# 1 Fibonacci Numbers Stage 4 Year 7 Press Ctrl-A ©2009 – Not to be sold/Free to use.

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1 Fibonacci Numbers Stage 4 Year 7 Press Ctrl-A ©2009 – Not to be sold/Free to use

2 Fibonacci Numbers Discovered by Leonardo Fibonacci in the year 1202 The sequence of Fibonacci numbers starts with 0 and 1. The other terms in the sequence are found by adding the previous two terms. 0, 1, 0+1 1, 1+1 2, 34... 13, 3, 21, 8, 5, 1+2 13+21 13+85+83+52+3 The Video 42

3 Fibonacci’s Tiles A tiling with squares whose sides are successive Fibonacci numbers in length 42

4 Fibonacci’s Spiral A Fibonacci spiral, created by drawing arcs connecting the opposite corners of squares in the Fibonacci tiling 42

5 Fibonacci’s Flowers The majority of flowers have a Fibonacci number as their number of petals. Some species include: 1. Lilies, irises and clover have 3 petals. 2. Buttercups and some delphiniums have 5 petals. 3. Other kinds of delphiniums have 8 petals. 4. Marigolds have 13 petals. 5. Some asters have 21 petals. 6. Daisies have 34, 55 or even 89 petals. Did you know that four leaf clover are rare because 4 is not a Fibonacci number? 42

6 Fibonacci’s Rabbits Each pair of rabbits can produce another pair of rabbits in each of the next two generations. Mum & Dad 42

7 Golden Fibonacci’s Golden Ratio An approximation for the Golden Ratio can be found by dividing consecutive ratios Golden Ratio ≈ 34 21 ≈ 1.619 Leonardo da Vinci was interested in the proportions in the human body 42

8 Golden Fibonacci’s Golden Body Ratio Floor to Navel - 97Height - 159 1 : 1.639 Elbow to Fingertips - 41 Underarm to Fingertips - 63 1 : 1.537 Width of Head - 16 Length of Head – 25 1 : 1.563 Hairline to Bottom of Nose - 13 Hairline to Chin - 21 1 : 1.615 Fingertip to 1st Knuckle - 4.2 Length of Finger - 7.1 1 : 1.690 1st Knuckle to 2nd Knuckle - 2.5 Fingertip to 1st Knuckle - 4.2 1 : 1.680 The table shows measurements (in centimetres) of my body and the ratio they are in. All of the ratios are reasonably close to the golden ratio, 1:1.168. 42

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