. |
| 00:17:02 | Fas- (inaudible). |
| 00:17:03 | Anyway do it fast. |
| 00:17:04 | Either one is fine. |
| 00:17:06 | Do it like as you did it. Your own method. |
| 00:17:12 | You shifted th- this to this side like this, huh? (inaudible) |
| 00:17:15 | Up to this side, right? Yes. That. |
| 00:17:17 | (inaudible) |
| 00:17:18 | Yes. |
| 00:17:21 | And make the triangle and parallel. |
| 00:17:24 | Oh. Oh. |
| 00:17:29 | Peace to that. |
| 00:17:30 | I won't do it. |
| 00:17:36 | What's up? Kada. What's up? Were you able to do it? Oh. You're sharp. |
| 00:17:41 | That's right. Lai, right? You got it right? Good. |
| 00:17:44 | Okay. Is this just this side? |
| 00:17:47 | It's also over here. |
| 00:17:48 | Yes. Right? |
| 00:17:50 | Oh? |
| 00:17:51 | I can't do it even with this. |
| 00:17:52 | This is okay? Is it okay? |
| 00:17:53 | This isn't parallel, right? It's bent, right? |
| 00:17:58 | It's bent, right? That means that for example |
| 00:18:01 | when you have drawn it like this, okay? |
| 00:18:04 | When you have drawn it like this, of the area over here and |
| 00:18:06 | the area over here, which seems to be bi- bigger? |
| 00:18:07 | Since it's bent like this, okay? |
| 00:18:11 | The area over here and over here. |
| 00:18:12 | Over here. |
| 00:18:13 | It seems to be sma- smaller, huh? |
| 00:18:14 | If it's between over here and over here which seems to be smaller? |
| 00:18:18 | Doesn't it seem somewhat that they are the same, huh? Seems somewhat? |
| 00:18:20 | I'll give up A B. |
| 00:18:22 | Yes. |
| 00:18:23 | It doesn't seem like it? If this is parallel then |
| 00:18:25 | don't you think it's okay with this? I think it's okay- okay but. |
| 00:18:28 | Oh. |
| 00:18:29 | They aren't parallel, right? They are bent like this, right? |
| 00:18:31 | All you have to do is draw it more exaggerated. In a figure like this, okay? |
| 00:18:34 | Um. For example, if there is one like this and okay? |
| 00:18:36 | When we cut it like this and did it... |
| 00:18:37 | Now. It's okay. |
| 00:18:39 | The base is the same. |
| 00:18:41 | How is that? |
| 00:18:42 | Are the areas of the triangles the same? |
| 00:18:44 | Over here and over here are the same. |
| 00:18:46 | Over here and over here are also the same. |
| 00:18:47 | I think it's better if we don't let him/her do it. |
| 00:18:48 | What? [ Laughter ] |
| 00:18:49 | The end and the end are the same and- |
| 00:18:51 | It's okay if this and this are the same, right? |
| 00:18:53 | This and this are the same and... |
| 00:18:54 | this and this are the same- ahh, which is it? |
| 00:18:56 | Oh. It's this. It's okay if these are the same but. The same- oh, it's wrong. |
| 00:18:59 | It's over here. I'm sorry. It's okay if this and this are the same, right? |
| 00:19:01 | It's not the same. |
| 00:19:02 | Well, I don't understand something, but- Hm. |
| 00:19:06 | Oh. I'm sorry. |
| 00:19:08 | Then- oh, it took a little bit of time, huh? Okay. |
| 00:19:09 | I'm saying you can't draw it. |
| 00:19:10 | Okay. Good. |
| 00:19:11 | Stop it. |
| 00:19:12 | Stop it, okay? |
| 00:19:13 | Stop it, okay? |
| 00:19:14 | Okay, then. Please return to your seats. |
| 00:19:15 | Teacher, he's drawing extra things. |
| 00:19:16 | Don't write it. |
| 00:19:17 | Teacher. This. |
| 00:19:18 | Okay, then the explanation. It'll take too much time. |
| 00:19:20 | Okay then. Everyone please return once to your seats. |
| 00:19:22 | Okay. |
| 00:19:23 | Since they are equal, so- |
| 00:19:25 | It's okay. Good luck. |
| 00:19:28 | Okay, then. |
| 00:19:29 | Am I doing it? |
| 00:19:30 | Yes. Good luck. |
| 00:19:31 | I don't understand it very well. Teacher, please listen to me. |
| 00:19:35 | Now it's time to listen. |
| 00:19:37 | Pay attention, okay? Okay. |
| 00:19:38 | He's not listening. |
| 00:19:39 | Jimbo. |
| 00:19:40 | Go ahead. |
| 00:19:41 | Is Chiba going to do it? |
| 00:19:42 | It's not me, right? |
| 00:19:43 | Okay. Hurry. Please do it. |
| 00:19:45 | This is okay? |
| 00:19:47 | Hm. First of all we make a triangle, okay? |
| 00:19:50 | [ Laughter ] |
| 00:19:52 | What are you saying? |
| 00:19:53 | You talk too much. |
| 00:19:54 | [ Laughter ] |
| 00:19:55 | You make a triangle, right? And then here... |
| 00:19:57 | His face is completely in the camera. |
| 00:19:58 | (inaudible)'s... |
| 00:19:59 | (inaudible) |
| 00:20:00 | (inaudible) |
| 00:20:01 | Draw a line para- para- parallel over here also and... |
| 00:20:03 | we make over here as the base. |
| 00:20:08 | As the base. Here. |
| 00:20:10 | Yes. |
| 00:20:11 | And then we make it the height and this triangle and... |
| 00:20:15 | That's the height? (inaudible) |
| 00:20:16 | Okay? |
| 00:20:18 | Which is it? |
| 00:20:19 | I think it's not that. |
| 00:20:20 | This triangle and a tri- somewhere. |
| 00:20:24 | [ Laughter ] |
| 00:20:25 | Uhm. The red triangle. |
| 00:20:26 | Oh. It's this, right? |
| 00:20:27 | Yes. |
| 00:20:28 | The red triangle is- |
| 00:20:30 | The area is... |
| 00:20:31 | Over here. Over here. Over here. |
| 00:20:32 | What is it? |
| 00:20:33 | Ya- |
| 00:20:34 | Well, they are the same, okay? |
| 00:20:35 | [ Laughter ] |
| 00:20:36 | The tri- over here. |
| 00:20:37 | Actually and the triangle over here- |
| 00:20:38 | Yes. |
| 00:20:41 | The fact is that the areas are the same, okay? |
| 00:20:42 | Hm. |
| 00:20:43 | Since the base and the height are the same so. |
| 00:20:46 | So� first of all... the fact is, we can draw a line here. |
| 00:20:50 | Yes, yes. Well, I don't know what I am saying, but- |
| 00:20:51 | (inaudible) |
| 00:20:54 | [ Laughter ] |
| 00:20:55 | No. We can understand enough, right? |
| 00:20:56 | Oh. You understand? |
| 00:20:57 | Is there anybody who does not understand? |
