1 00:00:00,210 --> 00:00:02,420 Hi again everybody and welcome back from the summer! 2 00:00:02,880 --> 00:00:07,420 My name is Jason, and one again this semester Collaborative Mathematics will 3 00:00:07,600 --> 00:00:10,020 be releasing monthly video challenges. 4 00:00:10,950 --> 00:00:14,000 If you are new to the project, you might want to check out our 5 00:00:14,180 --> 00:00:15,260 "How It Works" video. 6 00:00:15,830 --> 00:00:18,260 Otherwise, let's get right to it! 7 00:00:21,750 --> 00:00:25,110 I was a mathematics teacher for a number of years in the United Stated, and 8 00:00:25,290 --> 00:00:31,580 now I'm living in Oslo, Norway. And there's a lot that's different living abroad, 9 00:00:31,750 --> 00:00:32,950 compared to living in the US. 10 00:00:33,310 --> 00:00:37,570 But one of the things that's interesting is that in Norway, and in other countries too 11 00:00:37,710 --> 00:00:43,390 around the world, we use a different size of paper than I was used to from the 12 00:00:43,530 --> 00:00:44,130 United States. 13 00:00:44,460 --> 00:00:49,050 So in the United States, you might be familiar with this size of paper. This is 14 00:00:49,190 --> 00:00:54,910 called letter-sized paper in the US, but here in Norway and elsewhere, we use 15 00:00:55,210 --> 00:01:01,720 this size paper. It's different. It's called a4 size paper, and if I line them up like this 16 00:01:02,200 --> 00:01:06,450 you can see, maybe, that it's both wider and taller than a piece of 17 00:01:06,590 --> 00:01:08,720 US letter-sized paper. 18 00:01:09,770 --> 00:01:12,880 So that was interesting. The paper's different. Why not? 19 00:01:13,250 --> 00:01:19,200 But the mathematics teacher in me got really excited about a4 paper because... I 20 00:01:19,640 --> 00:01:24,420 like office products... but also because it has a very interesting property that when 21 00:01:24,560 --> 00:01:33,000 you fold it in half width-wise, along its longest dimension, you get of course 22 00:01:33,190 --> 00:01:35,370 another rectangle, a smaller rectangle. 23 00:01:35,610 --> 00:01:37,970 But this smaller rectangle is 24 00:01:38,360 --> 00:01:41,310 mathematically similar to the original one. 25 00:01:42,550 --> 00:01:46,400 And that doesn't always happen. If you try that with a piece of letter-size paper 26 00:01:46,490 --> 00:01:51,190 from the US. You fold it in half along its longer dimension, and of course you get 27 00:01:51,320 --> 00:01:54,680 a smaller rectangle, but this smaller rectangle is not mathematically similar 28 00:01:54,840 --> 00:01:56,210 to the original. 29 00:01:57,370 --> 00:02:02,070 But it is for a4 paper, and that's something that makes a4 paper unique, 30 00:02:02,260 --> 00:02:04,670 and it's something that I think is kind of cool. 31 00:02:05,770 --> 00:02:11,360 OK, so here is the international paper challenge. Picture, if you will, a piece of 32 00:02:11,510 --> 00:02:18,120 a4 paper that has the property I just described, and draw on it the largest 33 00:02:18,260 --> 00:02:20,450 possible circle that you can. 34 00:02:21,900 --> 00:02:29,000 The question is: what fraction of the paper is inside that circle? 35 00:02:30,650 --> 00:02:38,220 In other words: What fraction of a piece a4 paper is enclosed by the largest circle 36 00:02:38,410 --> 00:02:40,530 that can be drawn on that sheet? 37 00:02:41,200 --> 00:02:44,790 So, that's the challenge and I'm looking forward to some response videos with 38 00:02:44,970 --> 00:02:46,180 answers to that challenge. 39 00:02:46,610 --> 00:02:51,070 And, there's another way to participate because I'm curious about the most 40 00:02:51,190 --> 00:02:55,730 interesting piece of paper that you can find. We use different sizes of paper all 41 00:02:55,890 --> 00:03:02,940 the time. Here at my desk I happen to have 3"-by-5" note cards. If you look 42 00:03:03,090 --> 00:03:06,250 around your classroom, you might have different sizes of notecards, you might 43 00:03:06,690 --> 00:03:10,960 have one of those big poster paper pads with really huge pieces of paper. 44 00:03:11,390 --> 00:03:16,900 I'd like to hear what sorts of different, interesting paper you can find. 45 00:03:17,170 --> 00:03:24,160 Look in your pocket. You might have some cash. Here's a US 5-dollar bill. 46 00:03:24,290 --> 00:03:28,650 What fraction of a 5-dollar bill is enclosed by the largest circle that you 47 00:03:28,760 --> 00:03:29,740 could draw on it? 48 00:03:30,280 --> 00:03:35,200 Of course, I'm in Norway so we don't use dollars, we use kroner. This is a 49 00:03:35,350 --> 00:03:42,010 100-kroner note, and you can see that it's almost the same height but it's quite a bit 50 00:03:42,190 --> 00:03:48,780 shorter. What fraction of a Norwegian 100-kroner note is enclosed by the 51 00:03:48,910 --> 00:03:50,230 largest circle you could draw on it? 52 00:03:50,470 --> 00:03:53,540 You could ask that question about any piece of paper! So in your response 53 00:03:53,670 --> 00:03:58,030 videos, answer my challenge, but then challenge us with the most interesting 54 00:03:58,180 --> 00:04:02,160 piece of paper that you can find. Describe it and then ask that question about the 55 00:04:02,310 --> 00:04:04,420 circle, about your piece of paper. 56 00:04:05,480 --> 00:04:08,280 I look forward to seeing what you come up with and what happens next! 57 00:04:08,540 --> 00:04:09,830 So go out there and have fun!