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.