| 00:20:58 | [ Laughter ] |
| 00:20:59 | Oh. You don't understand? |
| 00:21:01 | I also don't understand. |
| 00:21:02 | You don't understand? Then one more time then. With this side. |
| 00:21:05 | This time please explain it, Ikeda. You're saying that it was a good explanation. |
| 00:21:07 | Okay, then applause. Wonderful. |
| 00:21:08 | Okay. |
| 00:21:10 | [ Laughter ] |
| 00:21:11 | People who didn't understand it please listen to it closely, okay? |
| 00:21:12 | First of all... |
| 00:21:13 | [ Laughter ] |
| 00:21:14 | After this. The place that has a weird place like this. |
| 00:21:15 | I got it. |
| 00:21:20 | In the place that is below this, like this draw a line and, |
| 00:21:24 | uhm, we make it into a triangle, okay? Ha- then this- |
| 00:21:29 | This. Something that has this side as a base? |
| 00:21:33 | That has it as a base? |
| 00:21:36 | Draw a line that is parallel to this base by |
| 00:21:40 | fitting it with this apex. And then the parallel line... hm? |
| 00:21:51 | Since the length of base doesn't change so... |
| 00:21:54 | and in between the parallel lines always- |
| 00:21:57 | The height is e- |
| 00:21:58 | The height doesn't change so... like this. Up to wherever you draw it, anywhere you draw it, |
| 00:21:59 | Yes. |
| 00:22:05 | the area doesn't change with this, this triangle that we got first. |
| 00:22:11 | So, uhm, it's just that even if we draw up to this best place's- end, |
| 00:22:17 | for this triangle and this yellow, this triangle, the areas don't change. |
| 00:22:24 | Okay. Thank you. Wonderful. |
| 00:22:27 | Okay. |
| 00:22:30 | Okay. Uhm, for now, okay? Since it's hard to see we will make it clearer. |
| 00:22:34 | The areas of this triangle and the red triangle over here, |
| 00:22:37 | and this triangle and the yellow triangle over here are the same areas. |
| 00:22:40 | So we want to do it so this here becomes straight like this, okay? |
| 00:22:43 | So that the corner here is gone. The angle, okay? |
| 00:22:45 | Then we were able to draw a straight line here. |
| 00:22:47 | That's what we can say. People who were able to d- who did it like this? |
| 00:22:50 | People who can say I drew it like this over here? |
| 00:22:51 | People who say I was able to draw it. |
| 00:22:53 | People who say I was able to do it like this way? People who say they were able to do both? |
| 00:22:56 | Okay. That's good. Uhm, then, okay? Next, uhm, |
| 00:22:59 | using this as a foundation, okay? |
| 00:23:03 | Oh. I don't know if it's using it as a foundation or not but- A quadrilateral. |
| 00:23:05 | Oh. Of course it can be crooked like this. |
| 00:23:07 | Well for now, um, (inaudible) quadrilateral. |
| 00:23:12 | Taking this quadrilateral... |
| 00:23:15 | without changing the area... make it into a triangle. |
| 00:23:24 | This shape of the quadrilateral, |
| 00:23:26 | without changing the area, please try making it into a triangle. |
| 00:23:32 | Okay, then... please think for three minutes |
| 00:23:36 | and try doing it in your own way. Okay begin. |
| 00:23:38 | We can't open our textbooks? |
| 00:23:40 | Right? |
| 00:23:41 | This (inaudible). |
| 00:23:43 | Teacher, can we open our textbooks, yet? |
| 00:23:45 | Hm? The textbooks? First try thinking about it by yourselves. |
| 00:23:48 | Okay? |
| 00:23:49 | You know that it was in the textbook, huh? |
| 00:24:05 | You're sharp, huh? |
| 00:24:32 | You're sharp. |
| 00:24:40 | We- well Maehata. |
| 00:24:47 | You can't do it with it just as it is, right? |
| 00:24:48 | I don't change this? |
| 00:24:49 | Uh huh. It's a quadrilateral, right? If it becomes wha- |
| 00:24:51 | what sided shape can you do the problem? |
| 00:24:53 | Triangle. |
| 00:24:54 | Yes. |
| 00:24:56 | If it becomes- what sided shape can you do the problem? |
| 00:25:00 | If it's just as it is it's a quadrilateral, right? |
| 00:25:02 | So we're to make a quadrilateral into a triangle? |
| 00:25:03 | Yes. |
| 00:25:04 | Right? If everybody had a triangle and parallel lines |
| 00:25:06 | then they can do it, huh? |
| 00:25:08 | Huh? |
| 00:25:10 | That's right. You're sharp. |
| 00:25:16 | That's good. |
| 00:25:18 | Hm. That's right, that's right, that's right. |
| 00:25:20 | You noticed a good point. That's right. That's right. That's right. That's right. |
| 00:25:23 | Teacher, the one we call the triangle isn't just one? |
| 00:25:24 | Huh? |
| 00:25:25 | One? |
| 00:25:26 | No. |
| 00:25:27 | In addition? |
| 00:25:28 | It may be that you can get many types, huh? |
| 00:25:29 | Is it okay with two? |
| 00:25:30 | It's okay even if it's two types or even it's three types. |
| 00:25:32 | Okay? |
| 00:25:34 | Bando. You're sharp. |
| 00:25:35 | Huh? |
| 00:25:36 | You're quite sharp. |
| 00:25:37 | What do we need to do to change this into that? How can we do it? |
| 00:25:41 | Triangle. |
| 00:25:42 | Triangle and yes. That's right, huh? |
| 00:25:45 | Since you can't do it just as it is so. |
| 00:25:48 | What are you saying. |
| 00:25:51 | Hm. |
| 00:25:52 | Oh. That's sharp, huh? You noticed a good point. |
| 00:25:55 | A triangle has been made, right? Then, okay? |
| 00:25:58 | When you look at it like this |
| 00:26:00 | then there is a triangle |
| 00:26:02 | and how can we change it, may I ask? |
| 00:26:04 | Hm? |
| 00:26:07 | Huh? |
| 00:26:08 | For example, do you want to think about it with the triangle over he- over here? |
| 00:26:10 | What did we have to do to make a triangle that has |
| 00:26:13 | the same area as this triangle, may I ask? |
| 00:26:15 | Can't you use what you saw on the TV screen. |
| 00:26:19 | That's right, huh? That's right, huh? Yes. (inaudible) |
| 00:26:22 | nicely at the bottom. |
