year 8 maths

3B
Circumference of circles
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3B Circumference of circles
REVISION
Since ancient times people have known about a special number that links a circle’s diameter to its
circumference. We know this number as pi (π). π is a mathematical constant that appears in formulas
relating to circles, but it is also important in many other areas of mathematics. The actual value of π has
been studied and approximated by ancient and more modern civilisations over thousands of years.
The Egyptians knew π was slightly more than 3 and approximated it to be 256 ≈ 3.16 . The Babylonians
used
25
8
≈ 3.125 and the ancient Indians used
339
108 ≈ 3.139 .
It is believed that Archimedes of Syracus (287−212 bce ) was the first person to use a mathematical
technique to evaluate π . He was able to prove that π was greater than 223
71 and less than 22 . In 480 ad , the
7
Chinese mathematician Zu Chongzhi showed that π was close to 335 ≈ 3.1415929 , which is accurate to
113
seven decimal places.
Before the use of calculators, the fraction 22 was commonly used as a good and simple approximation to π .
7
Interestingly, mathematicians have been able to prove that π is an irrational number, which means that
there is no fraction that can be found that is exactly equal to π . If the exact value of π was written down as
a decimal, the decimal places would continue forever with no repeated pattern.
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L et’s start: Discovering pi
Steps:
1 Find a circular object like a dinner plate or a wheel .
2 Use a tape measure or string to measure the circumference (in mm) .
3 Measure the diameter (in mm) .
4 Use a calculator to divide the circumference by the diameter. (It should be about 3.14 .)
5 Repeat steps 1 to 4 with a larger or smaller object.
■ Features of a circle
• Diameter (d) is the distance across the centre of a circle.
• Radius (r) is the distance from the centre to the circle. Note: d = 2r .
■ Circumference (C ) is the distance around a circle.
• C = 2πr or C = πd .
Circumference
Diameter
Radius
Key ideas
■ Pi (π) ≈ 3.14159 (correct to five decimal places)
22
• Common approximations include 3.14 and
7 .
• A more precise estimate for pi can be found on most calculators or on the internet.
Cambridge Maths NSW
Stage 4 Year 8 Second edition
ISBN 978-1-108-46627-1 © Palmer et al. 2018
Cambridge University Press
Photocopying is restricted under law and this material must not be transferred to another party.