2.3 The golden ratio
Have you ever heard of the golden ratio? To learn more about the golden ratio and play with the proportion, visit this site. One way to express the golden ratio is 
, which is approximately 1.61803398. This value describes the ratio found in many contexts, such as number patterns, geometry, and nature.
Some artists and architects have deliberately used the golden ratio in their work, but often the ratio of measurements is only approximately equal to the golden ratio. See, for instance, mathematician Keith Devlin’s article, ‘The myth that will not go away’.
When you see a claim that two measurements are in the golden ratio, be critical. Check the measurements and work out their ratio. You may get an answer that is approximately the value of the golden ratio, but this might have occurred by chance.
There have been many claims that the golden ratio occurs in the proportions of the human body. You can test this claim in the next activity!
Activity 12 The golden ratio and the human body: a match made in heaven?
For this activity, you will need a measuring tape and a friend.
- a.Stand with one arm out to your side. Ask your friend to measure the distance from your middle finger tip to your elbow. Record this value. Using the same unit of measurement, let your friend measure from your wrist to your elbow. Record this value too. Now calculate the ratio of the first measurement to the second.
- b.Repeat part (a) with measurements for your friend.
Answer
The ratios are probably somewhere between 1.5 and 1.7. However, there are variations in the proportions of the human body for different people, so you may have values different to these. (The value should be greater than 1 though, so if it isn’t, check your calculation!)
- c.It has been claimed that the ratio you calculated in parts (a) and (b) will reflect the golden ratio. Do you agree?
Answer
It is unlikely that the ratios are exactly equal to the golden ratio, 1.618. The ratio depends on how precisely you made the measurements and where from. For example, which part of the wrist did you use? If you repeated the measurements, would you get the same results? Sometimes a small change in the measurement can appear to give a ratio closer to the golden ratio. Although each of your ratios may be approximately equal to the golden ratio, this may just be a coincidence!
You might like to post your results on the unit forum.
You’ve reached the end of a unit with some fairly sophisticated concepts in it. Don’t worry if you need to go back and revisit any of these to cement the ideas.
Try the self-check section to see how you are getting on.