| 00:26:27 | Are there anymore other than this one? |
| 00:26:28 | The fact that you can get one on this side means that... |
| 00:26:31 | then if we extend it a little like this then... huh? |
| 00:26:34 | The fact that you got one like this means that... |
| 00:26:37 | Can't you make one on this side? |
| 00:26:40 | Okay? |
| 00:26:43 | Teacher. Teacher. |
| 00:26:44 | Are you done? You're sharp. |
| 00:26:47 | Then people who are done |
| 00:26:49 | please go to Instructor Ebina again. |
| 00:26:50 | And, uhm, then people who want hints |
| 00:26:52 | I will leave hint cards here |
| 00:26:53 | so please look at them and try doing it. |
| 00:26:55 | It's also fine to do it with your friends. |
| 00:26:58 | Okay begin. |
| 00:27:02 | Uhm. It's also fine for people who don't understand |
| 00:27:04 | to ask me. |
| 00:27:08 | Oh. But I don't think it's limited to one (inaudible). |
| 00:27:10 | There is one more. |
| 00:27:16 | Teacher. |
| 00:27:17 | Yes. |
| 00:27:18 | This is okay? |
| 00:27:19 | Yes. |
| 00:27:20 | How many? How many do I make? |
| 00:27:21 | I wonder how many can you make? |
| 00:27:23 | Is it okay with one? |
| 00:27:24 | Hm? |
| 00:27:25 | (inaudible) |
| 00:27:26 | Yes. It's okay if first of all you get one, but- |
| 00:27:29 | With one zero. |
| 00:27:30 | Is one all you made? |
| 00:27:31 | (inaudible) |
| 00:27:32 | In all? There's three. |
| 00:27:37 | How many can we make? This? |
| 00:27:38 | Hm. I wonder how many all of you can mak- make. |
| 00:27:40 | Oh, I see. That's what you mean. |
| 00:27:41 | Yes. The answer is not just one. |
| 00:27:53 | Oh. That's right, huh? Oh. That's right, huh? Oh. |
| 00:27:59 | I got it. |
| 00:28:00 | (inaudible) |
| 00:28:02 | It's fine with this, right? |
| 00:28:14 | Huh? It's wrong. |
| 00:28:15 | Huh? |
| 00:28:17 | Now. The ones I haven't got yet teacher (inaudible). |
| 00:28:25 | Wonderful. |
| 00:28:34 | Teacher. That's unfair. |
| 00:28:36 | There is no possibility. |
| 00:28:45 | Excuse me. It's okay with this, right? |
| 00:28:46 | Yes. If you got one on this side then- |
| 00:28:49 | (inaudible) I can get it over here and over here from this- |
| 00:28:50 | Hum? |
| 00:28:51 | You can do that too. And can't you make a triangle |
| 00:28:53 | over here that is the same as this? |
| 00:28:56 | Well that's right, huh? |
| 00:28:57 | Right? The same as before. |
| 00:28:58 | You can get it on the opposite side, right? |
| 00:28:59 | Would I know all of them doing it like that? |
| 00:29:01 | Hm. You'll notice them- If you notice them then that will be great. |
| 00:29:02 | Am I supposed to draw all of them? |
| 00:29:04 | I wonder how many ways it can be made? |
| 00:29:05 | Eight. |
| 00:29:06 | You're sharp. |
| 00:29:25 | I think it's the same area as this quadrangle |
| 00:29:28 | of the hint card and the notebook. |
| 00:29:33 | You're advanced to a good place in the problem. |
| 00:29:36 | Yes. |
| 00:29:37 | I got it. I got it. I got it. |
| 00:29:38 | Are you going to make it into an upright state? |
| 00:29:41 | Are you going to fold it like this? |
| 00:29:47 | If you have folded this then, okay? What kind of shape will it become? |
| 00:29:48 | Yes. |
| 00:29:49 | It won't at least overlap, right? |
| 00:29:50 | Yes. |
| 00:29:51 | I got it. |
| 00:29:52 | Well. |
| 00:29:53 | Because (inaudible). |
| 00:29:54 | Yes. You've gotten up to a good place in the problem. |
| 00:29:55 | But after th- that I'm having problems. |
| 00:29:56 | Yes. Then okay? |
| 00:29:57 | Yes. |
| 00:29:58 | If this corner- for example it's good if the corner here was gone, right? |
| 00:30:03 | I'll draw a line longer here, okay? Ones that are same as the area of this. |
| 00:30:08 | Things like these dr- are also the same, right? |
| 00:30:10 | Things like these are also the same, right? There's a lot, right? |
| 00:30:12 | For example, if the corner here becomes straight with this here and here then this is... |
| 00:30:16 | Teacher. |
| 00:30:17 | Parallel. (inaudible) |
| 00:30:18 | Does it have to be teacher Ebina who looks over my work? |
| 00:30:19 | Wai- It's okay to come to me to have your work looked at. |
| 00:30:20 | Triangle. |
| 00:30:21 | The fact is we're making a triangle- a quadrangle into a triangle you do what to one angle? |
| 00:30:23 | Nagai. It's because there's a lot of people waiting in line for teacher Ebina. |
| 00:30:26 | Reduce. |
| 00:30:27 | All you have to do is decrease it, right? That means that to reduce angles you take one- |
| 00:30:32 | Parallel. |
| 00:30:33 | Yes. We have to make it straight, right? Then you get a triangle like this. A triangle like this. And also? |
| 00:30:37 | (inaudible) It's okay with this line segment. |
| 00:30:40 | If you get one over here then this time also on this side... |
| 00:30:42 | Yes. We get the same thing. Okay? Are there any others? You can also do this side, right? |
| 00:30:44 | The same thing. |
| 00:30:47 | Teacher. |
| 00:30:48 | Please think about it in many ways. |
| 00:30:49 | It's not just one, right? Is it okay with this? |
| 00:30:51 | If you notice this one then, okay? |
| 00:30:52 | You'll also notice the one over here, huh? |
| 00:30:53 | You'll notice it, right? |
| 00:30:54 | [ Laughter ] |
| 00:30:55 | Why can't you d- it when you know it? |
| 00:30:58 | Hm. Ohba, how are you doing? |
| 00:31:00 | Hm. You've gotten to a good place in the problem, huh? |
| 00:31:03 | The fact that we're making a quadrilateral into a triangle means what happens to the number of angles? |
| 00:31:10 | I don't understand. |
| 00:31:11 | Hm. The number of angles goes from four to... |
| 00:31:13 | Three. |
| 00:31:14 | It becomes three, right? It's reduced by one, right? That means that here, |
