1 00:00:30,440 --> 00:00:32,796 Look around you. 2 00:00:34,200 --> 00:00:36,192 Look around you. 3 00:00:36,360 --> 00:00:38,716 (INAUDIBLE) 4 00:00:40,160 --> 00:00:42,470 Just look around you. 5 00:00:44,680 --> 00:00:47,434 Have you worked out what we're looking for? 6 00:00:48,720 --> 00:00:50,791 Correct. The answer is... 7 00:00:56,880 --> 00:00:59,270 This programme, "Maths", 8 00:00:59,480 --> 00:01:03,554 is discussed in chapter 3.1415926 of your textbook, 9 00:01:03,720 --> 00:01:05,916 which accompanies this series. 10 00:01:09,000 --> 00:01:11,754 Please ensure you have your copybook at hand, 11 00:01:11,920 --> 00:01:14,719 as you'll be asked to take down notes from the screen 12 00:01:14,880 --> 00:01:16,678 at various points throughout the programme. 13 00:01:18,240 --> 00:01:21,631 What's the largest number you can think of? 14 00:01:22,880 --> 00:01:25,076 Erm...100,000? 15 00:01:25,640 --> 00:01:28,553 999,000. 16 00:01:28,720 --> 00:01:30,632 A million. 17 00:01:30,800 --> 00:01:33,076 In actual fact, it's neither of these. 18 00:01:33,240 --> 00:01:35,914 The largest number is about 45 billion, 19 00:01:36,080 --> 00:01:40,393 although mathematicians suspect there may be even larger numbers. 20 00:01:43,720 --> 00:01:48,397 With so many different numbers to deal with, it can get confusing. 21 00:01:48,720 --> 00:01:51,189 Unless you use maths. 22 00:01:52,600 --> 00:01:59,313 Maths stands for Mathematical Anti-Telharsic Harfatum Septomin. 23 00:01:59,480 --> 00:02:02,632 Think of it as the language of numbers, 24 00:02:02,800 --> 00:02:04,200 with 1 equalling "A", 25 00:02:04,360 --> 00:02:08,115 2 equalling "The", 3 equalling "Hello" and so on. 26 00:02:10,160 --> 00:02:13,358 We use maths at almost every point of the day, 27 00:02:13,520 --> 00:02:16,513 whether we're working out how to thread our shoelaces, 28 00:02:17,120 --> 00:02:18,998 calculating the optimal moment 29 00:02:19,160 --> 00:02:21,755 at which to embark upon a conversation, 30 00:02:24,040 --> 00:02:25,474 or, if you can fly, 31 00:02:25,640 --> 00:02:28,394 planning your trajectory for the journey to work. 32 00:02:28,560 --> 00:02:30,153 (WHOOSH) 33 00:02:31,640 --> 00:02:33,711 (WHISTLING) 34 00:02:34,680 --> 00:02:39,436 But some situations require a much more thorough application of maths. 35 00:02:39,600 --> 00:02:41,910 Let's look at some examples. 36 00:02:42,080 --> 00:02:44,390 Have your pen and paper ready. 37 00:02:48,560 --> 00:02:52,952 Jean is shorter than Brutus, but taller than Imhotep. 38 00:02:53,120 --> 00:02:57,512 Imhotep is taller than Jean, but shorter than Lord Scotland. 39 00:02:58,640 --> 00:03:02,077 Lord Scotland is twice the height of Jean and Brutus combined, 40 00:03:02,240 --> 00:03:05,916 but only a tenth of the height of Millsy. 41 00:03:06,080 --> 00:03:09,312 Millsy is at a constant height of x-y. 42 00:03:09,480 --> 00:03:13,713 If Jean stands exactly one nautical mile away from Lord Scotland, 43 00:03:13,880 --> 00:03:15,997 how tall is Imhotep? 44 00:03:16,160 --> 00:03:19,995 We'll reveal the answers at the end of the programme. 45 00:03:21,440 --> 00:03:23,955 Take a look at this equation. 46 00:03:24,880 --> 00:03:28,157 It's known as cDonald's Theorem. 47 00:03:28,320 --> 00:03:32,758 If we plot its graph, we arrive at this unusual shape. 48 00:03:33,520 --> 00:03:38,276 A uniformly curved line that somehow joins up with itself 49 00:03:38,440 --> 00:03:41,160 that science has yet to find a name for. 50 00:03:41,320 --> 00:03:43,915 Can you think of a name for it? 51 00:03:44,080 --> 00:03:45,514 If you can, 52 00:03:45,680 --> 00:03:49,071 the Royal Mathematics Society would like to hear from you. 53 00:03:49,240 --> 00:03:53,871 They hold a competition each year to find a name for this figure. 54 00:03:54,040 --> 00:03:58,034 The final takes place in Nottingham on April the 4th of September. 55 00:03:58,200 --> 00:04:02,319 And you could win your school this computerised toast system. 56 00:04:02,480 --> 00:04:04,551 So good luck. 57 00:04:10,040 --> 00:04:14,956 Eight ladies go into eight shops at 8 o'clock in the morning. 