year 8 maths

Investigation
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Calculating phi
Phi is the ratio of the length to the breadth (height) of a golden spiral or a golden rectangle.
In the design you have drawn there are several golden rectangles.
Measure the length and breadth of each golden rectangle and calculate the value of phi (length divided by
breadth) for each.
Work out the average (mean) of all your calculations of phi. Compare your average with the actual value
1 + √5
of = 1.61803…
2
Golden rectangles in the human body
Investigate some of your own measurements and see how close they are to the golden ratio of
phi : 1 ≈ 1.6 : 1 .
Golden ratios in the human body include:
• total height : head to fingertips
• total height : navel (belly button) to floor
• height of head : width of head
• shoulder to fingertips : elbow to fingertips
• length of forearm : length of hand
• hip to floor : knee to floor
• length of longest bone of finger : length of middle bone of same finger
• eyes to the bottom of the chin : width of ‘relaxed’ smile
• width of two centre teeth : height of centre tooth
Research and class presentation
Research the internet to discover examples of golden rectangles in nature, human anatomy, architecture,
art or graphic design. Present your findings to your class using a PowerPoint presentation or a poster.
Cambridge Maths NSW
Stage 4 Year 8 Second edition
ISBN 978-1-108-46627-1 © Palmer et al. 2018
Cambridge University Press
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