| 00:31:20 | it's good if the angle in this quadrilateral is gone. For example, if here were to become straight. |
| 00:31:24 | Draw a parallel line and. |
| 00:31:26 | You get a triangle like this? Do you understand? Here and here are the same, right? |
| 00:31:31 | This okay? How about this side? Can't we make somewhere? Straight like this? |
| 00:31:37 | (inaudible) |
| 00:31:43 | How will it be I wonder? |
| 00:31:47 | Are you done? |
| 00:31:48 | I have gotten only one yet. |
| 00:31:49 | Then would you draw four. |
| 00:31:50 | Ahh. Can I borrow four. Ah. We don't have time. Ti- |
| 00:31:51 | Where do I draw it? |
| 00:31:57 | Teacher, I don't understand it very well, but- |
| 00:31:59 | Hm, okay? |
| 00:32:00 | There's eight. |
| 00:32:01 | Do you have your notebook? |
| 00:32:02 | I do. |
| 00:32:03 | Hm. |
| 00:32:04 | Then look at it. Teacher. |
| 00:32:07 | What is it? Snobbishly. (inaudible) |
| 00:32:13 | If it has become this, then can we do it? |
| 00:32:16 | You can't do it as it is a quadrilateral? |
| 00:32:19 | It's this. |
| 00:32:20 | Yes. |
| 00:32:21 | It's okay? |
| 00:32:23 | And also? |
| 00:32:25 | Here? |
| 00:32:26 | Don't you have to draw a parallel line to the triangle? |
| 00:32:29 | It's here. |
| 00:32:30 | Triangle and- hm. |
| 00:32:31 | Here? |
| 00:32:32 | Yes. |
| 00:32:33 | Teacher. |
| 00:32:34 | That's funny you know? |
| 00:32:36 | Then- wait a moment. I'm sorry, okay? |
| 00:32:39 | Then where is the tri- quadrilateral, oh, |
| 00:32:41 | triangle that's equal to the area here? Hm. |
| 00:32:43 | Here. |
| 00:32:44 | No, it's not. Since it's parallel like this so |
| 00:32:48 | in the parallel lines where is the qua-... that's equal to here? |
| 00:32:51 | This is a little off. Teacher. |
| 00:32:52 | Hm. That's right. It becomes more off. |
| 00:32:54 | Hm. (inaudible) here and here and (inaudible) to here. |
| 00:32:57 | Hm. Hm. You drew this and this? |
| 00:33:00 | Then okay? If you have drawn it on this side, okay? |
| 00:33:02 | Isn't there one more parallel line- a triangle? |
| 00:33:04 | Huh? |
| 00:33:05 | You cut it doing like this- doing it like this- |
| 00:33:06 | into two- doing it like this, right? The triangle is over here, right? |
| 00:33:08 | Then also over here. |
| 00:33:10 | If you cut it like this, then here with this |
| 00:33:12 | one diagonal line, would you get a triangle just over here? |
| 00:33:14 | I can do this. |
| 00:33:15 | And it comes over here and- |
| 00:33:16 | Yes. |
| 00:33:17 | Over here is also (inaudible). |
| 00:33:18 | Is it just over here? Won't it extend to this side? |
| 00:33:22 | Look. |
| 00:33:24 | You noticed things like this on this side, right? |
| 00:33:25 | Uh huh. |
| 00:33:26 | Then. This area and over here are the same, right? |
| 00:33:28 | Isn't there anything like this over here, okay? |
| 00:33:30 | Oh. Oh, oh, oh. |
| 00:33:32 | Hm? Oh. It's over here, huh? Over here. Over here. |
| 00:33:34 | Things like this. (inaudible) On this side. |
| 00:33:35 | Oh. |
| 00:33:36 | Oh. That's right, huh? |
| 00:33:37 | Right? If there is a right side then there is a left side also, right? |
| 00:33:39 | (inaudible) How about this? |
| 00:33:40 | Yes. Then triangles that are the same with this area are, |
| 00:33:43 | hm� there are a lot of these, right? |
| 00:33:46 | Ones like this. |
| 00:33:47 | Many different kinds. |
| 00:33:49 | And the fact that we're making a quadrilateral into a triangle means that we do what to one angle? |
| 00:33:51 | Get rid of it. |
| 00:33:52 | All you have to do is get rid of it, right? |
| 00:33:53 | Please get rid of one somewhere. When it moves to where would it disappear? |
| 00:33:54 | It's an interesting thought, huh? That's good, huh? I like ones like that. Well please think with this. In total there's a lot more. Good. |
| 00:33:57 | Yes. Here if you make this straight like this then this angle disappears, right? |
| 00:34:02 | This is one answer, right? The one before this one. Triangles like this. Also? |
| 00:34:07 | If there is one on this side then how about this side? |
| 00:34:09 | Yes. |
| 00:34:10 | Oh. |
| 00:34:11 | Hm. Where is it? |
| 00:34:12 | Here if there is one then- |
| 00:34:15 | Yes. |
| 00:34:16 | It's somewhere here, huh? |
| 00:34:17 | That's right. That's right. That's right. That's right. |
| 00:34:20 | That's right (inaudible) keeps on bending and the angle disappears. |
| 00:34:22 | Here? |
| 00:34:23 | Hm. Since we want to lose this angle so this... hm, isn't it a little bent? |
| 00:34:29 | Did you get it? |
| 00:34:31 | Yes. That's right. That's right. That's right. You're at a good point, |
| 00:34:34 | and then we want to get rid of this angle, right? From four to three. If it becomes like this then this angle? |
| 00:34:37 | It disappears. |
| 00:34:38 | It disappears, right? |
| 00:34:39 | Yes. |
| 00:34:40 | And if you get one on this side, then this time can't you also get it on this side? |
| 00:34:42 | Yes. |
| 00:34:44 | Am I to draw all of these? |
| 00:34:46 | This. This. |
| 00:34:47 | Phuse. For this there are t- two more, more. |
| 00:34:49 | Is it okay to change some? |
| 00:34:50 | Hm? |
| 00:34:51 | One that is a new (inaudible). |
| 00:34:52 | Why? |
| 00:34:53 | You're kidding. |
| 00:34:54 | You found a new one? That's good. |
| 00:34:55 | Then would you draw it then like this? If you have another one. |
| 00:34:57 | Well, it's okay with it here. |
| 00:34:58 | Hm. Please draw it. It's okay, it's correct. |
| 00:35:00 | (inaudible) |
| 00:35:02 | Can you shrink it? |
| 00:35:03 | Uh, well... |
| 00:35:04 | Well you don't understand it well? |
| 00:35:06 | But you were able to do it? You made this |
| 00:35:08 | triangle and this the same, right? |