58 00:04:15,120 --> 00:04:17,919 Each lady wants to buy eight spiders. 59 00:04:19,040 --> 00:04:23,751 For each spider, eight spider shoes must also be bought. 60 00:04:24,560 --> 00:04:28,349 But they only have L8 between them. 61 00:04:28,720 --> 00:04:30,871 With each spider costing 8 pence 62 00:04:32,200 --> 00:04:35,796 and each spider shoe costing 1/8 pence each, 63 00:04:35,960 --> 00:04:39,192 will the ladies have enough change for the bus home, 64 00:04:39,360 --> 00:04:44,230 a journey costing 8 pence per stop and made up of eight stops? 65 00:04:45,120 --> 00:04:50,070 Write down your answer, and we'll see how well you did later on. 66 00:04:51,320 --> 00:04:53,915 A pencil case. 67 00:04:54,080 --> 00:04:56,675 To the modern maths student, it's his toolbox, 68 00:04:56,840 --> 00:04:58,832 containing all the instruments necessary 69 00:04:59,000 --> 00:05:01,754 to carry out his calculations. 70 00:05:01,920 --> 00:05:04,310 Let's take a look inside. 71 00:05:04,480 --> 00:05:06,597 Have your copybooks ready. 72 00:05:07,080 --> 00:05:10,835 A pencil case wouldn' t be a pencil case without these. 73 00:05:11,000 --> 00:05:13,071 Pencils. 74 00:05:16,480 --> 00:05:18,517 Here's a protractor. 75 00:05:19,800 --> 00:05:21,757 A ruler. 76 00:05:25,840 --> 00:05:28,275 A pair of compasses. 77 00:05:33,320 --> 00:05:35,471 Razor blades. 78 00:05:38,680 --> 00:05:41,320 A calculator. 79 00:05:43,400 --> 00:05:45,596 And this. 80 00:05:48,040 --> 00:05:50,396 It's like a nougat, which, when chewed, 81 00:05:50,560 --> 00:05:54,520 stimulates the brain and improves mental agility. 82 00:05:55,880 --> 00:05:58,520 Garry Gum does have some side effects, 83 00:05:58,680 --> 00:06:02,959 for instance diarrhoea, so you may need to take some of this. 84 00:06:06,480 --> 00:06:09,473 Write that down in your copybook now. 85 00:06:17,320 --> 00:06:22,349 For this problem, you'll need to set your calculator to '"Maths". 86 00:06:22,520 --> 00:06:24,591 It's the future, 87 00:06:24,760 --> 00:06:28,470 and Queen Elizabeth III and Queen Elizabeth IV are going to a party 88 00:06:28,640 --> 00:06:30,677 held by Queen Elizabeth V. 89 00:06:30,840 --> 00:06:35,312 It's important that they choose their outfits carefully. 90 00:06:35,480 --> 00:06:39,190 Queen Elizabeth III has 40 dresses to choose from, 91 00:06:39,360 --> 00:06:43,400 whereas Queen Elizabeth IV has 4,000. 92 00:06:43,560 --> 00:06:46,553 Queen Elizabeth V has just one dress, 93 00:06:46,720 --> 00:06:52,478 but it has the ability to transform itself into the shape of any dress. 94 00:06:54,320 --> 00:06:56,198 The night before the party, 95 00:06:56,360 --> 00:06:58,636 Queen Elizabeth IV's handmaiden 96 00:06:58,800 --> 00:07:01,235 steals the patterns to Queen Elizabeth III's dresses, 97 00:07:01,400 --> 00:07:05,633 and makes 40 exact replicas. 98 00:07:05,800 --> 00:07:09,316 Can you calculate the probability that all three queens 99 00:07:09,480 --> 00:07:12,154 will be wearing the same dress at the party? 100 00:07:12,320 --> 00:07:16,599 And how many times can Queen Elizabeth V's dress change 101 00:07:16,760 --> 00:07:18,752 before it overheats? 102 00:07:18,920 --> 00:07:20,354 (SIZZLING) 103 00:07:23,040 --> 00:07:25,396 That's the last of your problems. 104 00:07:25,560 --> 00:07:28,951 You now have a few more seconds to finalise your calculations 105 00:07:29,120 --> 00:07:31,237 while the following film plays. 106 00:07:31,400 --> 00:07:33,312 (ANGRY MEOWING) 107 00:07:47,960 --> 00:07:50,520 Here are the answers to all your problems. 108 00:07:50,680 --> 00:07:53,673 Problem one, Imhotep is invisible. 109 00:07:55,440 --> 00:07:59,195 Problem two, the ladies were 8 pence short. 110 00:07:59,360 --> 00:08:00,840 (SIREN) 111 00:08:01,000 --> 00:08:04,630 And problem three, the party was cancelled. 112 00:08:07,240 --> 00:08:11,029 Now hand in your copybooks to your teacher or head of class. 113 00:08:13,920 --> 00:08:17,800 In the next programme, we will look at cosmetics.