In the second extract, Simon Singh interviews the mathematician Robin Wilson, and asks him how the Greeks managed to find out more about the decimals of .
Four thousand years ago, the Babylonians already knew that in order to nd how far it is round the rim of a ir le you take the diameter of the ir le and multiply it by something that's about 3 and a bit. But they didn't know 3 and what bit. . . How do we all this number the Babylonians were looking for?
II.
A limeri k
The following poem is alled a limeri k : It's a favourite proje t of mine A new value of
to assign
I would x it at three For it's simpler you see Than 3 point 1 4 1 5 9. 1. What value does the author give for
?
What does he think of this value ? 2. What do you think about his hoi e ?
III.
An abyss
Listen to the rst extra t from Simon Singh's programme, ll in the gaps, and then answer the questions in your notebook. 1 2 3
But, as Ian Stewart of Warwi k University points out,
is not exa tly
3:14 or 3 71 as some people prefer to write it. nearly equals 3 17 but it's not exa t and this is where the abyss opens up
exa tly
4
beneath your feet, be ause if you say what fra tion represents
5
then the answer is there isn't one. It's an irrational number, it's not
6
an exa t fra tion.
7
doing some advan ed mathemati al investigation where
3 71
is lose enough for most al ulations, but if I'm
is oming
8
1 up, and it does, then I wouldn't want to use 3 , be ause I'd know that 7
9
was wrong.
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Questions : 1. What kind of number is
3 17
?
Can you write it as an improper fra tion ? 2. Use your al ulator to nd out whi h one is a better approximation of
1 3.14 or 3 ? 7
:
3. What are rational numbers?
What an you say about the de imals of a rational number? 4. Is
a rational number ?
What an you say about the de imals of
IV.
?
Sear hing for the de imals
In the se ond extra t, Simon Singh interviews the mathemati ian Robin Wilson, and asks him how the Greeks managed to nd out more about the de imals of
.
1
What Ar himedes did was he took a ir le and he put inside it a reg-
2
ular hexagon. And he put round the outside a regular hexagon. And
3
he looked at the perimeters of the two hexagons and then said the
4
ir umferen e of the ir le, whi h is
5
doing that he got some very rough approximations for
6
He then doubled the number of sides, to 12, and got better approximations.
7
And he found that
8
a little bit more than
9
And this was the method that was used from then on for nding
2R,
is between these, and by
is just a little bit less than
10 3 71 .
3 17 ,
.
that's
22 , 7
and just
.
Questions : 1. Draw a ir le with a radius of 1.
Then draw a hexagon just inside the ir le, and a square just outside the ir le. 2. Perimeter of the hexagon :
a) Draw a triangle formed by two onse utive verti es of the hexagon and its
entre. b) What an you say about this triangle ?
) Use this information to nd out the perimeter of the hexagon.
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Page 2/3
3. Perimeter of the square :
a) How long is ea h side of the square ? b) So what is the value of the perimeter of the square ? 4. Con lusion : between what numbers is
V.
set ?
Ba k to Paris
1
In 1937,
to 707 de imal pla es was ins ribed on the domed eiling
2
of the Palais de la Dé ouverte in Paris.
3
a mistake. So it's ina
urate after the 527th de imal pla e. It makes
4
you wonder : wouldn't life be easier if we just hanged
5
short and simple ?
Unfortunately they made
to something
Questions : 1. Can the value of
be hanged to something short and simple ?
2. How many de imals of
do you think you an remember ?
Maybe you will nd it easier to remember this senten e : Can I nd a tri k re alling pi easily ? Count the number of letters in ea h of the words of this senten e ; in what situation an it be useful ?
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