| 00:35:11 | This. Then can't you get one on this side? |
| 00:35:13 | Still. Still how do I get it? |
| 00:35:15 | You don't understand it well? Is it okay? |
| 00:35:18 | There is something like this here, right? A triangle, huh? |
| 00:35:21 | Then how many triangles are there that are the same as this triangle? |
| 00:35:25 | The ones we call triangle's ar- triangles that are the same as this triangle's area. |
| 00:35:30 | There are ones like this and there are ones like this |
| 00:35:32 | and the fact is there are a lot of them. |
| 00:35:34 | Also a lot of them over here. Oh. This is. This. |
| 00:35:37 | If you look at it like this then it's a triangle and parallel lines, right? |
| 00:35:39 | And to fix triangles into quadrilaterals- Oh, I'm sorry. |
| 00:35:41 | The fact that we're making a quadrilateral into a triangle means... |
| 00:35:44 | all we have to do is reduce the angles by one, right? |
| 00:35:47 | That means that if this becomes straight, |
| 00:35:49 | then the angle here disappears, so you get |
| 00:35:52 | a triangle like this. |
| 00:35:54 | Then on the other side. |
| 00:35:55 | Then is this the only triangle that we can get? |
| 00:35:58 | Oh. |
| 00:36:00 | Teacher. Will methods like these also work- Oh, I'm sorry. |
| 00:36:04 | Yes. That's right, huh? You can also do that, right? |
| 00:36:06 | Can I also do that? |
| 00:36:08 | Hm? |
| 00:36:11 | But, this is triang- |
| 00:36:12 | It hasn't become a diagonal line. |
| 00:36:14 | Quadrilateral. Quadrilateral. |
| 00:36:15 | It's no good if it's a quadrilateral. It hasn't changed at all. |
| 00:36:16 | Teacher. I'll also do one for you. |
| 00:36:17 | First of all this diagonal line like this. |
| 00:36:18 | Triangle like these are (inaudible) okay? |
| 00:36:19 | Please do a different one. |
| 00:36:20 | It's like this. |
| 00:36:21 | Uhm. |
| 00:36:22 | The diagonal line isn't done, okay? |
| 00:36:23 | In the end this is- |
| 00:36:24 | Just now I made a little mistake. |
| 00:36:25 | You made a mistake? |
| 00:36:26 | Which diagonal line? |
| 00:36:28 | Hey, you. This isn't good if it's the middle point. |
| 00:36:29 | Huh? |
| 00:36:30 | It's not good if it's the middle point. It's not a triangle. This. |
| 00:36:31 | [ Laughter ] |
| 00:36:32 | Like this, like this. |
| 00:36:33 | Huh? |
| 00:36:34 | I don't understand this. |
| 00:36:35 | You drew it like this? |
| 00:36:36 | It's not a triangle. |
| 00:36:37 | This becomes straight and- |
| 00:36:38 | Oh. |
| 00:36:39 | That's wrong. That's wrong. That's wrong. |
| 00:36:40 | Oh. Over here? Huh? |
| 00:36:41 | This is where it's supposed to be straight, okay? |
| 00:36:42 | That's right. Straight. |
| 00:36:43 | It doesn't look straight, okay? |
| 00:36:44 | This. Straight. |
| 00:36:45 | Oh. That's right. That's right. That's right. Hey, it's crooked. |
| 00:36:47 | Like this. |
| 00:36:48 | If it's that, it's okay. Okay, okay, okay. Please have it drawn neatly. |
| 00:36:51 | Two. |
| 00:36:53 | How many methods have you found? |
| 00:36:55 | I don't know yet up to where I did. |
| 00:36:57 | You don't know anymore? The reasons? Yes. Quoi. |
| 00:36:59 | You've gotten to a good point in the problem. Then okay? |
| 00:37:02 | Since we're making a triangle into a quadri- oh, |
| 00:37:03 | I'm sorry a quadrilateral into a triangle- |
| 00:37:04 | So all you have to do is get rid of one angle okay? |
| 00:37:06 | For example, if you do it like this how is it? |
| 00:37:08 | Is better over here? |
| 00:37:10 | For example, when this becomes straight how about it? |
| 00:37:14 | If it becomes like this? |
| 00:37:17 | Also what do I do? |
| 00:37:19 | How about a triangle like this? |
| 00:37:20 | The area of the triangle over here is the same, right? This triangle and |
| 00:37:25 | this triangle are the same, right? This has become straight, right? |
| 00:37:28 | Then this becomes a triangle, right? |
| 00:37:30 | Do you understand? The problem? |
| 00:37:31 | Are you okay? Is there another one? |
| 00:37:34 | Yes. Then if you make this straight over here then |
| 00:37:36 | what kind of triangle will it be? |
| 00:37:37 | [ Laughter ] |
| 00:37:39 | Yes. Oh, you're making two triangles, huh? |
| 00:37:43 | Hm? It's good if you make it into- a triangle. |
| 00:37:45 | Just like before draw a line somewhere and try making a triangle. |
| 00:37:48 | If you draw a line wh- where then would you get a triangle? |
| 00:37:54 | It's like this, right? It's like this or like this, huh? |
| 00:37:56 | Area. Okay? What's up? |
| 00:37:59 | How many methods did you get? |
| 00:38:00 | Still only two. |
| 00:38:01 | First of all this is correct, huh? |
| 00:38:02 | No. Something. I thought something might be wrong. |
| 00:38:04 | Hm. Hm. Hm? You said it might be wrong. |
| 00:38:05 | Why did you think it might be wrong? |
| 00:38:06 | Something. The base (inaudible). |
| 00:38:08 | The question is where to put the base, right? |
| 00:38:11 | That's right. That's right. That's right. That's right. You're sharp. |
| 00:38:13 | Huh? Huh? |
| 00:38:14 | (inaudible) just us. |
| 00:38:15 | You're so noisy. Why don't you shut up? |
| 00:38:18 | She is so scary. |
| 00:38:20 | I'm not scary. |
| 00:38:26 | Chiba. How many methods did you get? |
| 00:38:28 | Two. |
| 00:38:29 | You got two, right? |
| 00:38:30 | Yes. You're done, right? |
| 00:38:33 | Yes. That's right. That's right. That's right. |
| 00:38:35 | It's good, okay? Then is it over with these with two? |
| 00:38:38 | Then how about this side? This side? |
| 00:38:40 | Isn't there one that's the same as this triangle? |
| 00:38:48 | How many did you get Ryu? |
| 00:38:50 | Are you worried thinking about it? |
| 00:38:51 | One. |
