A4 This is just another rectangle of the same proportions. 1.What are the ratios between the sizes of the various rectangles on this page? Write these as the ratio of each height to each width. 2.What is the unit ratio (i.e. the ratio cancelled down to 1:?) 3.What are the ratios of each area between the sizes of A5, A4, A3… paper? 4.How are the answers to questions 2 and 3 related and why does this make sense? 5.To whom, and which businesses, are the ideas developed here important? A5 A6

Phi  1.Find the ratios between each pair of consecutive numbers in the sequence above. What patterns do you notice? 2.Plot these ratios on a graph set out like the one shown on this page. 3.What is the special number called ‘phi’? (pronounced ‘fi’). 4.The sequence of numbers above is a very special pattern which is named after a famous Italian Mathematician. Use the internet (or other resources) to find out this name. 5.What is the rule for the sequence of numbers above? 6.Use squared paper to draw the curved sketch shown on this page, begin with a large rectangle that is 21 x 34 squares in size. What is the connection between the sequence and this pattern? (Can you predict the sizes of the smaller rectangles?) 7.To whom, and which businesses, are the ideas developed here important? 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89…

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