SUBJECTS: Maths
YEARS: 5–6, 7–8
The golden ratio, Phi: fact or fallacy?
What about the Fibonacci sequence? We are told this ratio and its cousin Fibonacci occur everywhere in nature. Let's see which of these claims stacks up when put to the test.
Things to think about
- 1.Continue the pattern 0, 1, 1, 2, 3, 5, 8, 13 … This is the Fibonacci sequence. We are told that if you take two adjacent Fibonacci numbers and divide them you will get very close to Phi (1.618). Put this to the test with a few Fibonacci pairs of numbers, for example 8 and 5. How close can you get to 1.618?
- 2.The accuracy of the golden ratio is tested here in four famous examples. In which of these four examples is Phi found? How does Marty Ross explain the way that the Fibonacci sequence occurs in nature?
- 3.One of the most famous claims about Phi's existence in nature is that a person's height divided by the distance from their naval to the floor is 1.618. Calculate this using your own body measurements and compare that to Phi. Now do the same for other people at home. Whose proportions are closest to the golden ratio?
- 4.The building designs of the Parthenon, Notre Dame and the Taj Mahal are said to be based on the golden ratio. Select two segments from one of these building designs (one must be larger than the other). Call one segment 'A' and the other 'B'. To test for Phi, measure a length for segment A. Compare that to a length of segment B. Express your finding as a ratio A/B. How close to 1.618 do you get?
Date of broadcast: 20 Jul 2006
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