| 00:38:52 | You were able to get one? This okay? |
| 00:38:55 | You got it, right? Something like this. |
| 00:38:57 | You got something like this, right? |
| 00:38:58 | Yes. |
| 00:38:59 | One that is the same as this, is this, right? |
| 00:39:00 | Yes. |
| 00:39:01 | Is the area that is the same as this triangle just this? |
| 00:39:02 | Sada. It's better to slide it to the other side. |
| 00:39:05 | Is it this? |
| 00:39:06 | Hmm. That's good, huh? |
| 00:39:07 | Hm. |
| 00:39:08 | Hm? Can't you make one on th- this side? |
| 00:39:09 | This side (inaudible) a lot. |
| 00:39:10 | Yes. I can. |
| 00:39:11 | You can, right? With that for now it will be two methods, right? |
| 00:39:13 | It doesn't look like it. It doesn't look like it. It doesn't look like it. |
| 00:39:15 | Did you understand the meaning? |
| 00:39:17 | Then is it just this side where we can draw parallel lines? |
| 00:39:20 | Over here? |
| 00:39:21 | You can draw it, right? |
| 00:39:22 | It's easy to see, huh? |
| 00:39:23 | Hm. |
| 00:39:24 | How about it? Are you done? |
| 00:39:25 | Yes. |
| 00:39:26 | Oh. |
| 00:39:27 | How many methods did you get? |
| 00:39:28 | Only two yet. |
| 00:39:29 | Two? |
| 00:39:32 | You found ones like these? Hm? This. Hm? Which is it? |
| 00:39:36 | One like this and- |
| 00:39:37 | And this. This. |
| 00:39:38 | Yes. |
| 00:39:41 | Oh. Over here, huh? |
| 00:39:42 | Hm. |
| 00:39:43 | Then, okay? There are parallel lines like this, right? |
| 00:39:46 | If the one that is the same as this triangle is this, then also at this side, |
| 00:39:51 | you got it huh? |
| 00:39:52 | (inaudible) [ Laughter ] |
| 00:39:54 | You want to do it? |
| 00:39:56 | Then would you do one of a different type? After you look for it. |
| 00:39:58 | I found eight. |
| 00:39:59 | Hm? |
| 00:40:00 | Eight. Eight. |
| 00:40:01 | Eight? You noticed the fact that there are eight? Splendid. |
| 00:40:08 | Oh. That's good, huh? Uh, you're doing well. |
| 00:40:12 | Are there others, Taniguchi? |
| 00:40:15 | Hm? |
| 00:40:16 | Then okay? Which ones did you get? This and... one like this and one like this, huh? |
| 00:40:22 | Now then, is it just this side where we can draw parallel lines? |
| 00:40:25 | This side. |
| 00:40:26 | You can also draw them over here, right? Then can't you transform this triangle? |
| 00:40:30 | Over here. |
| 00:40:31 | Yes. If you draw it over here, then the area that is the same as this triangle is... |
| 00:40:35 | this original figure has become somewhat harder to understand but- |
| 00:40:38 | This (inaudible). |
| 00:40:39 | Yes. Then it's okay to draw one more- one more or. |
| 00:40:46 | Hm. |
| 00:40:48 | That's good. This, okay? |
| 00:40:52 | You did it so it says this triangle and the triangle over here are the same, right? |
| 00:40:54 | Is it just this side where you can get it? |
| 00:40:56 | Over here also. |
| 00:40:57 | Hm? |
| 00:40:59 | Over here. |
| 00:41:00 | On this side? |
| 00:41:01 | We can do it. |
| 00:41:02 | We can do it, right? Then we can do it over here, right? |
| 00:41:04 | Then how about this? Is it just this side where we can do it? |
| 00:41:05 | This side. |
| 00:41:06 | We can do this side also, right? How about this? |
| 00:41:08 | Oh. You were able to do this. Over here. Hm? |
| 00:41:10 | No. |
| 00:41:15 | This is- you drew it like this and oh, |
| 00:41:17 | you drew it like this? Yes. Yes. Yes. This is good, huh? Oh. |
| 00:41:20 | This- it's the same as this, huh? |
| 00:41:21 | Draw over here and you can do this, right? If you do that. |
| 00:41:25 | You've gotten to a good point in the problem. |
| 00:41:37 | You found eight? |
| 00:41:38 | Yes. |
| 00:41:39 | That's amazing. |
| 00:41:40 | Eight? |
| 00:41:41 | How many did you get? |
| 00:41:42 | Huh? |
| 00:41:43 | How many did you get? |
| 00:41:44 | Huh? |
| 00:41:45 | How many? One. Did you get one? It's okay if you get one. |
| 00:41:46 | I could only get one. |
| 00:41:49 | Okay? You were close in getting the other, huh? |
| 00:41:51 | How did you get one? |
| 00:41:52 | Can I borrow this of yours, Usui? |
| 00:41:53 | No way. |
| 00:41:54 | Hm. Oh. It's okay, right? You got one, right? |
| 00:41:56 | Yes. |
| 00:41:57 | Then these are parallel, right? |
| 00:41:58 | Which? |
| 00:41:59 | This. This is parallel, right? This and this. |
| 00:42:00 | Huh? This? |
| 00:42:01 | Yes. |
| 00:42:02 | Then the triangle and this orange-colored object is the same, right? |
| 00:42:03 | Yes. |
| 00:42:04 | Then do you get it only on this side? |
| 00:42:05 | No. |
| 00:42:06 | Which side? |
| 00:42:07 | This side also. |
| 00:42:08 | Hm? We can get it over here also, right? |
| 00:42:10 | Already you found two. |
| 00:42:11 | Yeah. Oh. Is it that? |
| 00:42:12 | Yes. |
| 00:42:14 | Oh. With here (inaudible), huh? |
| 00:42:18 | (inaudible) Oh. That's terrible of you. (inaudible) |
| 00:42:22 | Is it okay? This? |
| 00:42:23 | I can see this. |
| 00:42:24 | That's terrible. |
| 00:42:25 | [ Laughter ] (inaudible) |
| 00:42:26 | That's terrible. |
| 00:42:27 | [ Laughter ] |
| 00:42:28 | (inaudible) |
| 00:42:29 | That's terrible. |
| 00:42:30 | (inaudible) |
| 00:42:31 | Huh? |
| 00:42:32 | The fact about selecting our class is a mistake. |
| 00:42:33 | [ Laughter ] |
| 00:42:34 | It's an excellent class right? |
| 00:42:37 | One more. Lastly... would you do it for us, okay? |
| 00:42:39 | I'll do it. |
| 00:42:41 | Well, please draw one that is not already there. |
| 00:42:43 | After you look for it yourself. Okay? |
| 00:42:45 | You're still going to it? |
| 00:42:48 | Try looking for it. |
| 00:42:49 | (inaudible)? |
| 00:42:50 | I always do it, right? |
| 00:42:51 | Hm. Look for it. One that's not there. |
| 00:42:52 | Teacher. Please tell me. |
