Sequences can be really useful. Special algorithms use the data of past crimes to try and predict when and where crime may occur in the future. In Los Angeles using these reduced crime by 12%!! Earthquakes can trigger aftershocks, and equations can be used to predict when the next one will happen.
Composers and instrument makers have been using the Fibonacci Sequence and the Golden Ratio for hundreds of years to compose and create music. An octave on the piano consists of 13 notes. Eight are white keys and five are black keys. A scale is composed of eight notes, of which the third and fifth notes create the foundation of a basic chord. In a scale, the dominant note is the fifth note, which is also the eighth note of all 13 notes that make up the octave. Eight divided by 13 equals 0.61538 ,the Golden Ratio!
Mozart for instance, based many of his works on the Golden Ratio – especially his piano sonatas. Lady Gaga put a key change at 111 out of 179 seconds in her song “Perfect Illusion” ,at the Golden Ratio.
GCSE mathematicians – you need to be able to work with sequences. For help, try our new guide “How to work with Sequences: Part 2”. It includes information about quadratic sequences. In addition there are explanations of how to work out the nth term. As always there are questions to try, and answers to check your understanding.
Click on the picture below to see the guide.
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