| 00:42:53 | May I wash my hands? |
| 00:42:55 | (inaudible) |
| 00:42:56 | Teacher. How many are there left? |
| 00:42:57 | I don't get it. |
| 00:42:58 | Hm? |
| 00:42:59 | Then this also? This also? |
| 00:43:01 | There are eight, right? If I remember. |
| 00:43:03 | There are one, two, three... |
| 00:43:04 | I don't understand it. |
| 00:43:05 | It's very hard to write on it. |
| 00:43:06 | Five, six, seven, eight, nine, ten types. |
| 00:43:07 | Hm? |
| 00:43:08 | I don't understand it from here. |
| 00:43:09 | Hm. You don't understand? |
| 00:43:11 | You got one here, right? |
| 00:43:12 | It's good with this as one. (inaudible) With this you got one. |
| 00:43:13 | What is it? |
| 00:43:15 | These are parallel, right? |
| 00:43:16 | This triangle and the triangle over here are the same, right? |
| 00:43:18 | And so you got a triangle here. See? |
| 00:43:19 | Ten types? |
| 00:43:20 | Oh. Oh. Is that true? |
| 00:43:22 | Right? Then if you get one on this side then? |
| 00:43:25 | Over here. |
| 00:43:26 | Yes. We can get it there, right? You've already got it. |
| 00:43:38 | Now then. Wait a minute. |
| 00:43:40 | I don't know anymore which ones are which. |
| 00:43:41 | Teacher. |
| 00:43:42 | Yes. |
| 00:43:43 | This is (inaudible). |
| 00:43:44 | Oh. You noticed a lot, huh? |
| 00:43:47 | How many types did you f- notice? |
| 00:43:49 | Hm. First of all, this is one, right? Two, right? Over here is three. Four. |
| 00:43:54 | Okay. Now, then this time is drawing diagonal lines just on this side? |
| 00:43:56 | Huh? |
| 00:43:59 | Hm? Other than this side can't you get a triangle? |
| 00:44:02 | A way to partition it? |
| 00:44:03 | Huh? |
| 00:44:04 | That's right. That's right. That's right. |
| 00:44:05 | Even on this side it's good if you think about it in the same way, okay? |
| 00:44:07 | This. I'm not sure, but did both of them come off? |
| 00:44:09 | The other one was still stuck here but. |
| 00:44:10 | I was able to make a hexagon into a triangle. |
| 00:44:13 | What? You want to make a hexagon into a triangle? |
| 00:44:14 | Yes. |
| 00:44:15 | All right. Then. |
| 00:44:16 | Actually I don't want to. |
| 00:44:17 | Since you, Phuse, are asking for it let's do it, okay? |
| 00:44:18 | You're going to make a hexagon into triangle? |
| 00:44:23 | Hm. |
| 00:44:31 | Okay. Were all of them found? |
| 00:44:33 | Yes. |
| 00:44:34 | You found them? These then are quadrilaterals, right? |
| 00:44:35 | The ones we're doing right now. |
| 00:44:37 | Do you want to do them all at once? |
| 00:44:38 | Do you want to do them all at once? |
| 00:44:39 | [ Laughter ] |
| 00:44:40 | Thank you. |
| 00:44:41 | I don't mind. [ Laughter ] |
| 00:44:42 | Penta- pentagon. Pentagon. Pentagon. |
| 00:44:43 | Six. Six. Six. |
| 00:44:44 | Take six. Si-. |
| 00:44:45 | If it's a pentagon isn't it (inaudible)? |
| 00:44:46 | (inaudible) |
| 00:44:47 | So what. (inaudible) |
| 00:44:49 | Who was that who said he or she found eight? |
| 00:44:50 | (inaudible) |
| 00:44:51 | It's these three. |
| 00:44:52 | Did you (inaudible)? |
| 00:44:53 | [ Laughter ] |
| 00:44:54 | Next, okay? Challenge to change a pentagon, okay? Make a pentagon into a triangle. |
| 00:44:55 | I don't know. At once change to a triangle from a circle. |
| 00:44:56 | Huh? |
| 00:44:57 | Cir- circle. |
| 00:44:58 | Make a circle into a triangle. |
| 00:44:59 | Huh? |
| 00:45:00 | It becomes more and more difficult. |
| 00:45:01 | Okay? |
| 00:45:04 | You found it... did you? Okay, then... one two... |
| 00:45:06 | one two... three... four, okay. One, huh? |
| 00:45:18 | One. Of this side. One. |
| 00:45:23 | Also isn't there one like this? |
| 00:45:26 | Didn't we do this? |
| 00:45:28 | One two. There isn't one on this side, right? |
| 00:45:30 | Is there one like this? Oh. Is it this? |
| 00:45:32 | Is it this? |
| 00:45:33 | That's right huh? |
| 00:45:34 | Normal. |
| 00:45:35 | Lately I've worked really hard for my life. |
| 00:45:36 | Also what else? |
| 00:45:37 | The line have- the lines have become messy. |
| 00:45:38 | Is it over with this? |
| 00:45:39 | There should be eigh- eight. |
| 00:45:40 | One, two. |
| 00:45:42 | What is this? This? |
| 00:45:43 | We haven't done that yet. |
| 00:45:44 | One two. |
| 00:45:45 | Hm? |
| 00:45:46 | There are eight of them see? There are even ten quadrangles. |
| 00:45:47 | Are all of them there? One, two, three, four, five, six. |
| 00:45:49 | There are only seven, see? |
| 00:45:50 | Why? |
| 00:45:51 | What is that over there? |
| 00:45:52 | I don't know anymore which is which. |
| 00:45:54 | One more. |
| 00:45:55 | The top of this one is this, right? |
| 00:45:57 | Is it this? Then it's this. Since it's the top of this. |
| 00:45:59 | I don't know anymore which is which. |
| 00:46:00 | What? |
| 00:46:01 | I don't know. |
| 00:46:02 | It's this, right? This one's |
| 00:46:03 | No. No. There is the bottom one see? Here. |
| 00:46:04 | I think we don't have the top one see? |
| 00:46:05 | It's two more. |
| 00:46:06 | Oh. The opposite side. |
| 00:46:07 | Oh. |
| 00:46:08 | Okay. Thank you. |
| 00:46:09 | Okay. |
| 00:46:10 | Okay then everyone please return to your seats at once. |
| 00:46:12 | Yasuda. Hasn't drawn it, okay? |
| 00:46:14 | Okay. I'm sorry. |
| 00:46:15 | Everyone, let's get to our seats. |
| 00:46:17 | Okay? |
| 00:46:18 | Okay, then... everybody, okay? Did it for us, okay? |
| 00:46:21 | Did you find eight? Good. |
| 00:46:23 | Uhm. I don't understand. |
| 00:46:26 | Teacher, there is no time left. |
| 00:46:27 | Huh? |
| 00:46:28 | Time. |
| 00:46:29 | There isn't time? That's true, huh? Now then... well, okay? |
| 00:46:36 | For the convenience of explanation we will put in symbols. |
| 00:46:40 | There were some who were doing it already labeled them, but okay? |
| 00:46:43 | We will make them A, B, C, D, okay? |
| 00:46:45 | And right now in the beginning we draw |
| 00:46:48 | a diagonal line through A to C and |
| 00:46:50 | draw a diagonal line from A to C and we will make a triangl- |
| 00:46:53 | we were able to make two, right? |
| 00:46:55 | And, uhm, if you ask which ones are the triangles |
| 00:46:58 | we found that go through this D are... this and |
| 00:47:02 | this, right? |
| 00:47:04 | This one is made like this on the bottom side like this. |
| 00:47:08 | This one is on the top side. |
| 00:47:10 | Since this triangle and the original triangle are the same, |
| 00:47:13 | so it becomes a fact that we changed this, um, |
| 00:47:16 | quadrilateral into a shape like this, right? |
| 00:47:19 | Uhm, next we drew in the same way through A C but |
| 00:47:22 | this time we drew the parallel line on the B side. |
| 00:47:26 | Okay? Those are this and... this, okay? |
| 00:47:30 | It's this and this, okay. Is everything okay? |
| 00:47:32 | Then I will ask. |
| 00:47:34 | Uhm. About how many people are there who says he or she found this |
| 00:47:36 | i- were able to find it? |
| 00:47:40 | Okay. People who say they were able to find this one. |
| 00:47:43 | There are about the same number of people, huh? |
| 00:47:44 | Um how about this one? |
| 00:47:46 | The D one. The sharp tri-. How about this one? |
| 00:47:49 | Okay. That's good. Thank you. Okay. |
| 00:47:50 | I don't understand all of them. |
| 00:47:51 | What is it? You don't understand? |
| 00:47:52 | On this side this time we will draw it on the B D side. |
| 00:47:54 | Then in the same way, um, which one is it? |
| 00:48:00 | Ones that we drew through B D and drew a parallel line through vertex A are |
| 00:48:03 | this and... this, okay? |
| 00:48:06 | Those are the triangle that we make on this side |
| 00:48:08 | and the triangle we make on the top, right? |
| 00:48:11 | And also the ones where we drew a line through B D |
| 00:48:14 | and we drew a parallel line on the C side are |
| 00:48:16 | this and... |
| 00:48:18 | which one is it? |
| 00:48:21 | Which one is it? |
| 00:48:23 | Is there none? |
| 00:48:24 | Is this it? |
| 00:48:26 | Huh? |
| 00:48:27 | It's wrong? Is this it? |
| 00:48:29 | This? Huh? Is it? |
| 00:48:31 | Okay then... for the time being, okay? |
| 00:48:33 | We don't have much time |
| 00:48:36 | but with the computer... |
| 00:48:38 | I will explain it a little, okay? |
| 00:48:40 | It's something. We have done it, but- |
| 00:48:42 | Well, the screen is not showing up. |
| 00:48:43 | It's showing. |
| 00:48:44 | It came out. |
| 00:48:45 | It's showing. Uhm, right now, |
| 00:48:47 | well, the symbols are different from over there, but on B D... |
| 00:48:50 | for now... we'll draw a line. |
| 00:48:53 | And we will connect A. |
| 00:48:55 | The parallel line is created. It's two parallel lines. |
| 00:48:58 | Then there are a lot of them |
| 00:49:01 | like this which are the same area as this triangle, okay? |
| 00:49:04 | There are many of them, |
| 00:49:06 | but� within these... |
| 00:49:08 | since, the fact is, we're making the quadrilateral into a triangle- |
| 00:49:11 | Meaning all we have to do is lose one of the angles. The angle here, okay? |
| 00:49:13 | When it becomes a straight line then |
| 00:49:15 | that will become a triangle. |
| 00:49:17 | Similarly, |
| 00:49:18 | if it's this side |
| 00:49:20 | when this becomes straight... |
| 00:49:22 | we get a triangle. |
| 00:49:24 | Then we have done quadrangles. |
| 00:49:26 | Next what do you want to do? (inaudible) |
| 00:49:28 | Five pentagon. |
| 00:49:29 | Six hexagon. |
| 00:49:30 | [ Laughter ] |
| 00:49:31 | Twelve-sided. |
| 00:49:32 | Phuse. You [ Bell ] want to do six by all means. |
| 00:49:33 | Then five. Transform pentagons into triangles. |
| 00:49:38 | This. |
| 00:49:39 | A pentagon's- try drawing a pentagon of your liking. Then penta- |
| 00:49:41 | I don't have a clue. |
| 00:49:43 | That's impossible. |
| 00:49:44 | It's impossible? |
| 00:49:45 | It's impossible. |
| 00:49:46 | You don't know if it is impossible until you try it. |
| 00:49:47 | Okay? Then let's try making the pentagon- |
| 00:49:48 | [ Laughter ] |
| 00:49:49 | into a triangle. |
| 00:49:52 | Right now? |
| 00:49:53 | No. I'll make that homework. |
| 00:49:55 | Okay? People who are interested |
| 00:49:57 | you can do ten-angled or twenty-angled or one hundred-angled or anything. |
| 00:49:59 | We- well, they were talking about doing a circle. |
| 00:50:00 | A circle? |
| 00:50:01 | A circle. |
| 00:50:02 | You'll make a circle into a triangle? It's not impossible. |
| 00:50:04 | Yes. |
| 00:50:06 | Label it A B C D E and quadr- |
| 00:50:09 | Cut the pentagon into a quadrilateral, quadrilateral and- |
| 00:50:11 | Yes. |
| 00:50:12 | (inaudible) the quadrilateral. |
| 00:50:13 | Oh. Yuki has just now told us the method of doing it. |
| 00:50:14 | The fact is... won't it be okay if, |
| 00:50:16 | first of all, you make the pentagon into a quadrilateral, |
| 00:50:17 | and then make the quadrilateral into a triangle- |
| 00:50:19 | is all. Okay then you worked very hard... |
| 00:50:22 | amazingly hard. Okay? |
| 00:50:25 | Then today let's get something to drink at the (inaudible). |
| 00:50:26 | It's wonderful, huh? |
| 00:50:27 | What? [ Laughter ] Okay, then we will end class. |
| 00:50:28 | (inaudible) |
| 00:50:31 | Stand. |
| 00:50:32 | Stop doing (inaudible). |
| 00:50:33 | Reward. Reward. |
| 00:50:40 | Okay. Then let's say the farewell properly. |
| 00:50:41 | Attention. |
| 00:50:44 | Bow. |
| 00:50:45 | Thank you very much. |